--- layout: archive title: Zulip Chat Archive permalink: /stream/113488-general/topic/build.20infrastructure.html ---
Ok, I think I am going to take a pause on "math in Lean", and do some infrastructure work.
lean --make
every time it sees anything change. Others can then cd ~/Dropbox/lean-box/yourname/
, ln -s ~/my-lean-project/
, and Dropbox will continuously deliver .olean
files back to their project directory. I've tried this before, and it works, at least on a single OS.sccache
, and see what would need to happen to make this work, as it seems like an excellent solution. If we need to patch Lean, no problem; elan
makes it very simple to work with forks these days.begin ... end
block caching may be feasible, but probably requiring a small patch to Lean. When he has time, I'll ask him what's involved.All of these seem more valuable than writing out explicit proofs of boring facts.
sounds good to me... nothing like a little fear of tedium to get the ball rolling on more advanced automation and caching :)
https://github.com/leanprover/lean/issues/1601 makes me slightly pessimistic about the third item
I think Keeley's idea is hackier than what Leo had in mind, and so may have an orthogonal set of issues. :-)
@Scott Morrison That sounds fantastic. I got the impression from Sebastian that Lean 3 might not be completely frozen, so minor tweaks might even be patched back into Lean.
Would it be an idea to develop some git hooks that look at your build server? And then instead of indexing by username, maybe index by git commit hash?
That way new users that install elan will automatically pull up to date oleans for the latest mathlib master.
@Scott Morrison What kind of specs will your build machine have? Can I contribute with my little monster, or is it just a drop in the ocean compared to yours? I've got a 16-threaded beast with 24G RAM, but it is pretty oldish (7 years?). When otherwise idle, it compiles mathlib from scratch in about 6 minutes (using 12 threads on average).
Let's wait and see if we can actually build something that works, first. :-) This machine is slightly bigger (18 Xeon W cores, and 128gb of RAM), with a similar compile time (I actually remember timing 7 minutes?) The hardware is not the hard part, in any case.
@Scott Morrison The poor little Xeon :D On caching: we can really get arbitrarily fancy. My config monad work should be done in a day, so I'll finally get on it. (I had a migraine today :()
I really think the biggest obstacle is just syntax. If people can figure out a way to override lean's use of tactic.execute
and tactic.step
, then you'll only need an import to do caching in vanilla lean. From reading the source code src/frontends/lean/tactic_notation.cpp
(see parse_tactic_class()
in that file), I don't think this is possible and I will have to change one line of code. Otherwise you will have to type extra character(s), like begin [cache] ... end
or begin [c] ... end
or maybe cbegin ... end
(but this would be vanilla supported).
The other option will be to point elan
to to the fork with a lean_version = "xxx"
in leanpkg.toml
, which will get everything working without touching begin ... end
blocks at all. This would be vanilla compatible---if you don't run the fork, you just don't get caching of these blocks.
My current understanding is that the actual caching implementation will not be too difficult. My "caching program" (not in the sense of an executable program), would be to first write fast expr
serialization. I can think of all sorts of things---like storing proofs hot in mutable state in a user_attribute---which we could tack-on to speed up a naive caching implementation after-the-fact.
I suspect we could get more speed using a buddy-process and some tricks with writing the proofs directly to bytecode and back again (I have a strategy for getting lean to do this without touching bytecode handling ourselves), but perhaps this should be saved for the future. Since begin...end
blocks can be processed in parallel, this step would definitely require a "buddy process" (such a thing would be completely invisible to the user, just like the communication processes that start up when you launch rewrite_search
's graph visualiser).
Awesome! I'm cheering for you!
Also worth noting is that I keep having ideas to try to trick [user_notation]
-like features into capturing a begin...end
, but all have failed. Maybe someone else will come up with a smart way to do it. That's the problem which has been making me hesitant, though, so I guess I'll press onward for now.
@Keeley Hoek How are you planning to deal with the nondeterminism issues described in the Github issue? That is, a cached proof term will most likely not be a valid term in the recomputed context, even though the input hasn't changed.
I'm not confident about what you mean Sebastian---which of course is a bit scary.
The plan was (at least to start---and what everything I mentioned up there was about) just remembering the entire proof term which was generated in a begin...end
block. The obvious impact is not having to re-run really expensive tactics which appear in that block, and only recompiling a small piece of a big file---or a huge chunk of mathlib if you changed a core file---if you only changed a proof, or added a new definition, etc. (I'm not claiming that any of this would be guaranteed to be safe, but I think Kenny's work is a testament to how much things could get better if you only have to run a by simp
once to figure out it actually did, for example.)
So even though we don't remember what individual tactics did, or guarantee that the proof we remembered will work at all, I think this could still be really useful. Especially because, even when definitions of theorems are broken or a lemma argument is changed generated proofs using them will not work, this kind of hard caching will still stop the spread of the recompilation like a cancer throughout the entire library---hopefully only 1 level of recompilation will need to be done.
the problem is that a context contains variables, identified by unique names, and these unique names will be different when you use an old term in a new context
I think this can be fixed by just remembering the variables by their position instead of their name, or using positional information to reconstruct a bad name
But do any such names actually appear in the final proof term? Like if I run #print my_lemma
, surely there won't be much state in there?
For example, if you have \lam x y z, begin exact f x end
then lean sees \lam x0 y1 z2, begin exact f x0 end
, and so if you store f x0
, then when lean reparses the exact same theorem it sees \lam x3 y4 z5, f x0
which doesn't typecheck
The pp names and unique names are still associated to the binders in the final proof term
and unique means something like globally unique since you turned on lean, I'm not sure how far you can push nonuniqueness
I'm not sure I understand. Do you mean a program like this:
structure my_struct := (n : ℕ) (g : ℕ → ℕ) def f (y : ℕ) : ℕ := 2 * y def a_constructor (n : ℕ) : my_struct := { n := n, g := λ x, begin exact f x end }
for example?
If I do
run_cmd (do e ← tactic.get_env, l ← e.get `a_constructor, tactic.trace l.value.to_raw_fmt )
I get
(lam n default (const nat []) (app (app (const my_struct.mk []) (var 0)) (lam x default (const nat []) (app (const f []) (var 0)))))
In particular, the x
is bound under the lambda, so I don't need to worry about matching up the x
with anything. Am I missing the point?
well, two things: first the lam
there is actually storing the unique id of the bound variable (so the var
doesn't have to)
and second, a tactic doesn't deal with closed terms, it is elaborated in an "open" context (with local constants in surrounding binders) corresponding to where begin ... end
actually appears
to_raw_fmt
doesn't print the unique ids to save our sanity, I guess
but you can pattern match it out
I'm looking at the expr
definition and it has lam : name → binder_info → expr → expr → expr
---In particular, I don't see any room for a secret id name
which could be stored in the second argument of the local_const
constructor, for example
But I see the problem if a local_const
(for example?) appears---and I understand your way to fix it, too
oh, I guess I was mistaken
looks like it's only when in a local context that you have to worry about the uids of local constants
Okay, so I can confirm that for sufficiently simple .lean
files, as long as you consistently use the same version of Lean (preferably provided by elan, following a leanpkg.toml file), that the .olean
files are completely cross platform.
With a very simple lean file containing #print "compiling"
and a few definitions, then syncing that file via Dropbox between a mac, windows, and linux computer, I can verify that the olean file produced on any of the 3, works on the other two.
Unfortunately once you scale up to "all of mathlib", Dropbox puts too many timestamps in the wrong order, and essentially isn't useful.
Repeatedly running lean --make
on two different computers (waiting for each to complete before running again) usually results in a small subset of mathlib being compiled each time you switch computers.
That said, I don't think I ever saw more than a minute of compiling on a single computer, so maybe it could be better than nothing...
sccache
will hopefully be much more awesome. :-)
That minute on your computers translates to 6 minutes on my laptop, or Chris's...
But sure, it still is helpful.
Ok, I will soon add some scripts that relentlessly run lean --make
on appropriate subdirectories, and try it out for real. (e.g. have my desktop machine compile for my laptop, and if anyone else wants to try it to)
Before doing fancy Dropbox things, why not trying to copy-paste what the main Lean repository is doing to produce lean nightlies and get a lean-community/mathlib-nightlies/ repository? Should I try to do that?
@Sebastian Ullrich do you have comments about the above plan? Is there anything I should know about why the Lean nightlies are setup that way?
You mean why is it a separate repo?
Yes, for instance
or any other comment
maybe no comment is needed
I suppose the Dropbox solution makes it easy to actually deliver the output to people
I really don't like to idea to ask people interested in mathlib to use Dropbox
The nightlies are in a separate repository so that they are not mixed with the official releases on the Github Releases page
I guess what you'd want to have is to point leanpkg
to a Github Release including .olean files instead of a git hash, just like with elan
. But that... would not be a small task.
Or alternatively have sccache
do that
What I mean is much more naive: I want to be able to write a tiny bash script that downloads a compiled version of mathlib inside the _target
subdirectory of the current directory, and uses touch to pretend every olean have just been created.
Yeah, that doesn't sound too bad to me
Ok, thanks. I'll try to do that
That can be a viable solution but if someone wanted to figure out how to setup sccache to share storable, I think that would be more effective. That way, we wouldn't have to upload a new version of mathlib every few day. Just compiling would get the mathlib that others have compiled
{% endraw %}Last updated: Apr 24 2020 at 19:02 UTC


enum class BatteryFlow
Represents a battery's flow. Charging when battery is charging, Discharging when discharging. An UNKNOWN state when state can't be known.


