diff --git a/.dockerignore b/.dockerignore index 3e32c0d..95f9414 100644 --- a/.dockerignore +++ b/.dockerignore @@ -1,7 +1,5 @@ .git .github/ -website/ -noah/ **/dist/ **/build/ **/*.yml diff --git a/.gitignore b/.gitignore index e69de29..496ee2c 100644 --- a/.gitignore +++ b/.gitignore @@ -0,0 +1 @@ +.DS_Store \ No newline at end of file diff --git a/README.md b/README.md index ba8fa26..1a73371 100644 --- a/README.md +++ b/README.md @@ -7,7 +7,6 @@ Welcome to the Ark monorepo. In this repository you can find: - `server` - a proof of concept of an Ark Service Provider. -- `website` - the website where to find documentation about Ark protocol and products. - `client` - the initial Ark wallet, served as CLI. diff --git a/website/.gitignore b/website/.gitignore deleted file mode 100644 index b2d6de3..0000000 --- a/website/.gitignore +++ /dev/null @@ -1,20 +0,0 @@ -# Dependencies -/node_modules - -# Production -/build - -# Generated files -.docusaurus -.cache-loader - -# Misc -.DS_Store -.env.local -.env.development.local -.env.test.local -.env.production.local - -npm-debug.log* -yarn-debug.log* -yarn-error.log* diff --git a/website/README.md b/website/README.md deleted file mode 100644 index aaba2fa..0000000 --- a/website/README.md +++ /dev/null @@ -1,41 +0,0 @@ -# Website - -This website is built using [Docusaurus 2](https://docusaurus.io/), a modern static website generator. - -### Installation - -``` -$ yarn -``` - -### Local Development - -``` -$ yarn start -``` - -This command starts a local development server and opens up a browser window. Most changes are reflected live without having to restart the server. - -### Build - -``` -$ yarn build -``` - -This command generates static content into the `build` directory and can be served using any static contents hosting service. - -### Deployment - -Using SSH: - -``` -$ USE_SSH=true yarn deploy -``` - -Not using SSH: - -``` -$ GIT_USER= yarn deploy -``` - -If you are using GitHub pages for hosting, this command is a convenient way to build the website and push to the `gh-pages` branch. diff --git a/website/babel.config.js b/website/babel.config.js deleted file mode 100644 index e00595d..0000000 --- a/website/babel.config.js +++ /dev/null @@ -1,3 +0,0 @@ -module.exports = { - presets: [require.resolve('@docusaurus/core/lib/babel/preset')], -}; diff --git a/website/blog/2023-12-14-liquidity-requirements/index.md b/website/blog/2023-12-14-liquidity-requirements/index.md deleted file mode 100644 index 390b909..0000000 --- a/website/blog/2023-12-14-liquidity-requirements/index.md +++ /dev/null @@ -1,486 +0,0 @@ ---- -authors: bordalix -description: Dive into the depths of Ark with our comprehensive guide on Liquidity Requirements. Explore how Ark liquidity intersect with Money Velocity -image: /img/ark-agora.png -slug: liquidity-requirements -tags: [liquidity, ark, bitcoin] -title: Understanding Ark Liquidity Requirements -unlisted: true ---- - -![Bitcoin agora](/img/ark-agora.png) - -This post discusses the liquidity requirements and calculates the funding needs of Ark Service Provider (ASP), as all transactions within Ark must be funded by the ASP. - - - -## What is Ark? - -Ark is a promising second-layer solution for Bitcoin that improves the scalability and privacy of the network. It offers the following benefits: - -- **No incoming liquidity required**: Receivers can accept payments without having to worry about having enough funds in their wallets. -- **Confidential payments**: Ark protects the confidentiality of recipients, which is not always possible with other second-layer solutions. -- **Scalable**: Ark is a solution for enabling the scalability of Bitcoin and applications and services which utilize the Bitcoin infrastructure. -- **Secure**: Ark is a secure solution that is built on top of the Bitcoin blockchain. - -:::tip -It's recommended to read the [nomenclature](/docs/learn/nomenclature) first. -::: - -## Ark liquidity requirements - -### Introduction - -When Alice wishes to board an Ark, she finances an output that is eligible to be recognized as a VTXO in a future round. This does **not** necessitate any liquidity from the ASP: - -```mermaid -flowchart LR - subgraph Onchain - direction LR - Alice - vtxo(10 BTC VTXO*) - Alice --> vtxo - end -``` - -:::info -Since this an onchain transaction, and VTXOs should be virtual, we marked it as VTXO\*. -::: - -When Alice makes her initial payment, for example, 1 BTC to Bob, the VTXO\* will be utilized to finance the [Pool transaction](/learn/nomenclature#pool-transaction-aka-ark-transaction), so again, the ASP will **not** need to supply any additional liquidity: - -```mermaid -flowchart LR - subgraph Onchain - direction LR - vtxo(10 BTC VTXO*) - pool(Pool transaction) - vtxo --> pool - end - subgraph Virtual - subgraph VTXOs - direction LR - change(9 BTC Alice) - bob(1 BTC Bob) - end - end - pool --> VTXOs -``` - -But if Alice tries to make a second payment, for example, 1 BTC to Charlie, she will now be utilizing a genuine virtual VTXO. In this case, the ASP will need to finance the following [Pool transaction](/learn/nomenclature#pool-transaction-aka-ark-transaction): - -```mermaid -flowchart LR - subgraph Onchain - direction LR - vtxo(10 BTC VTXO*) - pool(Pool transaction) - vtxo --> pool - ASP(9 BTC ASP) - pool2(Pool transaction 2) - ASP --> pool2 - end - subgraph Virtual - subgraph VTXOs - direction LR - change(9 BTC Alice) - bob(1 BTC Bob) - end - subgraph new_VTXOs - direction LR - charlie(1 BTC Charlie) - change2(8 BTC Alice) - end - forfeit(Forfeit to ASP) - change --> forfeit - end - pool --> VTXOs - pool2 --> new_VTXOs -``` - -Finally, let's assume Alice also pays 1 BTC to Dave: - -```mermaid -flowchart LR - subgraph Onchain - direction LR - vtxo(10 BTC VTXO*) - pool(Pool transaction) - vtxo --> pool - ASP(9 BTC ASP) - pool2(Pool transaction 2) - ASP --> pool2 - ASP2(8 BTC ASP) - pool3(Pool transaction 3) - ASP2 --> pool3 - end - subgraph Virtual - subgraph VTXOs - direction LR - bob(1 BTC Bob) - charlie(1 BTC Charlie) - change2(8 BTC Alice) - end - subgraph new_VTXOs - direction LR - dave(1 BTC Dave) - change3(7 BTC Alice) - end - forfeit(Forfeit to ASP) - change2 --> forfeit - end - pool --> VTXOs - pool2 --> VTXOs - pool3 --> new_VTXOs -``` - -### Summary - -- 10 BTC initial onboard from Alice -- 4 payments: - - Alice => Bob 1 BTC - - Alice => Charlie 1 BTC - - Alice => Dave 1 BTC -- total payments = 3 BTC -- ASP liquidity needed = 17 BTC - -As we can see, the liquidity needs for the ASP depends on the following factors: - -- Capital onboarded -- Value of the payments - -:::tip -While onboarding does not require any liquidity from the ASP, next payments will. -::: - -### The liquidity problem - -If the ASP exhausts its liquidity, it will have to cease accepting new payments and will be compelled to wait for the timelocks (4 weeks) on the on-chain transactions to expire in order to regain liquidity. - -To avoid the ASP from running out of funds, it must be able to anticipate how much liquidity will be required throughout a 4 week period. - -As we observed, the liquidity necessary during a period will rely on the capital onboarded and the number and value of payments made with that capital - -Given this, we can assume the