Updates
30 December 2019
Lopez Chihuahua Baby
Lopez Chihuahua Twins
29 December 2019
Dancin' Peformers Timbertop
World Parade - UK & Brazil
Fireplace
28 December 2019
Honey Fox Family
Honey Fox Baby in Blue
Honey Fox Baby in Pink
Spotter Meerkat Triplets
Irish Post Office
Robinson Red Pandas - Flair
Clip and Pin
Sheep Baby Carry Case
Tuxedo Cat Baby Carry Case
Timbertop Gift Dome
A Big Cheer for Cloverleaf Corners
Kennelworth Dalmatian Baby
27 December 2019
Dandelion Twins
Dandelion Butterglove Carry Case
Charcoal Cats
Persian Cats - Calico Critters
Truffle Boar Twins - Calico Critters
Hopscotch Rabbit Grandparents
Penguin Triplets - Calico Critters
Chocolate Grandparents - 2015
Pickleweeds Hedgehogs - Epoch
Happy Wedding 2019
Truffle Boar Family
Sunnybrook Spaniel Family
26 December 2019
Hazelnut Dormouse Baby
Hazelnut Dormouse Twins
Robinson Red Panda Family of 3
Red Panda Family - Calico Critters
Dappledawn Rabbit Baby in Blue
Dappledawn Rabbit Baby in Pink
Flair Dappledawn Rabbit Family
Happy Wedding
Norwood Mouse Brother
25 December 2019
Caramel Dog Family
Slydale Baby in Pink
Slick Slydale - Gold Tail
Slydale Baby in Blue
Bamboo Baby in Red
Bamboo Baby in Yellow
17 December 2019
Slydale Foxes - Tomy, US
Garden Rabbit Sister
Forrester Dog Father
Forrester Dog Sister
Blooming Flower Shop
Caroline Cottontail Bride
Exchange Student - Panda Sister
Exchange Student - Panda Brother
Recommended Furniture - 2019
Blue Bathroom Set
Limited Edition Light Up Furniture Set
16 December 2019
Marmalade Grandfather
Marmalade Grandmother
13 December 2019
Mulberry Raccoon Sister
Mulberry Raccoon Mother
Mulberry Raccoon Father
Mulberry Raccoon Brother
Pink Mulberry Baby
Blue Mulberry Baby
10 December 2019
Soyokaze Cat Sister
Pink Hamilton Hamster Baby
Norwood Mouse Father
Norwood Mouse Mother
8 December 2019
Polar Bear Family
7 December 2019
Blue Bramble Hedgehog Baby
Pink Bramble Hedgehog Baby
Mushroom Babies
Animal Mascot Babies
5 December 2019
Hawthorn Mouse Baby
Sugar Bear Family
Sugar Bear Twins
Seabreeze Rabbits
Britney's Ballet Recital
Bramble Hedgehog Twins
4 December 2019
Hawthorn Mouse Twins (Flair)
Hawthorn Mouse Twins (Epoch)
3 December 2019
Cottontail Baby (Epoch)
Fruit Babies
2 December 2019
Petite Bear Family (CC)
Alarm Clock
Banana Babies
Prince & Princesses
24 November 2019
Sheep Sister with Kitchen Set
World Parade - Russia & China
World Parade - Spain & Arabia
22 November 2019
Cottontail Baby with Mini Cottage
Milk Rabbit Baby with Mini House
Mulberry Raccoon with Mini House
21 November 2019
The Dingle's New Arrival
Sheep Family
Sheep Baby
20 November 2019
Fellini Wedding Cats
The Devon's New Arrival
19 November 2019
Willow Hall Puzzle
Country Bus Puzzle
Wilder Panda Family
Wilder Panda Twins
18 November 2019
Dresser Box
Hopscotch Rabbit Family
17 November 2019
Halloween Playhouse (US)
Winners Set
16 November 2019
Sunny Rabbit Family
Gingerbread Playhouse (US)
14 October 2019
Cello Concert
Cake Car
Luxury Armchair
Town Sign
Calico Critters TRU Display Sign
13 October 2019
Woolly Alpaca (Calico Critters)
Flair Chocolate Labrador Twins
Flair Chocolate Labrador Baby
2018 UK Club Tiffany Silk Cat
Town Chocolate Rabbit Baby - Purple
3 October 2019
Evergreen / Sweetwater Puzzle
18 September 2019
Taylor Timbertop
17 September 2019
Spice Rack
14 September 2019
Hazelnut Dormouse Family
Hawthorn Mouse Family
13 September 2019
Norwood Mouse Family
11 September 2019
Grand Piano Concert
10 September 2019
Laura Cakebread
08 September 2019
Chocolate Rabbit Baby
Chocolate Rabbit Father Set
Chocolate Rabbit Mother Set
Cottontail Rabbit Grandparents
Chocolate Rabbit Grandparents
Elephant Family
Marshmallow Mouse Family
Underwood Badger Family
Cottontail Rabbit Baby
Slydale Fox Family
Basil & Suzette (Tomy)
Basil & Suzette (Flair)
07 September 2019
Tomy Washing Machine
Flair Washing Machine
Epoch Washing Machine
Cottage Hospital
05 September 2019
Lambrook Sheep Twins
Wildwood Rabbit Grandparents
Gingerbread Playhouse
04 September 2019
Light Up Street Lamp
Urban Life Florist Cart
Flower Gifts Playset
Flair Periwinkle Rabbits
Stephanie Marshmallow Mouse
03 September 2019
Creamy Gelato Shop
Urban Life Telephone Box
Flushing Toilet Set
02 September 2019
Pre-Flock Figures
Shopping Bind Bags
Bamboo Panda Family
Yellow Labrador Family
Fenton Yellow Labradors - 3 Figures
30 August 2019
Evergreen Baby
Jeans and Tshirt
29 August 2019
Supermarket Owners
Outback Koalas (3 Figure)
Darwin Monkeys (3 Figure)
28 August 2019
Splashy Otter Family (CC)
Dollhouse
21 August 2019
Blue Dress Snowbunny Bride
Cute Dress Girls
19 August 2019
Radio & Camera
18 August 2019
Miranda Maple Cat
Marshmallow Mouse Snow Princess
Lulu Golightly Silk Cat
Classic Brown Writing Desk
Classic Brown Television & Telephone
Classic Brown Living Room
17 August 2019
Chestnut Raccoons
Periwinkle Rabbit Grandparents
EU Bramble Hedgehog Family
Sky Ride Bag
Luxury Bed
5 August 2019
Burl Timbertop
Telephone Box
Bouquet Skunks - Tomy
30 July 2019
Designer Studio
Baby Tree House
Blue & Green Dress Up Set
Purple & Pink Dress Up Set
Navy & Light Blue Dress Up Set
29 July 2019
Sweet Raspberry Home
Sewing Box
Wedding Puzzle
28 July 2019
Gourmet Kitchen Set
Mother at Home
Chic Dining Table Set
Lopez Chihuahua Family
First Aid Kit Box
Town Girls - Stella Chocolate
Cliff Babblebrook Story Book & Figure
27 July 2019
Buttercup Cat Family
Chocolate Rabbit Family (Flair)
Nutmeg the Pony
Cute Couple (Japan)
Dress Up Duo
Evergreen Bear Father (20th Anniversary)
26 July 2019
Grandfather at Home
Grandmother at Home
21 July 2019
Comfy Living Room
Timbertop Bears (Calico Critters)
Archive Blanket
Archive Tin
Caramel Cat Family
Caramel Cat Twins
Archive Notepad
11 July 2019
Norwood Mouse Twins
10 July 2019
Endeavour's First Day in Class
27 June 2019
20th Anniversary Beagles
Treehouse
Classic Brown Bed & Chest
Babblebrook & Timbertop Fathers Puzzle
Town Candy Bag
24 June 2019
Fashion Show Puzzle
Archive Puzzle
Letter Set - Pink
Letter Set - Beige
23 June 2019
Bullrush Frog Family (CC)
Bullrush Frog Twins (CC)
Father Christmas Gift Set
Stamp Pad - Blue
Stamp Pad - Pink
The Big Adventure DVD
School Field Trip
Fisher Cat Grandparents
Lovely Dress Chocolate Rabbit
Funtime Treehouse
22 June 2019
Thistlethorn Mouse Father (GiG)
Pigglywink Pig Family
Strawberry the Foal (Flair)
Marlowe Tuxedo Cat Family of 3
Kitchen Set (Japan, 2019)
21 June 2019
Freya Tote Bag
30 cm Freya
Lambrook Sheep Family
Fluffy Hamster Family
Father at Home
Kitchen Play Set
Wooly Alpaca Family
Archive Exhibition Guide Book
Archive Exhibition Tote Bag
Living Room Set (Japan, 2019)
19 June 2019
Cute Couple
Chocolate Rabbit Family of 3
Classic Brown Cupboard
Babblebrook Grandfather (GiG)
Babblebrook Brother (GiG)
18 June 2019
Dream Project Ducks
Splashy Otter Family (UK)
31 May 2019
Walnut Squirrel Baby
Walnut Squirrel Twins
Evergreen Bear Family (Flair)
Girl's Dressing Table
29 May 2019
Cuddle Bear Twins
28 May 2019
Silk Cat Baby Carry Case
Hazelnut Chipmunk Family
Hazelnut Chipmunk Twins
Apple & Jake's Ride 'n Play
Baby Friends
27 May 2019
Halloween House
Baby Pool & Sandbox
Beagle Family (CC)
Vegetable Garden
Snowbunny Bride
Beagle Baby Carry Case
Buckley Deer Baby Carry Case
Fiona & Ivy, Friends Forever
Farm Vegetable Patch
Patty & Paden's Double Stroller Set
Patty & Paden's Double Stroller (Green Box)
Professor Butterglove
Wedding Photographer
Meadows Mouse Baby Carry Case
Chocolate Rabbit Christmas Tree Baby
26 May 2019
Cottontail Rabbit Family (CC)
Celebration Beagle Family
Dale Sheep Family
The New Arrival
Dale Sheep Twins
25 May 2019
Hopper Kangaroo Family
Garden Barbecue Set
Epoch 50th Anniversary Chocolate Rabbits
Waddlington Duck Family
Hunter-Smyth Chocolate Labradors
Chocolate Labradors (CC)
Chocolate Labrador Triplets (CC)
Cake Shop Capsules
Forest Bakery Capsules
Beakers
24 May 2019
Neptune Sea Otter Family
Dark Teardrop Bear Twins
Cottontail Rabbit Grandfather
Cottontail Rabbit Grandmother
Beauty the Foal
22 May 2019
Let's Play Playpen
Ornate Garden Table & Chairs
Recommended Furniture
Melissa & Melody's Baby Bath Time
Christian's Bedtime Set
Melanie & Sparky Have a Play Date
Strawberry the Foal
Macavity Cat Grandparents (Millenium)
21 May 2019
Playground Set
Sylvanian Garden
Kitchen Cookware Set
Nursery Picnic
Nursery Playground Swing Set
20 May 2019
Beach Picnic
Chocolate Rabbit Twins
Garden Decoration Set
Woodland Picnic
19 May 2019
Maple Cat Twins
Maple Cat Baby
Fielding Field Mouse Baby
Cakebread Toy Poodle Twins
Keats Cream Cat Grandparents
18 May 2019
Ballroom Set
School Friends
School Pupils
School Play
Music Lesson Set
Dream Project Performers
17 May 2019
Country Dentist
Darwin Monkey Baby
Darwin Monkey Twins
Buttercup Cow Twins
Goldbacke Hamster Baby
16 May 2019
Country Nurse Set
Doctor Checkup Set
14 May 2019
Kitchen Unit
Kitchen & Living Room Collection
Mango Monkey Family
Giant Cottontail Rabbits
Forest Monkey Family
13 May 2019
Doctor with Bike
Doctor Murdoch
Sandy Cat Family (CC)
Sandy Cat Twins (CC)
Hopscotch Rabbit Twins
12 May 2019
Maple Cat Family (CC)
Marlowe Tuxedo Cat Triplets
Marlowe Tuxedo Cat Family (CC)
Bridesmaids Set
Billabong Koala Family (CC)
11 May 2019
Hamilton Hamster Family
Grocery Shopping
Bunk Beds (2017, Japan)
Ice Skating Duo
Maple Cat Family
10 May 2019
Hopscotch Rabbit Variation
Tuxedo Cats (CC, Variation)
Beach Fun & Games
Cakebread Toy Poodles (Calico Critters)
Cottontail Rabbit Family
9 May 2019
Butterglove Wedding Couple
8 May 2019
Doughty Chiffon Dog Family
Fenton Yellow Labrador Family
Periwinkle Milk Rabbit Baby (Blue)
Plush Furbanks Mother & Baby
Brother at Home
6 May 2019
Plush Lauren Fisher Cat
Persis Persian Cat Family
Harvey Grey Cat Twins
Honey Bear Family
Maces Mouse Grandparents
School Lunch Set
Sweetpea Rabbit Family
Wastepaper Bin
5 May 2019
Periwinkle Milk Rabbit Family
Sandy Striped Cat Family
School Music Set
Seaside Friends
Marlowe Tuxedo Cat Family
Osborne Bear Family
Polaris Polar Bear Family
Character Bag
Cuddle Bear Family
4 May 2019
Calbee Bear Mother & Baby
Calbee Bear Father & Daughter
Calbee Brother & Vegetable Patch
Calico Critters Silk Cat Family
Hopscotch Rabbit Family
3 May 2019
Baden & Mikaela's Camping Set
Ballet Lesson
Bikes & Picnic Set
Fielding Field Mouse Family
School & Picnic Set
1 May 2019
We Love Sylvanian Families Book & Milk Rabbit
Winter Sports Fun
Babblebrooks' New Arrival
Chocolate Rabbit Sister Set
Chocolate Rabbit Family Dinner Puzzle
30 April 2019
School Toilets
Skidoo
Day Trip Accessory Set
Deluxe Kitchen Set (Tan and Pink Box)
Deluxe Kitchen Set (green and pink)
29 April 2019
Fountain of Wishes
Glico Aunt Claire
Dinner Party Set
Epoch 60th Anniversary Chocolate Rabbit
Hoppily Ever After DVD
28 April 2019
Accessory Set
Angeles' Bedtime
Motorcycle & Sidecar
Orange Nursery Uniform
Chocolate Rabbit Baby - Yellow School Uniform
27 April 2019
Sister at Home
Walnut Squirrels - 3 Set
Trinket Box
Chocolate Rabbit Baby Set
26 April 2019
Otter Family (2018, Japan)
Connor & Kerri's Carriage Ride
Deluxe Bathroom Set
Outdoor Sports Fun
Grandma's Coffee Break
Barker Golden Labrador Family
25 April 2019
Brown Mouse Family
Maple Dog Family
Maple Dog Baby
Luxury Loo
Luxury Toilet
Play / Dinner Tray
Music Box
Small Bathroom Set
Kitchen Cooking Set
24 April 2019
Deer Family
Deer Baby
Living Room Suite
23 April 2019
2017 UK Premium Club Freya
2018 UK Premium Club Freya
2017 UK Premium Club Melinda Cakebread
22 April 2019
Furbanks Squirrels (Flair)
Hazel & Rhianna's Day Out
Breakfast Set
Sleeping Soundly Wind-Up Bed
Whiskers Cat Twins
Playtime with Father
Petite Bear Twins
Giant Taylor Timbertop
21 April 2019
Lettuce Snow-Warren
Family Room with Aquarium
Refrigerator (Tomy)
P.C. Bobby Roberts (Tomy)
Fisher Cat Family
Gray Cat Family
Ocher Rabbit Family
Woody House
Ocher Rabbit Baby
Pig Family
20 April 2019
Rocky Babblebrook (Calico Critters)
Celebration Underwood Badgers
Hopkins Champagne Rabbit Family
Cherrie's Day at the Seaside
Buttercup Friesian Cow Grandparents
Brightfield Goat Family
Bearbury Bear Grandparents
Breezy Babblebrook (Calico Critters)
Cakebread Toy Poodle Family
Maces Mouse Family
19 April 2019
DePembroke Corgi Family
18 April 2019
Board Game
6 April 2019
Chocolate Rabbit Grandparents (2012)
Bento Box
Deluxe Living Room
Daisy Timbertop
Buckley Deer Baby
Buckley Deer Twins
5 April 2019
Garden Rabbit Family
Drawing Room Set
Conservatory Living Room Set
4 April 2019
Flower Garden Puzzle
Ellwoods Elephants
3 April 2019
Babblebrook Rabbits (Tomy, US)
Waters Beaver Twins
Evergreen Bear Grandparents (Japan)
Pigglywink Pig Twins
Buckley Red Deer Family
Kirin X Sylvanian Families Dessert Molds
Rose Timbertop
Roxy Renard's Home Interior Set
Celebration Timbertop Bears
Waddington's Card Game
2 April 2019
Oven & Rack
Rustic Kitchen
Toaster & Cupboard
Dining Room Furniture
Parent's Bedroom Set
Drums
Village Postman
Sleep 'n Study Bedroom
Bedroom Furniture Set
Loft Bed
Floral Bedroom
Oven & Sink
1 April 2019
Luxury Four Poster Bed
30th Anniversary Playing Cards
Chocolate Rabbit Family Puzzle
Sylvanian Families with Bernard Cribbins DVD
Evergreen Grey Bear Family (Tomy)
31 March 2019
Stove & Sink (2017, Japan)
Dining Table (2017, Japan)
Delicious Breakfast
Kitchen Island
Mugs
30 March 2019
Babblebrook Beavers
Lavender Rabbits
Keats Cream Cats
Petite Little Bears
Alpaca Family (JP)
Five Door Refrigerator
Kirin X Sylvanian Families Bowls
28 March 2019
Dining Set (Tomy)
Country Kitchen (Tomy)
Bunk Beds (Calico Critters)
Homemade Pancakes
Banjo
27 March 2019
Chocolate Rabbit Family (Epoch)
Dappleawn Fawn Rabbit Family (Epoch)
26 March 2019
Sewing with Mother
Whiskers Cat Grandparents
Walnut Squirrel Family
Goldbacke Hamster Family
Cycling with Mother
23 March 2019
Huckleberry Hound Dogs
Buttercup Friesian Cows
Darwin Monkey Family
Hawthorn White Mouse Family
Bouquet Skunk Family
22 March 2019
Eric Renard's Playground Set
Cycling Adventure
Dream Project Mole Family
Bramble Hedgehog Family
21 March 2019
Harvey Grey Cats (Epoch)
Celebration Babblebrook Rabbits
Timbertop Bears (USA, Tomy)
Waters Beavers (USA, Tomy)
Wildwood Rabbits (USA, Tomy)
20 March 2019
Evergreen Grandparents (Flair)
Furbanks Squirrels (Tomy)