liquidity needed will be the consequence of a function of capital onboarded and a percentage of this capital utilized during the 4 weeks period. - -Therefore, how much capital can an ASP accept from users without risking not having enough capital to finance payments inside Ark? In other words, what proportion of the capital inside an Ark is transferred in a 4 week period? - -This is similar to the definition of Money Velocity, as defined by the St. Louis Fed: - -> The velocity of money is the frequency at which one unit of currency is used to purchase domestically-produced goods and services within a given time period. - -### Money Velocity (MV) - -Here are some Money Velocity numbers: - -- USD (Q3 2023): 1.327 -- Lightning (August 2023): 0.59 per month - -If we use a Money Velocity of 1.00 (for simplicity), this means that each BTC inside the Ark will be spent once (1.00) during that given period. Since the ASP must fund all transactions and onboarding, this means that for each 1 BTC added to the Ark, the ASP will need 1 BTC to fund the onboarding and 1 BTC to fund the transfers inside the Ark. With an initial balance of 100 BTC, this results in a limit of 50 BTC allowed to onboard (100 = 50 for onboarding + 50 for trades). - -If MV = 0.59, this means that those initial 100 BTC would allow for 62.89 BTC of onboarding, where (100 = 62.89 for onboarding + (69.89 \* 0.59 = 37.11) for trades). - -In reality, the Money Velocity of Ark is likely to be somewhere between 1.00 and 0.59. This means that the ASP will need to have a certain amount of liquidity on hand to fund both onboarded BTC and transfers inside the Ark. The amount of liquidity required will depend on the specific Money Velocity of Ark, which is not yet known for sure. - -Comparison table: - -| Money Velocity | Balance | +Onboard (BTC) | Inside Ark (BTC) | Transfers (BTC) | -| -------------: | ------: | -------------: | ---------------: | --------------: | -| 0.59 | 100.00 | 62.89 | 0.00 | 37.11 | -| 1.00 | 100.00 | 50.00 | 0.00 | 50.00 | -| 1.327 | 100.00 | 42.97 | 0.00 | 57.03 | - -After one month, all the funds used by the ASP, plus the funds sent by the users, become available again. This means that the ASP will have more available liquidity, so it can increase the allowed value for onboards. On the other hand, there is now more capital inside the Ark, so the ASP needs to reserve more capital to fund the transfers: - -| Money Velocity | Balance | +Onboard (BTC) | Inside Ark (BTC) | Transfers (BTC) | -| -------------: | ------: | -------------: | ---------------: | --------------: | -| 0.59 | 162.89 | 79.11 | 62.89 | 83.78 | -| 1.00 | 150 | 50.00 | 50.00 | 100.00 | -| 1.327 | 142.97 | 36.93 | 42.97 | 57.03 | - -Now, what would happen in a one-year period? - -:::info -You can run your own simulations with the Ark liquidity simulator. -::: - -### Simulating for 1 year - -Columns definition: - -- Inside Ark = Accumulated of allowed onboards -- ASP Balance = Initial balance + Inside Ark -- Reserved for trades = Inside Ark \* MV -- Remaining = Balance - Reserved for trades -- Allowed onboards = Remaining / (1 + MV) - -Money Velocity: 0.59 - -| Month | Inside Ark | ASP Balance | Reserved for trades | Remaining | Allowed onboards | -| ----: | :--------: | :---------: | :-----------------: | :-------: | :--------------: | -| 0 | 0.00 | 100.00 | 0.00 | 100.00 | 0.00 | -| 1 | 0.00 | 100.00 | 0.00 | 100.00 | 62.89 | -| 2 | 62.89 | 162.89 | 37.11 | 125.79 | 79.11 | -| 3 | 142.00 | 242.00 | 83.78 | 158.22 | 99.51 | -| 4 | 241.51 | 341.51 | 142.49 | 199.02 | 125.17 | -| 5 | 366.68 | 466.68 | 216.34 | 250.34 | 157.45 | -| 6 | 524.13 | 624.13 | 309.24 | 314.89 | 198.05 | -| 7 | 722.18 | 822.18 | 426.09 | 396.09 | 249.12 | -| 8 | 971.29 | 1,071.29 | 573.06 | 498.23 | 313.35 | -| 9 | 1,284.65 | 1,384.65 | 757.94 | 626.70 | 394.15 | -| 10 | 1,678.80 | 1,778.80 | 990.49 | 788.31 | 495.79 | -| 11 | 2,174.59 | 2,274.59 | 1,283.01 | 991.58 | 623.64 | -| 12 | 2,798.23 | 2,898.23 | 1,650.95 | 1,247.27 | 784.45 | - -Money Velocity: 1 - -| Month | Inside Ark | ASP Balance | Reserved for trades | Remaining | Allowed onboards | -| ----: | :--------: | :---------: | :-----------------: | :-------: | :--------------: | -| 0 | 0.00 | 100.00 | 0.00 | 100.00 | 0.00 | -| 1 | 0.00 | 100.00 | 0.00 | 100.00 | 50.00 | -| 2 | 50.00 | 150.00 | 50.00 | 100.00 | 50.00 | -| 3 | 100.00 | 200.00 | 100.00 | 100.00 | 50.00 | -| 4 | 150.00 | 250.00 | 150.00 | 100.00 | 50.00 | -| 5 | 200.00 | 300.00 | 200.00 | 100.00 | 50.00 | -| 6 | 250.00 | 350.00 | 250.00 | 100.00 | 50.00 | -| 7 | 300.00 | 400.00 | 300.00 | 100.00 | 50.00 | -| 8 | 350.00 | 450.00 | 350.00 | 100.00 | 50.00 | -| 9 | 400.00 | 500.00 | 400.00 | 100.00 | 50.00 | -| 10 | 450.00 | 550.00 | 450.00 | 100.00 | 50.00 | -| 11 | 500.00 | 600.00 | 500.00 | 100.00 | 50.00 | -| 12 | 550.00 | 650.00 | 550.00 | 100.00 | 50.00 | - -Money Velocity 1.327 - -| Month | Inside Ark | ASP Balance | Reserved for trades | Remaining | Allowed onboards | -| ----: | :--------: | :---------: | :-----------------: | :-------: | :--------------: | -| 0 | 0.00 | 100.00 | 0.00 | 100.00 | 0.00 | -| 1 | 0.00 | 100.00 | 0.00 | 100.00 | 42.97 | -| 2 | 42.97 | 142.97 | 57.03 | 85.95 | 36.93 | -| 3 | 79.91 | 179.91 | 106.04 | 73.87 | 31.74 | -| 4 | 111.65 | 211.65 | 148.16 | 63.49 | 27.28 | -| 5 | 138.94 | 238.94 | 184.37 | 54.57 | 23.45 | -| 6 | 162.39 | 262.39 | 215.49 | 46.90 | 20.15 | -| 7 | 182.54 | 282.54 | 242.23 | 40.31 | 17.32 | -| 8 | 199.86 | 299.86 | 265.22 | 34.64 | 14.89 | -| 9 | 214.75 | 314.75 | 284.98 | 29.78 | 12.80 | -| 10 | 227.55 | 327.55 | 301.96 | 25.59 | 11.00 | -| 11 | 238.55 | 338.55 | 316.55 | 22.00 | 9.45 | -| 12 | 248.00 | 348.00 | 329.09 | 18.90 | 8.12 | - -:::info Results - -Simulating the three different MV values over a one-year period, we can conclude the following: - -- If MV < 1, the ASP can onboard more BTC each month than in the previous month. -- If MV = 1, the allowed value for onboarding BTC is always the same (half of the initial balance). -- If MV > 1, the value of allowed BTC to onboard converges to 0 over time, with the maximum onboard value equal to (initial balance) / (MV - 1). - -::: - -:::note - -The Money Velocity (MV) for USD is quarterly. Assuming that M2 is constant and GDP is evenly distributed over the three months, the MV for one month should be ⅓ of the MV for the quarter, or 0.33. - -::: - -### Algorithm - -#### Allowed onboard value - -The value of allowed onboard BTC for this round will be: - -:::info Allowed onboard formula - -(Available balance - User’s funds in Ark \* MV) / (1 + MV) - -::: - -Where: - -- Available balance = Initial ASP balance + User’s funds -- User’s funds = All BTC onboarded by users until now -- MV = Money Velocity - -#### Money Velocity - -To calculate the value of Money Velocity: - -:::info Money Velocity formula - -Average for the last N rounds of (amount transferred / user’s funds) - -::: - -#### Rational - -The ASP keeps records of onboarded and transferred amounts from previous rounds, and uses them to calculate the Money Velocity (MV) for the current round. It then uses the MV to calculate the maximum amount that can be onboarded in the current round. - -If you've read this far, thank you! But now it's time for the bad news. - -## The UTXO model - -