Known for its soothing temperature all around the year, Wayanad is the ultimate destination to escape the scorching sun of North India. This place doesn’t only offer its cool temperature but along with that, it has untouched woods, misty mountains, and long spread plantations. Often called the spice garden of India, Wayanad is laid with many tourist places and vast orchards of various spices like cardamom, Black pepper, Star Anise, Fenugreek, Black cumin and more. These green orchards of distinct spices give this place a different fragrance which is further enriched with the aroma of coffee plantation, nutrition of organic fruits and vegetables and waving paddy fields.
Having said this much about the greenery in the city, it is understood that it will have numerous wildlife sanctuaries, reserves and national parks protecting the rural life of the forests. Adding to all the natural beauty you have India’s largest earth dam and Asia’s second-largest earth dam, Banasura Sagar Dam in Wayanad. Having mighty mountains, dense woods, and gushing rivers, Wayanad is a hub for trekking, hiking, mountaineering, rock climbing, rappelling, camping, and many more adventurous activities.


SCHEDULED
DEPARTED
| DATE | FROM | TO | FLIGHT Number |
TAIL NUMBER |
FLIGHT TIME |
SCHEDULED | PREDICTED | STATUS | ||
|---|---|---|---|---|---|---|---|---|---|---|
| DEPARTURE | ARRIVAL | DEPARTURE | ARRIVAL |
| icon |
apt
phrase |
||||
|
Humidity |
Temperature |
||||
|
Visibility |
Dew Point |
||||
|
Wind speed |
Pressure |
| Flight Information | |||
| Origin: | PHL | ||
| Destination: | ABC | ||
| Flight Number: |
WN1234 | ||
| Tail Number: |
5678 | ||
| Distance: | 200 miles | ||
| Scheduled Time: |
2 hrs & 0 mins | ||
| Scheduled Date: |
01 January 2015 | ||
| Scheduled Departure: |
00:00 UTC | ||
| Scheduled Arrival: |
00:00 UTC |
| × Previous Flight Information | |||
| Scheduled Interval: | 0 mins | ||
| Arrival Delay: | 0 mins |
| Departure Delay Information | |||
| Calculated Compulsary Delay: | 0 mins | ||
| Predicted General Delay: | 0 mins | ||
| Predicted Weather Delay: | 0 mins | ||
| Total Predicted Departure Delay: | 0 mins | ||
| Actual Departure Delay: | 0 mins |
| Arrival Delay Information | |||
| Predicted Arrival Delay: | 0 mins |


@* * Copyright 2017 HM Revenue & Customs * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. *@ @import models.WasAnyValueReceivedModel @import common.Constants @import uk.gov.hmrc.play.views.html.helpers.form @import views.html.helpers.{externalLink, backButtonWithProgress, errorSummary, formHiddenYesNoRadio, formInlineDateInput, textArea} @(wasAnyValueReceivedForm: Form[WasAnyValueReceivedModel])(implicit request: Request[_], messages: Messages) @additionalContent() = {
@Messages("page.investors.wasAnyValueReceived.additionalGuidance.title")
@Messages("page.investors.wasAnyValueReceived.guidance.definition")
@Messages("page.investors.wasAnyValueReceived.guidance.title")
@Messages("page.investors.wasAnyValueReceived.guidance.hint")