-How the UTXO Model Works - -In the UTXO model, each unit of cryptocurrency is treated as a unique and indivisible entity. When a user spends cryptocurrency, they are not actually spending their entire balance. Instead, they are spending specific UTXOs that they own. - -Each UTXO has two important pieces of information: - -- The amount of cryptocurrency: This is the value of the UTXO. -- A locking script: This is a script that specifies how the UTXO can be spent. The locking script typically requires a digital signature from the owner of the UTXO. - -When a user wants to spend cryptocurrency, they create a new transaction. This transaction has two parts: - -- Inputs: These are the UTXOs that the user is spending. -- Outputs: These are the new UTXOs that will be created as a result of the transaction. - -The locking scripts of the input UTXOs must be satisfied in order for the transaction to be valid. This ensures that only the rightful owner of the cryptocurrency can spend it. - -
- -### The change problem - -But since Ark uses a UTXO model, this MV theory doesn't work, as the ASP will also need to fund the change on each transaction. For example, if Alice has a 1 BTC VTXO and wants to pay Bob 0.2 BTC, the ASP will need to fund two new VTXOs: - -- 0.2 BTC to Bob -- 0.8 BTC to Alice (change) - -#### Some simulations - -Imagine that Alice boarded the Ark with 1 BTC. She has a 1 BTC VTXO and spends ⅓ of her money in the first month (MV = 0.33) using three payments of 0.11 BTC each. - -Let's also assume that these payments are inside Ark (to Bob), which means that the ASP will also need to fund Bob's VTXO. - -| Payment | Value | Alice VTXO | Bob VTXOs
(0.11 each) | Liquidity needed | Liquidity accum | -| :-----: | :---: | :--------: | :------------------------: | :--------------: | :-------------: | -| 0 | 0 | 1.00 | 0 | 0 | 0 | -| 1 | 0.11 | 0.89 | 1 | 1.00 | 1.00 | -| 2 | 0.11 | 0.78 | 2 | 0.89 | 1.89 | -| 3 | 0.11 | 0.67 | 3 | 0.78 | **2.67** | - -At the end of the transaction, Alice has one VTXO of 0.67 BTC and Bob has three VTXOs of 0.11 BTC each. - -:::danger Huge funding needs (factor of **8**) - -The ASP needed **2.67** of liquidity to support **0.33** traded inside Ark. - -::: - -Things get much worse if the user makes 10 payments instead of 3 (spending 0.033 BTC on each): - -| Payment | Value | Alice VTXO | Bob VTXOs
(0.033 each) | Liquidity needed | Liquidity accum | -| :-----: | :---: | :--------: | :-------------------------: | :--------------: | :-------------: | -| 0 | 0 | 1.00 | 0 | 0 | 0 | -| 1 | 0.033 | 0.97 | 1 | 1.00 | 1.00 | -| 2 | 0.033 | 0.93 | 2 | 0.97 | 1.97 | -| 3 | 0.033 | 0.90 | 3 | 0.93 | 2.90 | -| 4 | 0.033 | 0.87 | 4 | 0.90 | 3.80 | -| 5 | 0.033 | 0.84 | 5 | 0.87 | 4.67 | -| 6 | 0.033 | 0.80 | 6 | 0.84 | 5.51 | -| 7 | 0.033 | 0.77 | 7 | 0.80 | 6.31 | -| 8 | 0.033 | 0.74 | 8 | 0.77 | 7.08 | -| 9 | 0.033 | 0.70 | 9 | 0.74 | 7.81 | -| 10 | 0.033 | 0.67 | 10 | 0.70 | **8.52** | - -:::danger Huge funding needs (factor of **25**) - -The ASP needed **8.52** of liquidity to support **0.33** traded inside Ark. - -::: - -### Possible mitigations - -One can try to reduce these liquidity requirements by pushing several levers: - -- Reduce MV by reducing the timelock (e.g., 2 weeks instead of 1 month). -- Reduce transaction change by creating a set of UTXOs with a range of values on the first place, and then doing coin selection with the purpose of reducing change to the minimum possible. - -#### Reduce transaction change - -- Assuming MV = 0.33, and 10 payments of equal value during a month period -- Dividing Alice’s initial UTXO into 10, 100, and 1000 VTXOs - -Using a 1:10 ratio for VTXOs: - -| VTXO Value | Payment
number | Payment
value | VTXOs used | Alice balance | Alice VTXOs | Liquidity needed | Liquidity accum | -| :--------: | :-----------------: | :----------------: | :--------: | :-----------: | :---------: | :--------------: | :-------------: | -| 0.1 | 0 | 0.000 | 0 | 1.000 | 10 | 0.0 | 0.00 | -| 0.1 | 1 | 0.033 | 1 | 0.967 | 10 | 0.1 | 0.10 | -| 0.1 | 2 | 0.033 | 1 | 0.934 | 10 | 0.1 | 0.20 | -| 0.1 | 3 | 0.033 | 1 | 0.901 | 10 | 0.1 | 0.30 | -| 0.1 | 4 | 0.033 | 1 | 0.868 | 10 | 0.1 | 0.40 | -| 0.1 | 5 | 0.033 | 1 | 0.835 | 10 | 0.1 | 0.50 | -| 0.1 | 6 | 0.033 | 1 | 0.802 | 10 | 0.1 | 0.60 | -| 0.1 | 7 | 0.033 | 1 | 0.769 | 10 | 0.1 | 0.70 | -| 0.1 | 8 | 0.033 | 1 | 0.736 | 10 | 0.1 | 0.80 | -| 0.1 | 9 | 0.033 | 1 | 0.703 | 10 | 0.1 | 0.90 | -| 0.1 | 10 | 0.033 | 1 | 0.670 | 10 | 0.1 | 1.00 | - -Using a 1:100 ratio for VTXOs: - -| VTXO Value | Payment
number | Payment
value | VTXOs used | Alice balance | Alice VTXOs | Liquidity needed | Liquidity accum | -| :--------: | :-----------------: | :----------------: | :--------: | :-----------: | :---------: | :--------------: | :-------------: | -| 0.01 | 0 | 0.000 | 0 | 1.000 | 100 | 0.0 | 0.00 | -| 0.01 | 1 | 0.033 | 4 | 0.967 | 97 | 0.04 | 0.04 | -| 0.01 | 2 | 0.033 | 4 | 0.934 | 94 | 0.04 | 0.08 | -| 0.01 | 3 | 0.033 | 4 | 0.901 | 91 | 0.04 | 0.12 | -| 0.01 | 4 | 0.033 | 4 | 0.868 | 88 | 0.04 | 0.16 | -| 0.01 | 5 | 0.033 | 4 | 0.835 | 85 | 0.04 | 0.20 | -| 0.01 | 6 | 0.033 | 4 | 0.802 | 82 | 0.04 | 0.24 | -| 0.01 | 7 | 0.033 | 4 | 0.769 | 79 | 0.04 | 0.28 | -| 0.01 | 8 | 0.033 | 4 | 0.736 | 76 | 0.04 | 0.32 | -| 0.01 | 9 | 0.033 | 4 | 0.703 | 73 | 0.04 | 0.36 | -| 0.01 | 10 | 0.033 | 4 | 0.670 | 70 | 0.04 | 0.40 | - -Using a 1:1000 ratio for VTXOs: - -| VTXO Value | Payment
number | Payment
value | VTXOs used | Alice balance | Alice VTXOs | Liquidity needed | Liquidity accum | -| :--------: | :-----------------: | :----------------: | :--------: | :-----------: | :---------: | :--------------: | :-------------: | -| 0.001 | 0 | 0.000 | 0 | 1.000 | 1000 | 0.0 | 0.00 | -| 0.001 | 1 | 0.033 | 33 | 0.967 | 968 | 0.033 | 0.03 | -| 0.001 | 2 | 0.033 | 33 | 0.934 | 936 | 0.033 | 0.07 | -| 0.001 | 3 | 0.033 | 33 | 0.901 | 904 | 0.033 | 0.10 | -| 0.001 | 4 | 0.033 | 33 | 0.868 | 872 | 0.033 | 0.13 | -| 0.001 | 5 | 0.033 | 33 | 0.835 | 840 | 0.033 | 0.17 | -| 0.001 | 6 | 0.033 | 33 | 0.802 | 808 | 0.033 | 0.20 | -| 0.001 | 7 | 0.033 | 33 | 0.769 | 776 | 0.033 | 0.23 | -| 0.001 | 8 | 0.033 | 33 | 0.736 | 744 | 0.033 | 0.26 | -| 0.001 | 9 | 0.033 | 33 | 0.703 | 712 | 0.033 | 0.30 | -| 0.001 | 10 | 0.033 | 33 | 0.670 | 680 | 0.033 | 0.33 | - -Comparison table: - -| VTXO ratio | MV | # Payments | ASP liquidity needed | -| ---------: | ---: | ---------: | -------------------: | -| 10 | 0.33 | 10 | 1.00 | -| 100 | 0.33 | 10 | 0.40 | -| 1000 | 0.33 | 10 | 0.33 | - -:::info conclusion - -Dividing the initial UTXO into more VTXOs decreases the need for funding. - -::: - -## Conclusion - -The liquidity requirements for an ASP will depend on three major factors: - -- **Money Velocity**: This is not under the control of the ASP, and if it is higher than 1, the Ark capacity will converge to a fixed value. -- **The locktime period on VTXOs**: Reducing the locktime period will return the locked liquidity sooner. However, this also means that users will need to "recycle" their VTXOs sooner, which can be seen as a worse user experience. -- **The VTXO ratio**: In other words, this is the maximum allowed value for a given VTXO. At one extreme, the ASP could force all VTXOs to be of 1 sat, which would eliminate any "wasted" liquidity on change. However, this would also require millions of signatures from the user and ASP to construct a payment, which would cause a worse user experience. - -## References - -- Velocity of M2 Money Stock - by St Louis Fed - - -- Lightning Report - by River - - -- Cryptocurrencies and the Velocity of Money - by Ingolf Gunnar Anton Pernice, Georg Gentzen, and Hermann Elendner - diff --git a/website/blog/authors.yml b/website/blog/authors.yml deleted file mode 100644 index 4c42d88..0000000 --- a/website/blog/authors.yml +++ /dev/null @@ -1,5 +0,0 @@ -bordalix: - name: João Bordalo - title: Developer - url: https://github.com/bordalix - image_url: https://github.com/bordalix.png diff --git a/website/docs/developers/_category_.json b/website/docs/developers/_category_.json deleted file mode 100644 index 92c1537..0000000 --- a/website/docs/developers/_category_.json +++ /dev/null @@ -1,4 +0,0 @@ -{ - "label": "Developers", - "position": 2 -} diff --git a/website/docs/developers/get-started.md b/website/docs/developers/get-started.md deleted file mode 100644 index 7f46c14..0000000 --- a/website/docs/developers/get-started.md +++ /dev/null @@ -1,19 +0,0 @@ ---- -sidebar_position: 1 -title: 'Get Started' ---- - -:::info -🚧 This page is currently under development, and some concepts may not be entirely accurate. We greatly value your feedback and contributions. If you have any suggestions, corrections, or would like to submit edits, please do so through the pull request link available at the bottom of each page. -::: - -## Overview - -This guide will help you get started with integrating Ark into your applications. - -## Use cases - -- Create a Bitcoin wallet for your users with cheap and fast transactions. -- Integrate Ark and Lightning Network to provide a seamless experience for your users. -- Accept Bitcoin payments in your ecommerce store or point of sale. -- Create virtual payment channels between your users. \ No newline at end of file diff --git a/website/docs/intro.md b/website/docs/intro.md deleted file mode 100644 index bb6ba01..0000000 --- a/website/docs/intro.md +++ /dev/null @@ -1,71 +0,0 @@ ---- -description: Detailed information about the protocol, guidance on providing liquidity, and instructions on how to efficiently spend your coins off-chain in a secure manner -sidebar_position: 1 -slug: / -title: Introduction ---- - -**Welcome to Ark's developer hub.** Here, you'll find detailed information about the protocol, guidance on providing liquidity, and instructions on how to efficiently spend your coins off-chain in a secure manner. - -
- Noah designing the ark to onboard Bitcoin users -
- -### 🤔 Why Ark? - -Bitcoin is the world's most secure and censorship-resistant blockchain. However, it's not the fastest or the cheapest. Ark is a **second-layer solution** designed to **scale Bitcoin transactions**. It uses a shared UTXO model for confidential and off-chain payments through an intermediary server that cannot access your funds. - -### 👶🏼 ELI5: Ark in Simple Terms - -Consider the early private banks that issued banknotes in exchange for gold deposits. These banknotes were redeemable for gold at any time. The banknotes were more convenient to use than gold, but they were only as good as the bank that issued them. If the bank went bankrupt, the banknotes would become worthless. - -When Alice **deposits Bitcoin with a server** (akin to a digital bank), she receives a digital check, similar to a banknote but with a crucial difference. This check is akin to **a cheque with an expiration date**. - -The digital cheque Alice receives comes with an expiration date. To keep her funds secure and the cheque valid, she **must interact with the server at least once every month**. If Alice fails to do this, the server reserves the right to **claim the Bitcoin backing the cheque upon its maturity**. - -She can use this check for payment with anyone else using the same digital bank, bypassing the need to use the Bitcoin blockchain. Before expiration, the check can be **redeemed** for Bitcoin, or it can be **refreshed** by interacting with the server. - -Should the digital bank cease to exist, **users can still retrieve their digital gold without the bank's assistance**. This is similar to withdrawing gold from a defunct traditional bank, but in Ark's case, the process is enforced and automated by the Bitcoin blockchain. This ensures that your digital gold remains safe and accessible. - -### 🔨 How Does it Work? - -Start by exploring the [Nomenclature](./learn/nomenclature.md) to familiarize yourself with key concepts and terminology. Then, learn how to [Board the Ark](./learn/boarding.md), [Send Payments](./learn/payments.md), and eventually [Leave the Ark](./learn/leaving.md) to withdraw your funds back to the Bitcoin blockchain in case of server unresponsiveness. - -### 🏃‍♀️ Running Ark - -:::info -🚧 **Work in progress** -The Ark reference implementation is currently under development. Please check back soon for updates. -::: - -You can join an existing Ark service provider or run your own. - -- [Join an Ark as User](./user/intro.md) -- [Operate an Ark as Liquidity Provider](./provider/intro.md) - -### 👩‍💻 Integrate Ark - -:::info -🚧 **Work in progress** -The Ark libraries and developer tools are currently under development. Please check back soon for updates. -::: - -You can [integrate Ark](./developers/get-started.md) into your wallet or application to enable your users to send and receive Bitcoin payments off-chain. - -### ⌨️ Contributing - -We welcome contributions from the community. If you'd like to contribute to the reference implementation, please see the [Ark GitHub repository](https://github.com/ark-network/ark) repository. - -### 🤓 Protocol Specifications - -Follow the [BOATS GitHub repository](https://github.com/ark-network/boats) for updates. - -### ➰ Stay in the Loop - -- Join our community on [Telegram](https://t.me/ark_network_community). -- Ask questions or get help on [Stack Overflow](https://bitcoin.stackexchange.com/questions/tagged/ark). -- To propose protocol improvements, [open an issue on GitHub](https://github.com/ark-network/boats/issues/new). - -### ⚖️ License - -By contributing to this repository, you agree to license your work under the MIT license, unless specified otherwise. Contributions not originally authored by you must include a license header with the original author(s) and source. diff --git a/website/docs/learn/_category_.json b/website/docs/learn/_category_.json deleted file mode 100644 index b215632..0000000 --- a/website/docs/learn/_category_.json +++ /dev/null @@ -1,4 +0,0 @@ -{ - "label": "Learn", - "position": 1 -} diff --git a/website/docs/learn/boarding.md b/website/docs/learn/boarding.md deleted file mode 100644 index a8ac721..0000000 --- a/website/docs/learn/boarding.md +++ /dev/null @@ -1,52 +0,0 @@ ---- -sidebar_position: 2 -title: 'Boarding the Ark' ---- - -### Overview - -Alice wants to board the Ark of a well-known Ark service provider (ASP). It requires an on-chain transaction. - -Depending on the type of [Boarding transaction](./nomenclature#boarding-transaction) chosen by the ASP, the timeline is