@Beta
public class Rational
extends java.lang.Number
implements java.lang.Cloneable, java.lang.Comparable<java.lang.Object>
Dynamically sized means that (provided enough memory) the Rational numbers can't overflow (nor underflow); this characteristic is different from Java's data types int and long, but common with BigInteger (which implements only integer numbers, i.e. no fractions) and BigDecimal (which only implements precisely rational numbers with denominators that are products of 2 and 5 [and implied 10]). Arbitrary precision means that there is no loss of precision with common arithmetic operations such as addition, subtraction, multiplication, and division (BigDecimal loses precision with division, if factors other than 2 or 5 are involved). [Doubles and floats can overflow and underflow, have a limited precision, and only implement precisely rationals with a denominator that is a power of 2.]
Rational provides most operations needed in rational number space calculations, including addition, subtraction, multiplication, division, integer power, remainder/modulus, comparison, and different roundings.
Rational provides conversion methods to and from the native types long, int, short, and byte (including support for unsigned values), double (binary64), float (binary32), quad (binary128, quadruple), half (binary16), and BigInteger. Rational can parse and print many string representations: rational, dot notations, with exponent, even mixtures thereof, and supports different radixes/bases (2 to typically 36 [limited by BigInteger parsing implementation]).
Rational uses java.math.BigInteger (JDK 1.1 and later) internally.
Binary operations (e.g. add, multiply) calculate their results from a Rational object ('this') and one [Rational or long] argument, returning a new immutable Rational object. Both the original object and the argument are left unchanged (hence immutable). Unary operations (e.g. negate, invert) calculate their result from the Rational object ('this'), returning a new immutable Rational object. The original object is left unchanged.
Most operations are precise (i.e. without loss of precision); exceptions are the conversion methods to limited precision types (doubleValue, floatValue), rounding (round), truncation (bigIntegerValue, floor, ceiling, truncate), as well as obviously the printing methods that include a precision parameter (toStringDot, toStringDotRelative, toStringExponent).
Rational doesn't provide a notion of "infinity" ([+-]Infinity) and "not a number" (NaN); IEEE 754 floating point Infinity and NaN are rejected (throwing a NumberFormatException). Operations such as 0/0 result in an ArithmeticException.
Rational internally uses private proxy functions for BigInteger functionality, including scanning and multiplying, to enhance speed and to realize fast checks for common values (1, 0, etc.).
Constructor samples: normal rational form, abbreviated form, fixed point form, abbreviated fixed point form, [exponential] floating point form, different radixes/bases different from 10, doubles/floats:
Rational("-21/35") : rational -3/5 Rational("/3") : rational 1/3 Rational("3.4") : rational 17/5 Rational(".7") : 0.7, rational 7/10 Rational("-65.4E-3") : -327/5000 Rational("f/37", 0x10) : 3/11 Rational("f.37", 0x10) : 3895/256 Rational("-dcba.efgh", 23) : -46112938320/279841 Rational("1011101011010110", 2) : 47830 Rational(StrictMath.E) :<PHONE_NUMBER>868073/2251799813685248 Rational((float)StrictMath.E) : 2850325/1048576
Also accepted are denormalized representations such as:
Rational("2.5/-3.5"): -5/7 Rational("12.34E-1/-56.78E-1") : -617/2839
Printing: rational form, fixed point (dot) forms with different absolute precisions (including negative precision), with relative precisions, exponential form, different radix:
Rational("1234.5678") : "6172839/5000" Rational("1234.5678").toStringDot(6) : "1234.567800" Rational("1234.5678").toStringDot(2) : "1234.57" Rational("1234.5678").toStringDot(-2) : "1200" Rational("1234.5678").toStringDotRelative(6) : "1234.57" Rational("0.00012345678").toStringDotRelative(3) : "0.000123" Rational("1234.5678").toStringExponent(2) : "1.2E3" Rational("1011101011010110", 2).toString(0x10) : "bad6"
Usage: Rational operations can be conveniently chained (sample from Rational internal conversion from IEEE 754 bits):
Rational.valueOf(2).power(exponent) .multiply(fraction.add(Rational.valueOfUnsigned(mantissa))) .multiply(sign);
| Modifier and Type | Field and Description |
|---|---|
static int |
DEFAULT_RADIX
Default radix, used in string printing and scanning, 10 (i.e.
|
static int |
DEFAULT_ROUND_MODE
Default round mode, ROUND_HALF_UP.
|
static Rational |
MINUS_ONE
The constant minus-one (-1).
|
static Rational |
ONE
The constant one (1).
|
static int |
ROUND_CEILING
Rounding mode to round towards positive infinity.
|
static int |
ROUND_DOWN
Rounding mode to round towards zero.
|
static int |
ROUND_FLOOR
Rounding mode to round towards negative infinity.
|
static int |
ROUND_HALF_CEILING
Rounding mode to round towards nearest neighbor unless both neighbors are
equidistant, in which case to round ceiling.
|
static int |
ROUND_HALF_DOWN
Rounding mode to round towards nearest neighbor unless both neighbors are
equidistant, in which case to round down.
|
static int |
ROUND_HALF_EVEN
Rounding mode to round towards the nearest neighbor unless both neighbors
are equidistant, in which case to round towards the even neighbor.
|
static int |
ROUND_HALF_FLOOR
Rounding mode to round towards nearest neighbor unless both neighbors are
equidistant, in which case to round floor.
|
static int |
ROUND_HALF_ODD
Rounding mode to round towards the nearest neighbor unless both neighbors
are equidistant, in which case to round towards the odd neighbor.
|
static int |
ROUND_HALF_UP
Rounding mode to round towards nearest neighbor unless both neighbors are
equidistant, in which case to round up.
|
static int |
ROUND_UNNECESSARY
Rounding mode to assert that the requested operation has an exact result,
hence no rounding is necessary.
|
static int |
ROUND_UP
Rounding mode to round away from zero.
|
static Rational |
ZERO
The constant zero (0).
|
| Constructor and Description |
|---|
Rational(BigIntegerNumber numerator)
Construct a Rational from a numerator only, denominator is defaulted to
1.
|
Rational(BigIntegerNumber numerator,
BigIntegerNumber denominator)
Construct a Rational from numerator and denominator.
|
Rational(BigIntegerNumber unscaledValue,
int scale)
Construct a Rational from an unscaled value and a scale value, default
radix (10).
|
Rational(BigIntegerNumber unscaledValue,
int scale,
int radix)
Construct a Rational from an unscaled value and a scale value.
|
Rational(double value)
Construct a Rational from a [IEEE 754] double [size/precision] floating
point number.
|
Rational(float value)
Construct a Rational from a [IEEE 754] single [size/precision] floating
point number.
|
Rational(long numerator)
Construct a Rational from a long fix number integer representing
numerator, denominator is defaulted to 1.
|
Rational(long unscaledValue,
int scale,
int radix)
Construct a Rational from an unscaled fix number value and a scale value.
|
Rational(long numerator,
long denominator)
Construct a Rational from long fix number integers representing numerator
and denominator.
|
Rational(Rational that)
Clone a Rational.
|
Rational(java.lang.String strRational)
Construct a Rational from a string representation using DEFAULT_RADIX.
|
Rational(java.lang.String strRational,
int radix)
Construct a Rational from a string representation.
|
| Modifier and Type | Method and Description |
|---|---|
Rational |
abs() |
Rational |
add(long that)
Add a long fix number integer to this Rational and return a new Rational.
|
Rational |
add(Rational that)
Add a Rational to this Rational and return a new Rational.
|
BigIntegerNumber |
bigIntegerValue()
Convert to BigInteger, by rounding.
|
Rational |
ceil()
Ceiling, round towards positive infinity.
|
Rational |
clone()
Clone the current Rational.
|
int |
compareTo(BigIntegerNumber that)
Compare this Rational to a BigInteger.
|
int |
compareTo(long that)
Compare this Rational to a long.
|
int |
compareTo(java.lang.Object object)
Compare this Rational to an Object.
|
int |
compareTo(Rational that)
Compare this Rational to another Rational.
|
Rational |
divide(long that)
Divide this Rational through a long fix number integer and return a new
Rational.
|
Rational |
divide(Rational that)
Divide this Rational through another Rational and return a new Rational.
|
long |
doubleBitsValue()
Convert to IEEE 754 double float bits.
|
double |
doubleValue()
Convert to double floating point value.
|
boolean |
equals(java.lang.Object object)
Compare object for equality.
|
int |
floatBitsValue()
Convert to IEEE 754 single float bits.
|
float |
floatValue()
Convert to single floating point value.
|
Rational |
floor()
Floor, round towards negative infinity.
|
Rational |
fractionalPart()
Fractional part.
|
BigIntegerNumber |
getDenominator() |
BigIntegerNumber |
getNumerator() |
short |
halfBitsValue()
Convert this Rational to IEEE 754 half float (binary16) bits.
|
int |
hashCode()
Hash code.
|
Rational[] |
integerAndFractionalPart()
Return an array of Rationals with both integer and fractional part.
|
Rational |
integerPart()
Integer part.
|
int |
intValue()
Convert to int, by rounding and delegating to BigInteger.
|
int |
intValueExact()
Convert this Rational to an int, either returning an exact result (no
rounding or truncation needed), or throw an ArithmeticException.
|
Rational |
invert() |
boolean |
isInteger()
Integer predicate.
|
boolean |
isMinusOne()
Minus-one predicate.
|
boolean |
isNegative()
Negative predicate.
|
boolean |
isOne()
One predicate.
|
boolean |
isPositive()
Positive predicate.
|
boolean |
isZero()
Zero predicate.
|
long |
longValue()
Convert to long, by rounding and delegating to BigInteger.
|
long |
longValueExact()
Convert this Rational to a long integer, either returning an exact result
(no rounding or truncation needed), or throw an ArithmeticException.
|
Rational |
max(long that)
Return the maximum value of a Rational and a long fix number integer.
|
Rational |
max(Rational that)
Return the maximal value of two Rationals.
|
Rational |
min(long that)
Return the minimal value of a Rational and a long fix number integer.
|
Rational |
min(Rational that)
Calculate the minimal value of two Rationals.
|
Rational |
mod(long that)
Calculate the modulus of this Rational and a long fix number integer and
return a new Rational.
|
Rational |
mod(Rational that)
Calculate the modulus of this Rational and another Rational and return a
new Rational.
|
Rational |
multiply(long that)
Multiply a long fix number integer to this Rational and return a new
Rational.
|
Rational |
multiply(Rational that)
Multiply a Rational to this Rational and return a new Rational.
|
Rational |
negate() |
Rational |
pow(BigIntegerNumber exponent) |
Rational |
pow(int exponent)
Calculate this Rational's integer power and return a new Rational.
|
Rational |
pow(Rational exponent) |
static boolean |
quadBitsEqual(long[] a,
long[] b)
Compare two IEEE 754 quad size (quadruple precision, binary128) floating
point numbers (each represented as two longs).
|
long[] |
quadBitsValue()
Convert this Rational to IEEE 754 quad float (binary128, quadruple) bits.
|
Rational |
remainder(long that)
Calculate the remainder of this Rational and a long fix number integer
and return a new Rational.
|
Rational |
remainder(Rational that)
Calculate the remainder of this Rational and another Rational and return
a new Rational.
|
static void |
resetApproximationConfiguration(boolean enabled,
int precision,
java.math.RoundingMode roundingMode) |
static void |
resetApproximationConfigurationFromAICUtilConfiguration() |
Rational |
round()
Round by default mode (ROUND_HALF_UP).
|
Rational |
round(int roundMode)
Round.
|
static int |
setToStringDotRoundingMode(int roundingMode)
Set the toStringDot() rounding mode to be used.
|
int |
signum()
Signum.
|
Rational |
subtract(long that)
Subtract a long fix number integer from this Rational and return a new
Rational.
|
Rational |
subtract(Rational that)
Subtract a Rational from this Rational and return a new Rational.
|
java.lang.String |
toString()
Rational string representation, format "[-]numerator[/denominator]",
default radix (10).
|
java.lang.String |
toString(int radix)
Rational string representation, format "[-]numerator[/denominator]".
|
java.lang.String |
toStringDot(int precision)
Dot-format "[-]i.f" string representation, with a precision, default
radix (10).
|
java.lang.String |
toStringDot(int precision,
int radix)
Fixed dot-format "[-]i.f" string representation, with a precision.
|
java.lang.String |
toStringDotRelative(int precision)
Dot-format "[-]i.f" string representation, with a relative precision,
default radix (10).
|
java.lang.String |
toStringDotRelative(int precision,
int radix)
Dot-format "[-]i.f" string representation, with a relative precision.
|
java.lang.String |
toStringExponent(int precision)
Exponent-format string representation, with a relative precision, default
radix (10), "[-]i[.f]E[-]e" (where i is one digit other than 0 exactly; f
has no trailing 0);
|
java.lang.String |
toStringExponent(int precision,
int radix)
Exponent-format string representation, with a relative precision,
"[-]i[.f]E[-]e" (where i is one digit other than 0 exactly; f has no
trailing 0);
|
Rational |
truncate()
Truncate, round towards zero.
|
static Rational |
valueOf(BigIntegerNumber value)
Build a Rational from a BigInteger.
|
static Rational |
valueOf(byte value)
Build a Rational from a byte.
|
static Rational |
valueOf(double value)
Build a Rational from a [IEEE 754] double [size/precision] floating point
number.
|
static Rational |
valueOf(float value)
Build a Rational from a [IEEE 754] single [size/precision] floating point
number.
|
static Rational |
valueOf(int value)
Build a Rational from an int.
|
static Rational |
valueOf(long value)
Build a Rational from a long fix number integer.
|
static Rational |
valueOf(Rational value)
Convert this Rational to its constant (ONE, ZERO, MINUS_ONE) if possible.
|
static Rational |
valueOf(short value)
Build a Rational from a short.
|
static Rational |
valueOf(java.lang.String value)
Build a Rational from a String.
|
static Rational |
valueOfDoubleBits(long value)
Build a Rational from an IEEE 754 double size (double precision,
binary64) floating point number represented as long.
|
static Rational |
valueOfFloatBits(int value)
Build a Rational from an IEEE 754 single size (single precision,
binary32) floating point number represented as int.
|
static Rational |
valueOfHalfBits(short value)
Build a Rational from an IEEE 754 half size (half precision, binary16)
floating point number represented as short.
|
static Rational |
valueOfQuadBits(long[] value)
Build a Rational from an IEEE 754 quad size (quadruple precision,
binary128) floating point number represented as an array of two longs
(big endian; higher significant long first).
|
static Rational |
valueOfUnsigned(byte value)
Build a Rational from an unsigned byte.
|
static Rational |
valueOfUnsigned(int value)
Build a Rational from an unsigned int.
|
static Rational |
valueOfUnsigned(long value)
Build a Rational from an unsigned long fix number integer.
|
static Rational |
valueOfUnsigned(short value)
Build a Rational from an unsigned short.
|
public static final int DEFAULT_RADIX
public static Rational ZERO
public static Rational ONE
public static Rational MINUS_ONE
public static final int ROUND_UP
public static final int ROUND_DOWN
public static final int ROUND_CEILING
public static final int ROUND_FLOOR
public static final int ROUND_HALF_UP
public static final int ROUND_HALF_DOWN
public static final int ROUND_HALF_EVEN
public static final int ROUND_UNNECESSARY
public static final int ROUND_HALF_CEILING
public static final int ROUND_HALF_FLOOR
public static final int ROUND_HALF_ODD
public static final int DEFAULT_ROUND_MODE
public Rational(BigIntegerNumber numerator, BigIntegerNumber denominator)
numerator
- the rational's numerator.denominator
- the rational's denominator (quotient)public Rational(BigIntegerNumber numerator)
numerator
- the rational's numerator.public Rational(long numerator, long denominator)
numerator
- the rational's numerator.denominator
- the rational's denominator (quotient)public Rational(long numerator)
numerator
- the rational's numerator.public Rational(Rational that)
[As Rationals are immutable, this copy-constructor is not that useful.]
that
- a rational value that the newly constructed rational is to be a clone of.public Rational(java.lang.String strRational, int radix)
The supported string formats are: "[+-]numerator" "[+-]numerator/[+-]denominator" "[+-]i.f" "[+-]i" "[+-]iE[+-]e" "[+-]i.fE[+-]e" (latter two only with radix <= 10, due to possible ambiguities); numerator and denominator can be any of the latter (i.e. mixed representations such as "-1.2E-3/-4.5E-6" are supported). Samples: "-21/35", "3.4", "-65.4E-3", "f/37" (base 16), "1011101011010110" (base 2).
strRational
- a string prepresentation of a Rational number.radix
- the radix the string representation is meant to be in.public Rational(java.lang.String strRational)
The supported string formats are: "[+-]numerator" "[+-]numerator/[+-]denominator" "[+-]i.f" "[+-]i" "[+-]iE[+-]e" "[+-]i.fE[+-]e" (latter two only with radix <= 10, due to possible ambiguities); numerator and denominator can be any of the latter (i.e. mixed representations such as "-1.2E-3/-4.5E-6" are supported). Samples: "-21/35", "3.4", "-65.4E-3", "f/37" (base 16), "1011101011010110" (base 2).
strRational
- a string prepresentation of a Rational number.public Rational(BigIntegerNumber unscaledValue, int scale, int radix)
unscaledValue
- an unscaled value representation of a Rational.scale
- the scale to be associated with the unscaledValueradix
- the radix the rational is meant to be in.public Rational(BigIntegerNumber unscaledValue, int scale)
unscaledValue
- an unscaled value representation of a Rational.scale
- the scale to be associated with the unscaledValuepublic Rational(long unscaledValue, int scale, int radix)
unscaledValue
- an unscaled value representation of a Rational.scale
- the scale to be associated with the unscaledValueradix
- the radix the rational is meant to be in.public Rational(double value)
value
- double value from which a Rational is to be constructed.public Rational(float value)
value
- double value from which a Rational is to be constructed.public BigIntegerNumber getNumerator()
public BigIntegerNumber getDenominator()
public static int setToStringDotRoundingMode(int roundingMode)
roundingMode
- the rounding mode to use when toStringDot() is called.public boolean isPositive()
Indicates whether this Rational is larger than zero. Zero is not positive.
[For convenience.]
public boolean isNegative()
Indicates whether this Rational is smaller than zero. Zero isn't negative either.
[For convenience.]
public boolean isZero()
Indicates whether this Rational is zero.
[For convenience and speed.]
public boolean isOne()
Indicates whether this Rational is 1.
[For convenience and speed.]
public boolean isMinusOne()
Indicates whether this Rational is -1.
[For convenience and speed.]
public boolean isInteger()
Indicates whether this Rational convertible to a BigInteger without loss of precision. True iff denominator/quotient is one.
public java.lang.String toString(int radix)
Sample output: "6172839/5000".
radix
- the radix to use.public java.lang.String toString()
Default string representation, as rational, not using an exponent.
Sample output: "6172839/5000".
Overwrites Object.toString().
toString
in class java.lang.Object
public java.lang.String toStringDot(int precision, int radix)
Precision may be negative, in which case the rounding affects digits left of the dot, i.e. the integer part of the number, as well.
Sample output: "1234.567800".
Possible loss of precision.
precision
- the precision to use.radix
- the radix to use.public java.lang.String toStringDot(int precision)
Sample output: "1234.567800".
Possible loss of precision.
precision
- the precision to use.public java.lang.String toStringDotRelative(int precision, int radix)
If the relative precision is zero or negative, "0" will be returned (i.e. total loss of precision).
Possible loss of precision.
precision
- the precision to use.radix
- the radix to use.public java.lang.String toStringDotRelative(int precision)
If the relative precision is zero or negative, "0" will be returned (i.e. total loss of precision).
Possible loss of precision.
precision
- the precision to use.public java.lang.String toStringExponent(int precision, int radix)
Sample output: "1.2E3".
Possible loss of precision.
precision
- the precision to use.radix
- the radix to use.public java.lang.String toStringExponent(int precision)
Sample output: "1.2E3".
Possible loss of precision.
precision
- the precision to use.public Rational add(Rational that)
If one of the operands is zero, [as an optimization] the other Rational is returned.
that
- the rational to be added to this rational.public Rational add(long that)
that
- a long to be added to this rational.public Rational subtract(Rational that)
If the second operand is zero, [as an optimization] this Rational is returned.
that
- the rational to be subtracted from this rational.public Rational subtract(long that)
that
- the long value to be subtracted from this rational.public Rational multiply(Rational that)
If one of the operands is one, [as an optimization] the other Rational is returned.
that
- the rational to be multiplied with this rational.public Rational multiply(long that)
that
- the long to be multiplied with this rational.public Rational divide(Rational that)
If the second operand is one, [as an optimization] this Rational is returned.
that
- the rational to be divided by this rational.public Rational divide(long that)
that
- the long to be divided by this rational.public Rational pow(int exponent)
The integer exponent may be negative.
If the exponent is one, [as an optimization] this Rational is returned.
exponent
- the exponent to raise this rational bypublic Rational pow(BigIntegerNumber exponent)
public Rational remainder(Rational that)
The remainder result may be negative.
The remainder is based on round down (towards zero) / truncate. 5/3 == 1 + 2/3 (remainder 2), 5/-3 == -1 + 2/-3 (remainder 2), -5/3 == -1 + -2/3 (remainder -2), -5/-3 == 1 + -2/-3 (remainder -2).
that
- the rational to be divided by this rational to get a
remainder.public Rational remainder(long that)
that
- the long to be divided by this rational to get a
remainder.public Rational mod(Rational that)
The modulus result may be negative.
Modulus is based on round floor (towards negative). 5/3 == 1 + 2/3 (modulus 2), 5/-3 == -2 + -1/-3 (modulus -1), -5/3 == -2 + 1/3 (modulus 1), -5/-3 == 1 + -2/-3 (modulus -2).
that
- the rational to be divided by this rational to get a
mod.public Rational mod(long that)
that
- the long to be divided by this rational to get a
mod.public int signum()
public Rational abs()
public Rational negate()
public Rational invert()
public Rational min(Rational that)
that
- the other rational to test.public Rational min(long that)
that
- the other long to test.public Rational max(Rational that)
that
- the other rational to test.public Rational max(long that)
that
- the other long to test.public boolean equals(java.lang.Object object)
Overwrites Object.equals(Object).
equals
in class java.lang.Object
object
- the object to be compared with this for equality.public int hashCode()
Overwrites Object.hashCode().
hashCode
in class java.lang.Object
public int compareTo(Rational that)
that
- the Rational value to be compared to.public int compareTo(BigIntegerNumber that)
that
- the BigInteger value to be compared to.public int compareTo(long that)
that
- the long value to be compared to.public int compareTo(java.lang.Object object)
Object can be Rational/BigInteger/Long/Integer/Short/Byte.
Implements Comparable.compareTo(Object) (JDK 1.2 and later).
A sample use is with a sorted map or set, e.g. TreeSet.
Only Rational/BigInteger/Long/Integer objects allowed, method will throw otherwise.
For backward compatibility reasons we keep compareTo(Object) additionally to compareTo(Rational). Comparable<Object> is declared to be implemented rather than Comparable<Rational>.
compareTo
in interface java.lang.Comparable<java.lang.Object>
public BigIntegerNumber bigIntegerValue()
Possible loss of precision.
public long longValue()
Possible loss of precision.
Overwrites Number.longValue().
longValue
in class java.lang.Number
public int intValue()
Possible loss of precision.
Overwrites Number.intValue().
intValue
in class java.lang.Number
public double doubleValue()
Possible loss of precision.
Overwrites Number.doubleValue().
doubleValue
in class java.lang.Number
public float floatValue()
Note that Rational's [implicit] [default] rounding mode that applies [too] on indirect double to Rational to float rounding (round-half-up) may differ from what's done in a direct cast/coercion from double to float (e.g. round-half-even).
Possible loss of precision.
Overwrites Number.floatValue().
floatValue
in class java.lang.Number
public long doubleBitsValue()
Possible loss of precision.
public int floatBitsValue()
Possible loss of precision.
public short halfBitsValue()
As a short value is returned rather than a int, care has to be taken no unwanted sign expansion happens in subsequent operations, e.g. by masking (x.halfBitsValue()&0xffffl) or similar (x.halfBitsValue()==(short)0xbc00).
Possible loss of precision.
public long[] quadBitsValue()
The bits are returned in an array of two longs, big endian (higher significant long first).
Possible loss of precision.
public long longValueExact()
public int intValueExact()
public static Rational valueOf(Rational value)
value
- the value to be converted if possible.public static Rational valueOf(java.lang.String value)
[Roughly] equivalent to new Rational(value)
.
value
- the value to be converted to a rational.public static Rational valueOf(BigIntegerNumber value)
Equivalent to new Rational(value)
.
value
- the value to be converted to a rational.public static Rational valueOf(long value)
[Roughly] equivalent to new Rational(value)
.
As an optimization, commonly used numbers are returned as a reused constant.
value
- the value to be converted to a rational.public static Rational valueOf(int value)
value
- the value to be converted to a rational.public static Rational valueOf(short value)
value
- the value to be converted to a rational.public static Rational valueOf(byte value)
value
- the value to be converted to a rational.public static Rational valueOf(double value)
value
- the value to be converted to a rational.public static Rational valueOf(float value)
value
- the value to be converted to a rational.public static Rational valueOfUnsigned(long value)
The resulting Rational is positive, i.e. the negative longs are mapped to 2**63..2**64 (exclusive).
value
- the value to be converted to a rational.public static Rational valueOfUnsigned(int value)
The resulting Rational is positive, i.e. the negative ints are mapped to 2**31..2**32 (exclusive).
value
- the value to be converted to a rational.public static Rational valueOfUnsigned(short value)
The resulting Rational is positive, i.e. the negative shorts are mapped to 2**15..2**16 (exclusive).
value
- the value to be converted to a rational.public static Rational valueOfUnsigned(byte value)
The resulting Rational is positive, i.e. the negative bytes are mapped to 2**7..2**8 (exclusive).
value
- the value to be converted to a rational.public static Rational valueOfDoubleBits(long value)
An IEEE 754 double size (binary64) number uses 1 bit for the sign, 11 bits for the exponent, and 52 bits (plus 1 implicit bit) for the fraction/mantissa. The minimal exponent encodes subnormal nubers; the maximal exponent encodes Infinities and NaNs.
Infinities and NaNs are not supported as Rationals.
The conversion from the bits to a Rational is done without loss of precision.
value
- the value to be converted to a rational.public static Rational valueOfFloatBits(int value)
An IEEE 754 single size (binary32) number uses 1 bit for the sign, 8 bits for the exponent, and 23 bits (plus 1 implicit bit) for the fraction/mantissa. The minimal exponent encodes subnormal nubers; the maximal exponent encodes Infinities and NaNs.
Infinities and NaNs are not supported as Rationals.
The conversion from the bits to a Rational is done without loss of precision.
value
- the value to be converted to a rational.public static Rational valueOfHalfBits(short value)
An IEEE 754 half size (binary16) number uses 1 bit for the sign, 5 bits for the exponent, and 10 bits (plus 1 implicit bit) for the fraction/mantissa. The minimal exponent encodes subnormal nubers; the maximal exponent encodes Infinities and NaNs.
Infinities and NaNs are not supported as Rationals.
The conversion from the bits to a Rational is done without loss of precision.
value
- the value to be converted to a rational.public static Rational valueOfQuadBits(long[] value)
An IEEE 754 quad size (binary128, quadruple) number uses 1 bit for the sign, 15 bits for the exponent, and 112 bits (plus 1 implicit bit) for the fraction/mantissa. The minimal exponent encodes subnormal nubers; the maximal exponent encodes Infinities and NaNs.
Infinities and NaNs are not supported as Rationals.
The conversion from the bits to a Rational is done without loss of precision.
value
- the value to be converted to a rational.public static boolean quadBitsEqual(long[] a, long[] b)
a
- the first value to compare.b
- the second value to compare.public Rational round(int roundMode)
Round mode is one of {
ROUND_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR,
ROUND_HALF_UP, ROUND_HALF_DOWN, ROUND_HALF_EVEN,
ROUND_HALF_CEILING, ROUND_HALF_FLOOR, ROUND_HALF_ODD,
ROUND_UNNECESSARY, DEFAULT_ROUND_MODE (==ROUND_HALF_UP)
.
If rounding isn't necessary, i.e. this Rational is an integer, [as an optimization] this Rational is returned.
Possible loss of precision.
roundMode
- the rounding mode to use.public Rational round()
Possible loss of precision.
public Rational floor()
Possible loss of precision.
public Rational ceil()
Possible loss of precision.
public Rational truncate()
Possible loss of precision.
public Rational integerPart()
Possible loss of precision.
public Rational fractionalPart()
Possible loss of precision.
public Rational[] integerAndFractionalPart()
Integer part is returned at offset 0; fractional part at offset 1.
public Rational clone() throws java.lang.CloneNotSupportedException
clone
in class java.lang.Object
java.lang.CloneNotSupportedException
public static void resetApproximationConfigurationFromAICUtilConfiguration()
public static void resetApproximationConfiguration(boolean enabled, int precision, java.math.RoundingMode roundingMode)