different. - -### 🧳 Boarding with Luggage - -- Alice must be online **at least once every 4 weeks** to keep her funds safe -- If ASP is unresponsive, Alice can claim her funds back in **24 hours** -- Easier for the ASP since all VTXOs are born equal -- To unlock the boarding address Alice needs to make two transactions: - -```mermaid -flowchart LR - V["VTXO's timeout after 24 hrs"] - Covenant --> V -``` - -#### Timeline of events - -1. Alice creates a [Boarding transaction](./nomenclature#with-luggage) -2. Alice adds any inputs she wants to cover the values the [VTXO](./nomenclature#vtxo-1) she will receive, plus on-chain fees -3. Alice adds an output with **2 spending paths**: - - This funds will belong to the ASP after 4 weeks: - - `(ASP after 4w)` - - A covenant output that forces coins to be spent by a [VTXO](./nomenclature#vtxo-1) with an output script with **2** spending paths: - - `(Alice + ASP)` - - `(Alice after 24h)` -4. Alice notifies ASP about the [Boarding transaction](./nomenclature#with-luggage) -5. Alice has now a promise of a [VTXO](./nomenclature#vtxo-1) enforced by a covenant - -### 🎒 Boarding without Luggage - -- Alice don't need to worry about being online to maintain access to her funds after boarding -- If ASP is unresponsive, Alice can claim her funds back in **1 year** -- ASP must be aware of the timeout on the [Boarding transaction](./nomenclature#without-luggage) to prevent double spending - -#### Timeline of events - -1. Alice creates a [Boarding transaction](./nomenclature#without-luggage) -2. Alice adds any inputs she wants to cover the values the [VTXO](./nomenclature#vtxo-1) she will receive, plus on-chain fees. -3. Alice adds an output with **2** spending paths: - - `(Alice + ASP)` - - `(Alice after 1y)` -4. Alice notifies ASP about the [Boarding transaction](./nomenclature#without-luggage) -5. Alice can have this deposit to be accepted as if it were a normal [VTXO](./nomenclature#vtxo-1) born in an Ark [Pool transaction](./nomenclature#pool-transaction-aka-ark-transaction) diff --git a/website/docs/learn/leaving.md b/website/docs/learn/leaving.md deleted file mode 100644 index 8dfb4e2..0000000 --- a/website/docs/learn/leaving.md +++ /dev/null @@ -1,66 +0,0 @@ ---- -sidebar_position: 4 -title: 'Leaving the Ark' ---- - -### Overview - -Alice wants to leave the Ark and get her funds back on-chain. It requires an on-chain transaction. - -### Cooperative exit - -#### Timeline of events - -1. Alice tells ASP she wants to trade [VTXO](./nomenclature#vtxo-1) for UTXO -2. ASP (with Alice) prepares next [Pool transaction](./nomenclature#pool-transaction-aka-ark-transaction): - - an additional output is added, locked by `Alice` -3. Alice creates a [Forfeit transaction](./nomenclature#forfeit-transaction): - - spends from VTXO (1) with `Alice + ASP` - - adds connector output from Pool transaction (2) as input - - signs it and send it to the ASP -4. ASP broadcasts [Pool transaction](./nomenclature#pool-transaction-aka-ark-transaction) -5. Alice has now a new UTXO -6. For at most 4 weeks, Alice will be able to double spend her [VTXO](./nomenclature#vtxo-1), but if she does it, the ASP will have time (24 hours) to grab the funds from the [VTXO](./nomenclature#vtxo-1) to itself using the [Forfeit transaction](./nomenclature#forfeit-transaction) - -### Non-cooperative exit - -If ASP is unresponsive, Alice can unilaterally exit revealing the branch of the Pool transaction that locks her funds. - -#### Timeline of events - -1. Assuming a [VTXO](./nomenclature#vtxo-1) tree with radix of 2 and 8 [VTXOs](./nomenclature#vtxo-1): - -```mermaid -flowchart TB - tx1(TX 1) --> tx2(TX 2) - tx1 --> tx3(TX 3) - tx2 --> tx4(TX 4) - tx2 --> tx5(TX 5) - tx3 --> tx6(TX 6) - tx3 --> tx7(TX 7) - tx4 --> v1(VTXO 1) - tx4 --> v2(VTXO 2) - tx5 --> v3(VTXO 3) - tx5 --> v4(VTXO 4) - tx6 --> v5(VTXO 5) - tx6 --> v6(VTXO 6) - tx7 --> v7(VTXO 7) - tx7 --> v8(VTXO 8) -``` - -2. Assuming VTXO 1 and 2 belong to Alice and Bob -3. Alice reveals the [VTXO](./nomenclature#vtxo-1) tree to spend the [Shared Output](./nomenclature#shared-output-aka-shared-utxo). -4. Alice doesn't need to reveal the entire tree, just enough to validate it: - -```mermaid -flowchart TB - tx1(TX 1) --> tx2(TX 2) - tx1 --> tx3(TX 3) - tx2 --> tx4(TX 4) - tx2 --> tx5(TX 5) - tx4 --> v1(VTXO 1) - tx4 --> v2(VTXO 2) -``` - -5. Alice will need to wait 24 hours to be able to spend her [VTXO](./nomenclature#vtxo-1). This gives enough time to the ASP to prevent any double spend attempts by Alice. -6. Bob can also spend his [VTXO](./nomenclature#vtxo-1) in 24 hours, or do nothing and maintain his [VTXO](./nomenclature#vtxo-1) on the Ark. diff --git a/website/docs/learn/nomenclature.md b/website/docs/learn/nomenclature.md deleted file mode 100644 index a377589..0000000 --- a/website/docs/learn/nomenclature.md +++ /dev/null @@ -1,155 +0,0 @@ ---- -sidebar_position: 1 -title: 'Nomenclature' -toc_max_heading_level: 5 ---- - -:::info -🚧 This page is currently under development, and some concepts may not be entirely accurate. We greatly value your feedback and contributions. If you have any suggestions, corrections, or would like to submit edits, please do so through the pull request link available at the bottom of each page. -::: - -## Intervenients - -### ASP - -ASPs are always-on servers that provide liquidity to the network, similar to how Lightning service providers work. - -### Users - -Any user that onboards the Ark or receives a payment inside an Ark. - -### VTXO - -Ark has a UTXO set that lives off the chain. These utxos are referred to as virtual UTXOs or VTXOs in short. - -## Moments - -### Boarding the Ark - -When a User sends funds to the Ark and gets VTXOs in return. - -### Unilateral exit - -When a user decides to withdraw his funds from the Ark to mainchain, without asking the ASP for permission. - -### Round - -Periodic transaction crafted by the ASP that hits mainchain and creates new VTXOs. - -## Transactions - -### Notes - -- In an optimistic scenario, transactions marked with a **\*** should never hit onchain. -- All time periods used on timelocks (**5s**, **24h**, **4w**, **1y**) are arbitrary: any ASP can use different values. - -### Legend - -- **A**: Alice pubkey -- **ASP**: ASP pubkey -- **cov\*\*(script)**: covenant that forces the spending transaction to have a mandatory first output with the **script** -- **and(A,B)**: both conditions needed to unlock -- **or(A,B)**: only one condition needed to unlock -- **and(A, or(S, after(24h)**: (Alice and Server) or (Alice after 24h) - -### VTXO\* - -- A Virtual UTXO: it looks like an UTXO but it should never hit onchain, thus a Virtual UTXO - -| Inputs | Outputs | -| ---------------------------- | ------------------------------------ | -| Boarding or Pool transaction | `(Alice + ASP) or (Alice after 24h)` | - -### Boarding transaction - -There are 2 different ways a user can board the Ark: - -- With luggage -- Without luggage - -Different ASPs can use different ways for users to board their Ark. - -#### With luggage - -- Initially proposed by [Steven Roose](https://roose.io/presentations/understanding-ark.pdf) -- Alice funds an output that can be **accepted as a VTXO** in a future round -- A covenant forces the creation of an output with the same script as [**VTXO**](#vtxo-1). No need for interactivity after funding it, anyone can spend. -- **ASP** can unlock after a timeout ie. _4 weeks_ -- Alice is **required to be online** to maintain access to funds: after the timeout, ASP becomes the only owner funds - -| Inputs | Outputs | -| ------------ | ----------------------------------------------------------- | -| Alice’s UTXO | `(ASP after 4w) or cov((Alice + ASP) or (Alice after 24h))` | - -#### Without luggage - -- Initially proposed by [Burak](https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2023-May/021694.html) -- Alice funds an output that can be **accepted as a VTXO** in a future round -- If ASP is not cooperative, **Alice** can unlock after a timeout ie. _1 year_ -- Alice is **not required to be online** to maintain access to funds: after the timeout, she becomes the only owner of the funds - -| Inputs | Outputs | -| ------------ | ----------------------------------- | -| Alice’s UTXO | `(Alice after 1y) or (Alice + ASP)` | - -### Forfeit transaction\* - -- Insurance for the ASP, in case Alice tries to double spend her VTXO after spending it inside Ark -- Before the ASP funds Bob’s VTXO in the next Pool transaction, he must receive this transaction signed by Alice -- Uses a connector from the next Pool transaction to achieve atomicity - -| Inputs | Outputs | -| ------------------------------------ | ------- | -| VTXO spending `Alice + ASP` | `ASP` | -| Connector from next Pool transaction | - -### Pool transaction (aka Ark transaction) - -- Funded by the ASP, creates VTXOs -- Has at least two outputs: - - A shared output with a VTXOs tree - - A connectors output with a connectors tree -- A new transaction is broadcasted every 5 seconds - -| Inputs | Outputs | -| -------- | ----------------- | -| ASP UTXO | Shared output | -| | Connectors output | - -### Shared output (aka Shared UTXO) - -- Represents a tree of transactions -- In an optimistic scenario, this tree is never revealed -- Each leaf on this tree represents a VTXO - -```mermaid -flowchart LR - subgraph Onchain - shared(Shared output) - end - subgraph Virtual - tx1(TX 1) --> tx2(TX 2) - tx1 --> tx3(TX 3) - tx2 --> v1(VTXO 1) - tx2 --> v2(VTXO 2) - tx3 --> v3(VTXO 3) - tx3 --> v4(VTXO 4) - end - shared --> tx1 -``` - -- Tree can have a radix higher than 2 (ex: radix 4) - -```mermaid -flowchart LR - subgraph Onchain - shared(Shared output) - end - subgraph Virtual - tx1(TX 1) --> v1(VTXO 1) - tx1 --> v2(VTXO 2) - tx1 --> v3(VTXO 3) - tx1 --> v4(VTXO 4) - end - shared --> tx1 -``` diff --git a/website/docs/learn/payments.md b/website/docs/learn/payments.md deleted file mode 100644 index 5f3793c..0000000 --- a/website/docs/learn/payments.md +++ /dev/null @@ -1,25 +0,0 @@ ---- -sidebar_position: 3 -title: 'Payments' ---- - -### Overview - -Alice wants to send funds to Bob inside the Ark. - -- All Ark payments and transactions are off-chain. -- Bob doesn't need to have funds inside the Ark to receive funds. (ie. inbound liquidity problem) -- Bob doesn't need to be online to receive funds -- Bob wil be required to be online **at least once every 4 weeks** to keep his funds safe. - -### Timeline of events - -1. Alice tells ASP to send [VTXO](./nomenclature#vtxo-1) to Bob -2. ASP (with Alice) prepares next [Pool transaction](./nomenclature#pool-transaction-aka-ark-transaction) -3. Alice creates a [Forfeit transaction](./nomenclature#forfeit-transaction): - - spends from VTXO (1) via `Alice + ASP` - - adds connector output from Pool transaction (2) as input - - signs (SIGHASH_ALL) and sends it to the ASP -4. ASP broadcasts [Pool transaction](./nomenclature#pool-transaction-aka-ark-transaction) -5. Bob has now a new [VTXO](./nomenclature#vtxo-1) -6. For at most 4 weeks, Alice will be able to double spend her [VTXO](./nomenclature#vtxo-1), but if she does it, the ASP will have time to grab the funds from the [VTXO](./nomenclature#vtxo-1) to itself using the [Forfeit transaction](./nomenclature#forfeit-transaction) diff --git a/website/docs/provider/_category_.json b/website/docs/provider/_category_.json deleted file mode 100644 index bb74b6e..0000000 --- a/website/docs/provider/_category_.json +++ /dev/null @@ -1,4 +0,0 @@ -{ - "label": "Create an Ark", - "position": 3 -} diff --git a/website/docs/provider/coordinator/_category_.json b/website/docs/provider/coordinator/_category_.json deleted file mode 100644 index f2e68a6..0000000 --- a/website/docs/provider/coordinator/_category_.json +++ /dev/null @@ -1,4 +0,0 @@ -{ - "label": "Coordinator", - "position": 3 -} \ No newline at end of file diff --git a/website/docs/provider/coordinator/configure-cli.md b/website/docs/provider/coordinator/configure-cli.md deleted file mode 100644 index 0aac7ee..0000000 --- a/website/docs/provider/coordinator/configure-cli.md +++ /dev/null @@ -1,46 +0,0 @@ ---- -sidebar_position: 5 -title: Configure the CLI ---- - -Now that your service is up and running you can configure the `coordinator` CLI to interact with it. - -The CLI makes use of a configuration file stored in its datadir - defaults to `~/.coordinator-cli` on Linux, `~/Library/Application\ Support/Coordinator-cli` on MacOS. - -You can customize the datadir path of your coordinator cli by exporting the environment variable `export ARK_COORDINATOR_CLI_DATADIR=path/to/datadir`. - -:::tip -Add this env var to your bash profile otherwise you'll need to always export it when running `coordinator` commands. -::: - -You can manage the configuration of your CLI with the features of the `coordinator config` command. Following, you can learn all what you can do with this command. - -### Initialize CLI config - -You can initialize the configuration of your CLI by the means of flags - -```bash -$ coordinator config init -``` - -This command brings the configuration of your CLI to its default status unless you don't specify a flag for those params you want to tweak. - -Run `coordinator config init --help` to see all available configuration flags. - -### Customize CLI config - -You can change granular params of the CLI's configuration by using the `set` subcommand as shown below: - -```bash -$ coordinator config set no-tls true -``` - -### Show CLI config - -You can take a look at the configuration of your CLI with: - -```bash -$ coordinator config -``` - -You've learned everything about configuring the CLI, let's see how it does let you interact with the Coordinator. \ No newline at end of file diff --git a/website/docs/provider/coordinator/configure-service.md b/website/docs/provider/coordinator/configure-service.md deleted file mode 100644 index eddbc83..0000000 --- a/website/docs/provider/coordinator/configure-service.md +++ /dev/null @@ -1,26 +0,0 @@ ---- -sidebar_position: 4 -title: Configure the Coordinator ---- - -The Coordinator can be configured by exporting environment variables at startup, or by adding a configuration file to its datadir. - -### Configure with environment variables - -The following table lists all the environment variables available, along with a brief description and their default values: - -| Name | Description | Default Value | -|---|---|---| -| ARK_COORDINATOR_DATADIR | Let's you change the service's datadir path | `~/.coordinatord` (Linux).