- get(String) - Method in class tk.playerforcehd.chat.config.properties.AbstractPropertie
-
- get(String) - Method in interface tk.playerforcehd.chat.config.properties.IPropertie
-
- getDirSize(File) - Method in class tk.playerforcehd.chat.utils.FileHelperUtil
-
- getFileName() - Method in class tk.playerforcehd.chat.config.properties.AbstractPropertie
-
- getJarLocation() - Method in class tk.playerforcehd.chat.start.Main
-
Returns the location where the server has been started, so it can used to manage the server files in the current folder.
- getLogDataDir() - Method in class tk.playerforcehd.chat.start.Main
-
- getLogger() - Method in class tk.playerforcehd.chat.start.Main
-
- getMainDataDir() - Static method in class tk.playerforcehd.chat.start.Main
-
- getMainInstance() - Static method in class tk.playerforcehd.chat.start.Main
-
- getPluginDataDir() - Method in class tk.playerforcehd.chat.start.Main
-
- getProgrammName() - Method in class tk.playerforcehd.chat.start.Main
-
- getProgrammVersion() - Method in class tk.playerforcehd.chat.start.Main
-
- getProperties() - Method in class tk.playerforcehd.chat.config.properties.AbstractPropertie
-
- getProperties() - Method in interface tk.playerforcehd.chat.config.properties.IPropertie
-
- Getter - Annotation Type in tk.playerforcehd.chat.annotation.type
-
This annotation is to mark getters in classes, it's only for better syntax
- GZipCompressionException - Exception in tk.playerforcehd.chat.exception
-
Get thrown when anything went wrong by compressing or decompressing a gzip file
- GZipCompressionException() - Constructor for exception tk.playerforcehd.chat.exception.GZipCompressionException
-
- GZipCompressionException(String) - Constructor for exception tk.playerforcehd.chat.exception.GZipCompressionException
-
- GZipCompressionException(Throwable) - Constructor for exception tk.playerforcehd.chat.exception.GZipCompressionException
-
- GZipCompressionException(String, Throwable) - Constructor for exception tk.playerforcehd.chat.exception.GZipCompressionException
-
- GZipCompressionException(String, Throwable, boolean, boolean) - Constructor for exception tk.playerforcehd.chat.exception.GZipCompressionException
-
- GZIPCompressUtilErrorManager - Class in tk.playerforcehd.chat.exception.manager
-
When a error happens by booting the server, this manager will handle the stacktrace
- GZIPCompressUtilErrorManager(Main) - Constructor for class tk.playerforcehd.chat.exception.manager.GZIPCompressUtilErrorManager
-