`~/Library/Application\ Support/Coordinatord` (MacOS). | - -### Configure with file - -You can configure the Coordinator by adding a `config.json` file to its datadir. - -Below, you can see all the props you can add to the config file: - -```json -{ - //TBD -} -``` \ No newline at end of file diff --git a/website/docs/provider/coordinator/intro.md b/website/docs/provider/coordinator/intro.md deleted file mode 100644 index d2bd8cf..0000000 --- a/website/docs/provider/coordinator/intro.md +++ /dev/null @@ -1,17 +0,0 @@ ---- -sidebar_position: 1 -title: Overview ---- - -# Ark Coordinator - -The Coordinator handles the perpetual creation of new Ark rounds every 5 seconds. - -It can be served in one of the following ways: - -* [Dockerized application](run-docker.md) -* [Standalone application](run-standalone.md) - - - -Once your coordinator is up and running you can [configure the CLI](configure-cli.md) to interact with it. \ No newline at end of file diff --git a/website/docs/provider/coordinator/run-docker.md b/website/docs/provider/coordinator/run-docker.md deleted file mode 100644 index 1bf1a29..0000000 --- a/website/docs/provider/coordinator/run-docker.md +++ /dev/null @@ -1,30 +0,0 @@ ---- -sidebar_position: 3 -title: Run with Docker ---- - -The Coordinator can be served as a dockerized application by following the steps below: - -1. Install [Docker](https://docs.docker.com/engine/install) - if you're on Linux, don't forget the [post-installation steps](https://docs.docker.com/engine/install/linux-postinstall/)! -2. Download the latest image of the connector with `docker pull ghcr.io/ark-network/coordinatord:latest` -3. Create a `coordinatord/` folder in your current directory - to mount the datadir as external volume - and start the dockerized service with - -```bash -$ docker run -it -d --name coordinatord \ - -u - -v "$(pwd)/coordinatord:/home/ark/.coordinatord" \ - -e ARK_COORDINATOR_LOG_LEVEL=5 \ - ghcr.io/ark-network/coordinatord:latest -``` - -You can check the logs of the service at anytime by running `docker logs coordinatord`. - -The dockerized Coordinator can be configured by the means of environment variables or by adding a `config.json` file to the `coordinatord/` folder you've created. Learn more about this by visiting [this section](configure-service.md). - -The service comes also with an embedded CLI, so it's enough for you to create an alias like the following to use it: - -```bash -$ alias coordinator="docker exec coordinatord coordinator" -``` - -Take a look at how to [configure the CLI](configure-cli.md) before start interacting with the running Coordinator. diff --git a/website/docs/provider/coordinator/run-standalone.md b/website/docs/provider/coordinator/run-standalone.md deleted file mode 100644 index e8c99fa..0000000 --- a/website/docs/provider/coordinator/run-standalone.md +++ /dev/null @@ -1,23 +0,0 @@ ---- -sidebar_position: 2 -title: Run Standalone ---- - -The Coordinator can be served as a standalone binary by following the steps below: - -1. Download the lastest [release](https://github.com/ark-network/ark-coordinator/releases) of the service and the CLI for Linux or MacOS. -2. Rename the binaries `coordinatord` and `coordinator` , move them to your _PATH_ (eg. `/usr/local/bin`), and grant them exec permissions with `chmod +x /usr/local/bin/coordinatord` and `chmod +x /usr/local/bin/coordinator`. -3. Start the service with - -```bash -ARK_COORDINATOR_LOG_LEVEL=5 -coordinatord & > ~/ark-logs/coordinator.logs.txt & -``` - -The command above redirects all the logs to the file `~/ark-logs/coordinator.logs.txt`. Therefore you can check the logs of the service at anytime by consulting that file. - -The Coordinator service makes use of a datadir - defaults to `~/.coordinatord` on Linux, `~/Library/Application\ Support/Coordinatord` on MacOS - that can be customized by exporting the environment variable `export ARK_COORDINATOR_DATADIR=path/to/datadir` at its startup. - -You can configure the Coordinator by the means of environment variables or by adding a `config.json` file to the service's datadir. Learn more about this by visiting [this section](configure-service.md). - -Once the service is started you can [configure the CLI](configure-cli.md) and start interacting with it. diff --git a/website/docs/provider/coordinator/use-cli.md b/website/docs/provider/coordinator/use-cli.md deleted file mode 100644 index f792a99..0000000 --- a/website/docs/provider/coordinator/use-cli.md +++ /dev/null @@ -1,56 +0,0 @@ ---- -sidebar_position: 6 -title: Use the CLI ---- - -Now that your CLI is configured to connect with the running Coordinator, let's take a look at what it makes you capable of. - -### List pool transactions - -You can retrieve the list of pool transactions made in a certain time range with: - -```bash -$ coordinator pools --start --end -``` - -You can omit the `--end` flag if you want to retrieve all pool transactions from a certain time unitl now. - -For each pool tx, you can see details like the txid, status, and amount of liquidity added to the Ark. - -You can also list all pool transactions created so far with: - -```bash -$ coordinator pools --all -``` - -Run `coordinators pools --help` to see the full list of available flags. - -### Get pool transaction details - -You can get details about a specific pool transaction with: - -```bash -$ coordinator pool --id -``` - -### Register inputs and outptus - -You can manually register the VTXOs you're going to spend and the related receivers with: - -```bash -$ coordinator register --inputs '[{"txid": "", "vout": }]' --outputs '[{"pubkey": "", "amount": }]' -``` - -The Coordinator answers with a message containing the virtual (forfeit) transaction spending your coins and the list of all the new VTXOs created in the next round - including those you registered. - - - -### Finalize input and outputs - -Once you signed the virtual transaction you can send it back to the Coordinator and finalize the process with: - -```bash -$ coordinator finalize --vtx -``` - -In response you get the id of the pool transaction that is going to be broadcasted by the server. diff --git a/website/docs/provider/gateway/_category_.json b/website/docs/provider/gateway/_category_.json deleted file mode 100644 index 3180cd1..0000000 --- a/website/docs/provider/gateway/_category_.json +++ /dev/null @@ -1,4 +0,0 @@ -{ - "label": "Gateway", - "position": 2 -} \ No newline at end of file diff --git a/website/docs/provider/gateway/intro.md b/website/docs/provider/gateway/intro.md deleted file mode 100644 index c2aba47..0000000 --- a/website/docs/provider/gateway/intro.md +++ /dev/null @@ -1,8 +0,0 @@ ---- -sidebar_position: 1 -title: Overview ---- - -# Ark Gateway - -The Gateway handles users' requests to onboard (join) and offboard (leave) the Ark. diff --git a/website/docs/provider/intro.md b/website/docs/provider/intro.md deleted file mode 100644 index 986fb98..0000000 --- a/website/docs/provider/intro.md +++ /dev/null @@ -1,11 +0,0 @@ ---- -sidebar_position: 1 ---- - -# Introduction - -The Ark Service Provider (ASP) is composed by 3 services that have different responsibilities: - -- Gateway, handles (on/off)boarding requests -- Coordinator, handles coinjoin rounds and creation of pool txs (every 5 secs) -- Treasury, handles verification & approval of pool txs, and operations altering the capacity of the service diff --git a/website/docs/provider/treasury/_category_.json b/website/docs/provider/treasury/_category_.json deleted file mode 100644 index 8c1a4de..0000000 --- a/website/docs/provider/treasury/_category_.json +++ /dev/null @@ -1,4 +0,0 @@ -{ - "label": "Treasury", - "position": 4 -} \ No newline at end of file diff --git a/website/docs/provider/treasury/intro.md b/website/docs/provider/treasury/intro.md deleted file mode 100644 index a0f464f..0000000 --- a/website/docs/provider/treasury/intro.md +++ /dev/null @@ -1,10 +0,0 @@ ---- -sidebar_position: 1 -title: Overview ---- - -# Ark Treasury - -The Treasury is in charge of verifying and approving pool transactions created by the Coordinator. - -It does also handles the management of the ASP capacity - ie. depositing or removing funds - and liquidity - monitoring/sweeping expired VTXOs. diff --git a/website/docs/roadmap/_category_.json b/website/docs/roadmap/_category_.json deleted file mode 100644 index ff109d0..0000000 --- a/website/docs/roadmap/_category_.json +++ /dev/null @@ -1,4 +0,0 @@ -{ - "label": "Roadmap", - "position": 5 -} diff --git a/website/docs/roadmap/index.md b/website/docs/roadmap/index.md deleted file mode 100644 index 293ae4b..0000000 --- a/website/docs/roadmap/index.md +++ /dev/null @@ -1,84 +0,0 @@ -# Roadmap - -The roadmap provides an overview of the planned projects and modules for the Ark network. It outlines the current development status and expected functionalities of each module. Please note that the roadmap is subject to change as the project evolves. - -For the latest updates and progress reports, please check the this page regularly. - -## Projects - -### ☁️ `arkd` - Ark Service Provider Daemon - -- Status: Pre-Alpha - -The `arkd` is the Ark daemon, the initial implementation of an