Veronica Eulenberg
Software Engineer
Fixing and customizing user-focused, responsive-design and cross-browser compatible solutions with various customers since 2017.
HTML CSS JavaScript jQuery React Node PHP MySQL WordPress
Fixing and customizing user-focused, responsive-design and cross-browser compatible solutions with various customers since 2017.
HTML CSS JavaScript jQuery React Node PHP MySQL WordPress


XVFB(1) XVFB(1) NAME Xvfb - virtual framebuffer X server for X Version 11 SYNOPSIS Xvfb [ option ] ... DESCRIPTION Xvfb is an X server that can run on machines with no display hardware and no physical input devices.  The primary use of this server was intended to be server testing. The fb code for any depth can be exercised with this server without the need for real hardware that supports the desired depths. The X community has found many other novel uses for Xvfb, including testing clients against unusual depths and screen configurations, doing batch processing with Xvfb as a background rendering engine, load testing, as an aid to porting the X server to a new platform, and providing an unobtrusive way to run applications that don't really need an X server but insist on having one anyway. OPTIONS In addition to the normal server options described in the Xserver(1) man‐ ual page, Xvfb accepts the following command line switches: -screen screennum WxHxD This option creates screen screennum and sets its width, height, and depth to W, H, and D respectively. By default, only screen 0 exists and has the dimensions 1280x1024x8. -pixdepths list-of-depths This option specifies a list of pixmap depths that the server should support in addition to the depths implied by the supported screens. list-of-depths is a space-separated list of integers that can have values from 1 to 32. -fbdir framebuffer-directory This option specifies the directory in which the memory mapped files containing the framebuffer memory should be created. See FILES. This option only exists on machines that have the mmap and msync sys‐ tem calls. -shmem This option specifies that the framebuffer should be put in shared memory. The shared memory ID for each screen will be printed by the server. The shared memory is in xwd format. This option only exists on machines that support the System V shared memory interface. If neither -shmem nor -fbdir is specified, the framebuffer memory will be allocated with malloc(). -linebias n This option specifies how to adjust the pixelization of thin lines. The value n is a bitmask of octants in which to prefer an axial step when the Bresenham error term is exactly zero. See the file Xserver/mi/miline.h for more information. This option is probably only useful to server developers to experiment with the range of line pixelization possible with the fb code. -blackpixel pixel-value, -whitepixel pixel-value These options specify the black and white pixel values the server should use. FILES The following files are created if the -fbdir option is given. framebuffer-directory/Xvfb_screen<n> Memory mapped file containing screen n's framebuffer memory, one file per screen. The file is in xwd format. Thus, taking a full-screen snapshot can be done with a file copy command, and the resulting snapshot will even contain the cursor image. EXAMPLES Xvfb :1 -screen 0 1600x1200x32 The server will listen for connections as server number 1, and screen 0 will be depth 32 1600x1200. Xvfb :1 -screen 1 1600x1200x16 The server will listen for connections as server number 1, will have the default screen configuration (one screen, 1280x1024x8), and screen 1 will be depth 16 1600x1200. Xvfb -pixdepths 3 27 -fbdir /var/tmp The server will listen for connections as server number 0, will have the default screen configuration (one screen, 1280x1024x8), will also support pixmap depths of 3 and 27, and will use memory mapped files in /var/tmp for the framebuffer. xwud -in /var/tmp/Xvfb_screen0 Displays screen 0 of the server started by the preceding example. SEE ALSO X(7), Xserver(1), xwd(1), xwud(1), XWDFile.h AUTHORS David P. Wiggins, The Open Group, Inc. X Version 11 xorg-server 1.12.4 XVFB(1)


For the fig-swirl: Melt butter over medium heat in a saucepan. Add brown sugar and stir to dissolve. Halve all of the figs and toss in the saucepan with water and lemon juice. Cook over medium heat, stirring frequently, until you have a chunky-jammy mixture. Add salt with one or two stirs, set aside and let cool completely.
Ice cream: In a small pot over medium heat, combine milk, and granulated sugar until sugar is completely. dissolved and the milk is just barely lukewarm. Whisk in the egg yolks. Set mixture in the fridge and wait until the fig mixture is cooled.
Using an ice cream machine, pour liquids into the frozen basin and process according to manufacturer instructions, i.e., let spin and thicken for 20 minutes before adding mascarpone, fig jam mixture, and the nuts. Continue to process for +/- 10 minutes. Pour semi-frozen mixture into a pyrex dish of glass tupperware. Freeze for at least two hours before serving.
☐ 11/2 cups milk
☐ 1/2 cups mascarpone
☐ 1/2 tsp pink salt
☐ 1 lb Black Mission Figs
☐ 1/2 cup brown sugar
☐ 2-4 tbsp water
☐ 11/2 cups heavy cream
✅ 1/3 granulated sugar
✅ 2 egg yolks
☐ 1 lemon, juiced
☐ 2 tbsp butter
☐ 1 cup honey roasted pecans, roughly chopped
Vanessa Stevenson
Food enthusiast, photography fan. Add a pinch of raw foodism and that's pretty much who I am.


Some quick example text to build on the card title and make up the bulk of the card's content.
Go somewhereSome quick example text to build on the card title and make up the bulk of the card's content.
Go somewhereSome quick example text to build on the card title and make up the bulk of the card's content.
Go somewhereSome quick example text to build on the card title and make up the bulk of the card's content.
Go somewhereThe building block of a card is the .card
.card-body
Use it whenever you need a padded section within a card.
With supporting text below as a natural lead-in to additional content.
Card titles are used by adding .card-title
& .card-subtitle
for subtitle of card.
Some quick example text to build on the card title and make up the bulk of the card's content.
Card link Another linkAdd an optional header and/or footer within a card.
With supporting text below as a natural lead-in to additional content.
Go somewhereAdd an optional header and/or footer within a card.
With supporting text below as a natural lead-in to additional content.
Go somewhereUsing the grid, wrap cards in columns and rows as needed..col-1 to .col-12
With supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereYou can quickly change the text alignment.text-center .text-right
.
With supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereUsing the utility, you can give direct width class to card like.w-25, w-50, w-75, w-100
With supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereUsing the grid, wrap cards in columns and rows as needed..col-1 to .col-12
With supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereCards include various options for customizing their backgrounds, borders, and color..card-primary info, warning, danger
With supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereCards include various options for customizing their backgrounds, borders, and color..card-primary info, warning, danger
With supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereWith supporting text below as a natural lead-in to additional content.
Go somewhereUse card groups to render cards as a single, attached element with equal width and height columns.
This is a wider card with supporting text below as a natural lead-in to additional content. This content is a little bit longer.
Last updated 3 mins ago
This card has supporting text below as a natural lead-in to additional content.
Last updated 3 mins ago
This is a wider card with supporting text below as a natural lead-in to additional content. This card has even longer content than the first to show that equal height action.
Last updated 3 mins ago
With action elements.
With supporting text below as a natural lead-in to additional content.
Use card groups to render cards as a single, attached element with equal width and height columns.
This is a wider card with supporting text below as a natural lead-in to additional content. This content is a little bit longer.
Last updated 3 mins ago
This card has supporting text below as a natural.
Last updated 3 mins ago
This is a wider card with supporting text below as a natural lead-in to additional content. This card has even longer content than the first to show that equal height action. supporting text below as a natural lead-in to additional content
Last updated 3 mins ago
Cards can be organized into Masonry-like columns with just CSS by wrapping them in card-columns
This is a longer card with supporting text below as a natural lead-in to additional content. This content is a little bit longer.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Integer posuere erat a ante.
This card has supporting text below as a natural lead-in to additional content.
Last updated 3 mins ago
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Integer posuere erat.
This card has supporting text below as a natural lead-in to additional content.
Last updated 3 mins ago
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Integer posuere erat a ante.
This is a wider card with supporting text below as a natural lead-in to additional content. This card has even longer content than the first to show that equal height action.
Last updated 3 mins ago


Thanks for reaching out to me
Email is probably the easiest way to get ahold of me<EMAIL_ADDRESS>You may also reach me on:
Twitter
StackOverflow
GitHub
Quora
Look forward to chatting.
return to home


Tips for first-principles calculations for point defects¶
As mentioned in the Tutorial of pydefect, the neighboring atoms near the defect are initially slightly perturbed to break the symmetry. And, some defects tend to move back to the symmetric atomic configuration during the structure optimization. Some other defects might recover a part of symmetry operations.
Even in these cases, the s
Tips for hybrid functional calculations¶
Hybrid functionals, especially HSE06 functional and those with different exchange mixing parameters and/or screening distances, have been regularly used for point-defect calculations.
Usually, calculations with a hybrid functional are a few tens more expensive than those with a functional based on the local or semilocal density approximation. Therefore, we need to take a little ingenuity to reduce their computational costs.
For this purpose, we regularly prepare the WAVECAR files obtained using GGA. (Although we also relax the atomic positions using GGA beforehand in some cases, it would be inappropriate for point-defect calculations, because site symmetry of a defect calculated by GGA could be different from that by hybrid functionals. Furthermore, electronic structures of defects could also be different.)
One can create the INCAR file for generating WAVECAR files using the GGA with the following command, for instance.
- ::
grep -v LHFCALC INCAR | grep -v ALGO | sed s/”NSW = 50”/”NSW = 1”/ > INCAR-pre


Who plays in the Orange Bowl 2020? Teams, date, schedule for New Year’s 6 bowl game
by Eli BoettgerThe 2020 Orange Bowl matchup has been unveiled after each of the 40 bowls were announced Sunday afternoon.
No. 6 Florida takes on Virginia in an SEC-vs.-ACC battle in the Orange Bowl. Florida most recently played in the Orange Bowl in 2002; Virginia is making its first appearance.
Get the Latest NCAA odds & betting advice at Sports Insider
Sporting News has you covered with the info you need to watch and follow along with the Orange Bowl:
When is the Orange Bowl 2020?
- Date: Dec. 30
- Time: 8 p.m. (ET)
- TV broadcast: ESPN
- Location: Hard Rock Stadium, Miami Gardens, Fla.
The 2020 Orange Bowl is at the Hard Rock Stadium in Miami Gardens, Fla., and will be televised at 8 p.m. (ET) on ESPN.
Who plays in the Orange Bowl 2020?
The 2020 Sugar Bowl will feature Florida and Virginia.
The Gators and Cavaliers have played just once all-time. No. 19 Florida pummeled Virginia 55-10 in 1959, and the two teams haven't faced off since.
Florida finished the regular season 10-2 with a 6-2 record in SEC play. The Gators' signature win was a 24-13 victory over No. 7 Auburn in October.
Virginia finished the regular season 9-4 with a 6-2 record in ACC play. Virginia has yet to record a top-25 win but defeated rival Virginia Tech for the first time since 2003 on Nov. 29.
MORE: College football bowl schedule
Orange Bowl 2020 odds
This section will be updated when opening odds are released.
Florida vs. Virginia three things to watch
Florida's running game
Three Gators have recorded four rushing touchdowns this season (Lamical Perine, Dameon Pierce and Emory Jones). Perine leads the way with 118 attempts and 539 rushing yards. Florida is 6-1 when Perine has at least 10 carries.
Can Virginia put up enough points?
Virginia has played just two top-25 games all season, tallying 20 points in a September loss to Notre Dame and scoring 17 points against Clemson in the ACC championship loss. Florida hasn't allowed more than 28 points all season.
Bryce Perkins
Virginia quarterback Bryce Perkins has recorded five passing touchdowns and five interceptions in losses this season, but has 13 passing touchdowns and six interceptions in wins. He will need to be sharp against Florida's stingy defense in order to pick up the win.
New Year's Six bowl schedule 2020
| Date | Bowl | Matchup | Time (TV channel) |
| Dec. 28 | Cotton Bowl | Penn State vs. Memphis | Noon ET (ESPN) |
| Dec. 28 | Peach Bowl | LSU vs. Oklahoma (CFP semis) | 4 p.m. ET (ABC) |
| Dec. 28 | Fiesta Bowl | Ohio State vs. Clemson (CFP semis) | 8 p.m. ET (ABC) |
| Dec. 30 | Orange Bowl | Florida vs. Virginia | 8 p.m. ET (ESPN) |
| Jan. 1 | Rose Bowl | Wisconsin vs. Oregon | 5 p.m. ET (ESPN) |
| Jan. 1 | Sugar Bowl | Georgia vs. Baylor | 8:45 p.m. ET (ESPN) |


Which is the best definition for
a probe sequence?
The order in which collision resolution
will visit the slots of the hash table
- It is another name for a hash function
- The order in which the hash function will visit the slots of the hash table
- It is another name for collision resolution
Probing is part of collision resolution.
The probe sequence tells you where to look next.


{{ extend './../layout/TPMain.html' }} {{block "style"}} {{/block}} {{block "wrapper"}}
This project is built by NodeJS, Express, MongoDB and Layui.
Make tasks easier, more efficient and faster.
Never put off till tomorrow what may be done today.


|
Panda3D
|
This class is an abstraction for evaluating NURBS curves. More...
Public Member Functions | |
| __init__ () | |
| __init__ (const NurbsCurveEvaluator) | |
| NurbsCurveResult | evaluate (const NodePath rel_to) |
| Returns a NurbsCurveResult object that represents the result of applying the knots to all of the current values of the vertices, transformed into the indicated coordinate space. More... | |
| NurbsCurveResult | evaluate (const NodePath rel_to, const LMatrix4 mat) |
| Returns a NurbsCurveResult object that represents the result of applying the knots to all of the current values of the vertices, transformed into the indicated coordinate space, and then further transformed by the indicated matrix. More... | |
| float | getExtendedVertex (int i, int d) |
| Returns an n-dimensional vertex value. More... | |
| float | getKnot (int i) |
| Returns the value of the nth knot. More... | |
| list | getKnots () |
| int | getNumKnots () |
| Returns the number of knot values in the curve. More... | |
| int | getNumSegments () |
| Returns the number of piecewise continuous segments in the curve. More... | |
| int | getNumVertices () |
| Returns the number of control vertices in the curve. More... | |
| int | getOrder () |
| Returns the order of the curve as set by a previous call to set_order(). More... | |
| const LVecBase4 | getVertex (int i) |
| Returns the nth control vertex of the curve, relative to its indicated coordinate space. More... | |
| LVecBase4 | getVertex (int i, const NodePath rel_to) |
| Returns the nth control vertex of the curve, relative to the given coordinate space. More... | |
| NodePath | getVertexSpace (int i, const NodePath rel_to) |
| Returns the coordinate space of the nth control vertex of the curve, expressed as a NodePath. More... | |
| list | getVertices () |
| normalizeKnots () | |
| Normalizes the knot sequence so that the parametric range of the curve is 0 More... | |
| output (Ostream out) | |
| reset (int num_vertices) | |
| Resets all the vertices and knots to their default values, and sets the curve up with the indicated number of vertices. More... | |
| setExtendedVertex (int i, int d, float value) | |
| Sets an n-dimensional vertex value. More... | |
| setExtendedVertices (int i, int d, PNStdfloatConst[] values, int num_values) | |
| Simultaneously sets several extended values in the slots d through (d + num_values - 1) from the num_values elements of the indicated array. More... | |
| setKnot (int i, float knot) | |
| Sets the value of the nth knot. More... | |
| setOrder (int order) | |
| Sets the order of the curve. More... | |
| setVertex (int i, const LVecBase3 vertex, float weight) | |
| Sets the nth control vertex of the curve. More... | |
| setVertex (int i, const LVecBase4 vertex) | |
| Sets the nth control vertex of the curve, as a vertex in 4-d homogeneous space. More... | |
| setVertexSpace (int i, const NodePath space) | |
| Sets the coordinate space of the nth control vertex. More... | |
| setVertexSpace (int i, str space) | |
| Sets the coordinate space of the nth control vertex. More... | |
| Public Member Functions inherited from ReferenceCount | |
| int | getRefCount () |
| Returns the current reference count. More... | |
| ref () | |
| Explicitly increments the reference count. More... | |
| bool | testRefCountIntegrity () |
| Does some easy checks to make sure that the reference count isn't completely bogus. More... | |
| bool | testRefCountNonzero () |
| Does some easy checks to make sure that the reference count isn't zero, or completely bogus. More... | |
| bool | unref () |
| Explicitly decrements the reference count. More... | |
Additional Inherited Members | |
| Static Public Member Functions inherited from ReferenceCount | |
| static TypeHandle | getClassType () |
| Public Attributes inherited from ReferenceCount | |
| int | ref_count |
| The current reference count. More... | |
This class is an abstraction for evaluating NURBS curves.
It accepts an array of vertices, each of which may be in a different coordinate space (as defined by a NodePath), as well as an optional knot vector.
This is not related to NurbsCurve, CubicCurveseg or any of the ParametricCurve-derived objects in this module. It is a completely parallel implementation of NURBS curves, and will probably eventually replace the whole ParametricCurve class hierarchy.
| __init__ | ( | ) |
| __init__ | ( | const | NurbsCurveEvaluator | ) |
| NurbsCurveResult evaluate | ( | const NodePath | rel_to | ) |
Returns a NurbsCurveResult object that represents the result of applying the knots to all of the current values of the vertices, transformed into the indicated coordinate space.
| NurbsCurveResult evaluate | ( | const NodePath | rel_to, |
| const LMatrix4 | mat | ||
| ) |
Returns a NurbsCurveResult object that represents the result of applying the knots to all of the current values of the vertices, transformed into the indicated coordinate space, and then further transformed by the indicated matrix.
| float getExtendedVertex | ( | int | i, |
| int | d | ||
| ) |
Returns an n-dimensional vertex value.
See set_extended_vertex(). This returns the value set for the indicated dimension, or 0.0 if nothing has been set.
| float getKnot | ( | int | i | ) |
Returns the value of the nth knot.
| list getKnots | ( | ) |
| int getNumKnots | ( | ) |
Returns the number of knot values in the curve.
This is based on the number of vertices and the order.
| int getNumSegments | ( | ) |
Returns the number of piecewise continuous segments in the curve.
This is based on the knot vector.
| int getNumVertices | ( | ) |
Returns the number of control vertices in the curve.
This is the number passed to the last call to reset().
| int getOrder | ( | ) |
Returns the order of the curve as set by a previous call to set_order().
| const LVecBase4 getVertex | ( | int | i | ) |
Returns the nth control vertex of the curve, relative to its indicated coordinate space.
Returns the nth control vertex of the curve, relative to the given coordinate space.
Returns the coordinate space of the nth control vertex of the curve, expressed as a NodePath.
| list getVertices | ( | ) |
| normalizeKnots | ( | ) |
Normalizes the knot sequence so that the parametric range of the curve is 0
. 1.
| output | ( | Ostream | out | ) |
| reset | ( | int | num_vertices | ) |
Resets all the vertices and knots to their default values, and sets the curve up with the indicated number of vertices.
You must then call set_vertex() repeatedly to fill in all of the vertex values appropriately.
| setExtendedVertex | ( | int | i, |
| int | d, | ||
| float | value | ||
| ) |
Sets an n-dimensional vertex value.
This allows definition of a NURBS surface or curve in a sparse n-dimensional space, typically used for associating additional properties (like color or joint membership) with each vertex of a surface.
The value d is an arbitrary integer value and specifies the dimension of question for this particular vertex. Any number of dimensions may be specified, and they need not be consecutive. If a value for a given dimension is not specified, is it implicitly 0.0.
The value is implicitly scaled by the homogenous weight value–that is, the fourth component of the value passed to set_vertex(). This means the ordinary vertex must be set first, before the extended vertices can be set.
| setExtendedVertices | ( | int | i, |
| int | d, | ||
| PNStdfloatConst[] | values, | ||
| int | num_values | ||
| ) |
Simultaneously sets several extended values in the slots d through (d + num_values - 1) from the num_values elements of the indicated array.
This is equivalent to calling set_extended_vertex() num_values times. See set_extended_vertex().
| setKnot | ( | int | i, |
| float | knot | ||
| ) |
Sets the value of the nth knot.
Each knot value should be greater than or equal to the preceding value. If no knot values are set, a default knot vector is supplied.
| setOrder | ( | int | order | ) |
Sets the order of the curve.
This resets the knot vector to the default knot vector for the number of vertices.
The order must be 1, 2, 3, or 4, and the value is one more than the degree of the curve.
| setVertex | ( | int | i, |
| const LVecBase3 | vertex, | ||
| float | weight | ||
| ) |
Sets the nth control vertex of the curve.
This flavor sets the vertex as a 3-d coordinate and a weight; the 3-d coordinate values are implicitly scaled up by the weight factor.
| setVertex | ( | int | i, |
| const LVecBase4 | vertex | ||
| ) |
Sets the nth control vertex of the curve, as a vertex in 4-d homogeneous space.
In this form, the first three components of the vertex should already have been scaled by the fourth component, which is the homogeneous weight.
| setVertexSpace | ( | int | i, |
| const NodePath | space | ||
| ) |
Sets the coordinate space of the nth control vertex.
If this is not specified, or is set to an empty NodePath, the nth control vertex is deemed to be in the coordinate space passed to evaluate().
This specifies the space as a fixed NodePath, which is always the same NodePath. Also see setting the space as a path string, which can specify a different NodePath for different instances of the curve.
| setVertexSpace | ( | int | i, |
| str | space | ||
| ) |
Sets the coordinate space of the nth control vertex.
If this is not specified, or is set to an empty string, the nth control vertex is deemed to be in the coordinate space passed to evaluate().
This specifies the space as a string, which describes the path to find the node relative to the rel_to NodePath when the curve is evaluated.


{{appType}} {{appName}}
Home
Reports
Structure Ad Hoc
Structure Ad Hoc (Mobile)
Report Browser
Hist Scan Trend
Custom Reporting
Formula Editor
Report Builder
Scheduling
Report Builder
My Scheduled Reports
Vuew Other Schedules
My Preferences
My Profile
My Cellgroups
LTE Watcher Notifications
4
eNodeB 10001 Alarm triggered
eNodeB 20001 alarm
eNodeB 30001 alarm
eNodeB 40001 alarm


Hello {{committee_head}}!
The user {{user_name}} wants to join the committee {{committee_name}} in TigerTracker.
Please click the link below to take action.
Brought to you by the Services Team.
{{time_stamp}} Peek a boo! Have a nice day.


We use a large block of connected links for our pagination, making links hard to miss and easily scalable—all while providing large hit areas. Pagination is built with list HTML elements so screen readers can announce the number of available links. Use a wrapping
In addition, as pages likely have more than one such navigation section, it’s advisable to provide a descriptive aria-label
for the
aria-label="Search results pages"
.
Pagination links are customizable for different circumstances. Use .disabled
for links that appear un-clickable and .active
to indicate the current page.
While the .disabled
class uses pointer-events: none
to try to disable the link functionality of s, that CSS property is not yet standardized and doesn’t account for keyboard navigation. As such, you should always add
tabindex="-1"
on disabled links and use custom JavaScript to fully disable their functionality.
You can optionally swap out active or disabled anchors for , or omit the anchor in the case of the prev/next arrows, to remove click functionality and prevent keyboard focus while retaining intended styles.
Fancy larger or smaller pagination? Add .pagination-lg
or .pagination-sm
for additional sizes.


Don't be afraid to reset: Some puzzles are literally impossible
Avoid the Math Snags when Possible: They will waste time and time is money
Don't be afraid to reset: Some puzzles are literally impossible
Avoid the Math Snags when Possible: They will waste time and time is money
Despite your best efforts to avoid math of all kinds. Your favorite planned feature uses intense multi variable calculus. If you want to continue making this game, you must solve this important equation. In all games, you will learn that not only will you sometimes run into math but that many of the best of things much better based off math. Learn to love it, because if you dont... Your in for a long, sad ride... Possibly involving 1000's of Permeutations......
Not Really. This is going to test your reaction time. The longer you wait after we finished "checking", the more money you lose ;)
No one paid attention to your screw up because nobody cared anyway. People thought you were worthless before (If they even knew you existed) and you've done nothing to prove them wrong. However, part of the beauty of being invisible is that if you mess up, nobody notices. So you can try again without shame
Unfortunately, your game is terrible. Nobody plays it because after playing it, they avoided talking about it. And it wasn't because they hated you. It was because just thinking about your game made them gag a little bit. So essentially you can see it as you wasted your time and money.
However...
The truth is...
This is pracice. Every Game you make is practice. The successful ones and the failures. Everyones first is special. No question about that. But, just like in every field, the more you know and the more you get done, the better you will become.
And after all is said in done, don't worry about your successes and failures. Just realize you were practicing patience, mathematics, logic and understanding fun. You will get better. And if you don't, Read some damn articles about it and force yourself to. ;)


SPGSHOP: Short Pressure Is Kicking In For Heating Oil Prices
by Oleum ResearchSummary
- With distillate storage withdrawing again, stockpile shortage heightens, but price seasonality remains unfavorable in November.
- Net speculative positioning is neutral this week, but the interest on the heating oil blend decelerates steeply.
- While distillate fundamentals stiffen moderately, crack spread dip robustly, indicating that a pullback is nearing.
Investment thesis
Since our last publication on the S&P GSCI Heating Oil Index Excess Return (SPGSHOP), the price of the ETF has slightly moved, declining 0.05% to $210.08 against our bullish recommendation.
In spite of that, our view has now turned bearish for the following weeks, as the complex continues to be oversupplied, net spec interest dipped significantly in the past week and price seasonality remains unfriendly for the month of November.
With distillate storage withdrawing again, stockpile shortage heightens, but price seasonality remains unfavorable in November
According to the EIA, U.S. reserves of distillates, the blend from which derives heating oil, declined slightly over the week ending November 1, down 0.52% (w/w) to 119.1m barrels. While this constitutes the seventh withdrawal in a row, stockpiles decreased moderately over the month, down 6.43%, whereas SPGSHOP advanced 3.03% (m/m) to $210.16.
With this decline, the storage picture of the distillate complex further deteriorates, reaching a deficit of 9.7% or 12 743k barrels compared to the five-year average and standing 3% or 3 725k barrels below last year levels.
Source: EIA, Oleum Research
In front of that, in the past 10-years, stock seasonality weakened significantly over the month of November, with average withdrawals reaching the highest pace of the year, down 6.7%. While declining storage is likely to have a positive impact on heating oil futures and its proxy SPGSHOP, price seasonality is slightly unfavorable for the complex, declining in average 0.4% on the corresponding period, countering the positive effect of the former.
Source: EIA, Oleum Research
Furthermore and in spite of refining utilization rates declining moderately over the past week, down 1.94% (w/w) to 86%, capacity will fully return by the end of the month, providing headwinds for the heating oil futures and SPGSHOP.
Source: EIA, Oleum Research
Speculative positioning
During the week ending November 11, speculators lifted slightly their bets on Nymex heating oil futures, sending net spec positioning back into short territory. The cumulative length reached a net short length of 257 contracts, following the brief net long positioning attained last week.
Source: CFTC
These moves have been mostly attributable to robust long liquidations, down 8.7% (w/w) to 52 857 contracts and have been partially offset by strong short coverings, down 8.01% (w/w) to 53 114 contracts.
While the battle between longs and shorts is now hanging by a thread, the concomitant decreases witnessed this week points toward a significant decline in speculative interest.
That being said, the sentiment remains neutral for the time being, but declining interest is bearish for the blend and its proxy, SPGSHOP.
Since the beginning of 2019, Nymex heating oil future contracts advanced moderately, up 7.45% to $80.45 per barrel, whereas SPGSHOP’s YTD performance lost 2.16% to $208.12.
While distillate fundamentals stiffen moderately, crack spread dip robustly, indicating that a pullback is nearing
Over the past four weeks, the balance between distillate supply and demand has tightened moderately, following a somewhat steadying aggregate supply, up 0.8% to 4.8m barrels per day and a rapid ramp up of demand, up 6.4% to 4.2m barrels per day.
Besides, in the past week, the moderate deterioration of distillate exports, down 3.75% (w/w) to 974k barrels per day and the doubling of distillate imports, further weighed on the complex’ fundamental picture. That being said, the complex is slightly oversupplied for the moment, somewhat weighing on the appreciation of heating oil futures and SPGSHOP.
Source: EIA, Oleum Research
Nevertheless, distillate crack spreads are still healthy, but the sharp dip seen in the past days, down 16.65% to $17.94 per barrel, points toward a weakening of heating oil pricing.
Source: Quandl, Oleum Research
Concomitantly, the Brent future curve is unchanged compared to last week, aside for the slim tick up seen in M3. On the other hand, the slope of heating oil futures edged higher in the next eight months, providing higher margins for refiners and its backwardation pattern increased, indicating an appreciation of the roll-yield, which is slightly positive for SPGSHOP.
Conclusion
While distillate storage enters a deeper shortage, price seasonality is unfavorable for the month of November.
Besides and although net spec length is marginally in the bearish territory, crack spreads dipped significantly and supply-demand dynamics remain oversupplied.
That being said, our view on the complex has changed and we are now expecting a deterioration of the SPGSHOP price in the following weeks.
We look forward to reading your comments.
Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.


Stage 0: Introduction to programming
World wide webTags & elements
HTML documents are made of HTML elements.  They simply follow what we humans tell them to do.HTML Playground
I am going to learn to love code.If you forget the closing tag, everything will be italic or bold or anything else what the tag tells.
HTML Attributes anchor - links my favorite learning websiteSpan -inline / Div - block
Block create invisbile boxes.