ASP (Ark Service Provider) as a standalone always-on server. -It uses [Ocean](https://github.com/vulpemventures/ocean) as Bitcoin and Liquid wallet backend. -It exposes a gRPC interface that Ark wallets can use to interact with the Provider. - -- [x] Setup Ocean Wallet for funding rounds -- [ ] Start producing rounds from Ark wallets - - [x] Register VTXOs to be spent & new VTXOs to be created - - [x] Build congestion control tree - - [x] Root node - - [x] VTXOs Script - - [x] Tap Leaf Script Validation - - [x] Unroll Clause Transaction Builder. - - [ ] Verifiy forfeit transactions -- [x] Sign & Broadcast Pool transactions -- [x] Sweep expired VTXOs -- [ ] Accept VTXOs from Boarding transactions -- [ ] Detect double spends to recover with forfeit transactions - -### 🌐 Ark Explorer - -Status: Not started yet - -The Ark Explorer module will consist of a console and an Electrum-like server. It will allow users to retrieve VTXOs, pool transactions, and access transaction data. More details about this module will be provided as development progresses. - -### 👩‍💻 `ark` - Ark CLI - -- Status: Pre-Alpha - -The `ark` module will be an Ark wallet implemented as a command line interface (CLI). It will also be in the alpha status, indicating that it is still being developed and may have some limitations. - -- [x] Create and manage Ark wallets -- [x] Connect to an Ark Service Provider. -- [ ] Send and receive Ark transactions - - [x] Join a round - - [ ] Validate Tree and Sign forfeit transaction - - [x] Finalize a Tree -- [ ] on-boarding - - [ ] Boarding address Script - - [ ] Tap Leaf Script Validation -- [ ] off-boarding - - [x] Cooperative exit - - [ ] Unilateral exit - -### 🚰 Ark Faucet - -Status: Alpha - -The Ark Faucet allows users to request testnet VTXOs for testing purposes, without having to onboard to the Ark provider. - -### 📱 Ark Mobile App - -Status: Not started yet - -The Ark App module will serve as a reference implementation for an Ark wallet as Mobile App. It will provide a user-friendly interface for managing Ark transactions and other wallet-related functionalities. - -### 🖥️ Ark Desktop App - -Status: Not started yet - -The Ark Desktop module will be a reference implementation for an Ark wallet as a desktop application. It will provide a user-friendly interface for managing Ark transactions and other wallet-related functionalities. - -### 👨🏻‍💻 Ark SDK - -Status: Not started yet - -Rust-based SDK with first-class support Java, Swift and JavaScript bindings for implementing Ark wallets and interacting with ASPs. It will provide a set of APIs for managing wallets, transactions, and other Ark-related functionalities. - -### 🗼 Ark Tower - -Status: Not started yet - -Delegate automatic refereshes of VTXOs to trust-minimized Ark Tower nodes. Additional information about this module will be shared as development continues. diff --git a/website/docs/user/_category_.json b/website/docs/user/_category_.json deleted file mode 100644 index f5287e8..0000000 --- a/website/docs/user/_category_.json +++ /dev/null @@ -1,4 +0,0 @@ -{ - "label": "Join the Ark", - "position": 4 -} diff --git a/website/docs/user/ark-cli.md b/website/docs/user/ark-cli.md deleted file mode 100644 index 420bb47..0000000 --- a/website/docs/user/ark-cli.md +++ /dev/null @@ -1,71 +0,0 @@ ---- -sidebar_position: 2 -title: Ark CLI ---- - -The Ark CLI allows you to interact with the Ark Service Provider (ASP). It is a command line tool that can be used to create and manage your Ark Wallet. - -## Configure the CLI - -The CLI requires an initial setup to initialize the wallet and connect to the ASP: - -```bash -$ ark init init --password --ark-url -``` - -You can also restore a wallet by specifying the hex encoded private key with the `--prvkey` flag. - -## Receive VTXO - -### Get receiving address - -You can print your onchain and offchain receiving addresses to receive funds with: - -```bash -$ ark receive -``` - -This command also shows the list of relays used to reach the ASP. - -:::tip -testnet only: `ark faucet` to receive newly created VTXO from the service provider. -::: - -### Print balance - -You can see both the onchain and offchain balance of the wallet with: -```bash -$ ark balance -``` - -## Send VTXO(s) - -You can make an offchain payment by sending to either one or many receivers: - -```bash -$ ark send --to --amount -$ ark send --receivers '[{"to": "", "amount": }, ...]' -``` - -The amount must be specified in _sats_ unit. - -## Redemption - -### Collaborative redemption - -You can redeem onchain your funds by collaborating with the ASP with: - -```bash -$ ark redeem --address --amount -``` - -Any change produced with this operation goes to your offchain address. - -### Unilateral redemption - -If the ASP is unresponsive you can redeem all your offchain funds unilaterally with: - -```bash -$ ark redeem --address --force -``` - diff --git a/website/docs/user/intro.md b/website/docs/user/intro.md deleted file mode 100644 index 4c30ba2..0000000 --- a/website/docs/user/intro.md +++ /dev/null @@ -1,6 +0,0 @@ ---- -sidebar_position: 1 -title: Overview ---- - -An Ark client is a software that allows users to interact with the Ark Service Provider. It can be a Browser Extension, a Progressive Web Application, a desktop or mobile app. \ No newline at end of file diff --git a/website/docusaurus.config.js b/website/docusaurus.config.js deleted file mode 100644 index 751cada..0000000 --- a/website/docusaurus.config.js +++ /dev/null @@ -1,162 +0,0 @@ -// @ts-check -// Note: type annotations allow type checking and IDEs autocompletion - -const lightCodeTheme = require('prism-react-renderer/themes/synthwave84') -const darkCodeTheme = require('prism-react-renderer/themes/dracula') - -/** @type {import('@docusaurus/types').Config} */ -const config = { - title: 'Ark', - tagline: 'TBD', - favicon: 'img/ark-logo.png', - url: 'https://arkdev.info', - baseUrl: '/', - organizationName: 'Ark', - projectName: 'Ark Website', - onBrokenLinks: 'throw', - onBrokenMarkdownLinks: 'warn', - i18n: { - defaultLocale: 'en', - locales: ['en'], - }, - - presets: [ - [ - 'classic', - /** @type {import('@docusaurus/preset-classic').Options} */ - ({ - docs: { - routeBasePath: '/docs', - sidebarPath: require.resolve('./sidebars.js'), - editUrl: 'https://github.com/ark-network/ark/edit/master/website/', - exclude: [ - '**/provider/gateway/**', - '**/provider/coordinator/**', - '**/provider/treasury/**', - '**/user/ark-cli.md', - ], - }, - blog: { - showReadingTime: true, - editUrl: - 'https://github.com/ark-network/ark/edit/master/website/blog', - - blogTitle: 'Blog', - blogDescription: 'Posts about Ark development', - }, - }), - ], - ], - - themeConfig: - /** @type {import('@docusaurus/preset-classic').ThemeConfig} */ - ({ - // Replace with your project's social card - image: 'img/ark-banner.png', - navbar: { - title: 'Ark', - logo: { - alt: 'Ark Logo', - src: 'img/ark-logo.png', - srcDark: 'img/ark-logo.png', - }, - items: [ - { - type: 'docSidebar', - sidebarId: 'tutorialSidebar', - position: 'left', - label: 'Docs', - }, - { to: '/blog', label: 'Blog', position: 'left' }, - { - href: 'https://github.com/ark-network', - label: 'GitHub', - position: 'right', - }, - ], - }, - footer: { - links: [ - { - title: 'LEARN', - items: [ - { - label: 'Nomenclature', - to: '/docs/learn/nomenclature', - }, - { - label: 'Board an Ark', - to: '/docs/learn/boarding', - }, - { - label: 'Send Payments', - to: '/docs/learn/payments', - }, - { - label: 'Leave an Ark', - to: '/docs/learn/leaving', - }, - ], - }, - { - title: 'DOCS', - items: [ - { - label: 'Overview', - to: '/docs', - }, - { - label: 'Join an Ark', - to: '/docs/user/intro', - }, - { - label: 'Create an Ark', - to: '/docs/provider/intro', - }, - ], - }, - { - title: 'COMMUNITY', - items: [ - { - label: 'Telegram', - href: 'https://t.me/ark_network_community', - }, - { - label: 'Stack Exchange', - href: 'https://bitcoin.stackexchange.com/questions/tagged/ark', - }, - { - label: 'Github', - href: 'https://github.com/ark-network', - }, - ], - }, - { - title: 'MORE', - items: [ - { - label: 'Blog', - to: '/blog', - }, - ], - }, - ], - }, - colorMode: { - defaultMode: 'light', - disableSwitch: false, - respectPrefersColorScheme: true, - }, - prism: { - theme: lightCodeTheme, - darkTheme: darkCodeTheme, - }, - }), - markdown: { - mermaid: true, - }, - themes: ['@docusaurus/theme-mermaid'], -} - -module.exports = config diff --git a/website/package.json b/website/package.json deleted file mode 100644 index 2829726..0000000 --- a/website/package.json +++ /dev/null @@ -1,44 +0,0 @@ -{ - "name": "ark-website", - "version": "0.0.0", - "private": true, - "scripts": { - "docusaurus": "docusaurus", - "start": "docusaurus start", - "build": "docusaurus build", - "swizzle": "docusaurus swizzle", - "deploy": "docusaurus deploy", - "clear": "docusaurus clear", - "serve": "docusaurus serve", - "write-translations": "docusaurus write-translations", - "write-heading-ids": "docusaurus write-heading-ids" - }, - "dependencies": { - "@docusaurus/core": "2.4.3", - "@docusaurus/preset-classic": "2.4.3", - "@docusaurus/theme-mermaid": "2.4.3", - "@mdx-js/react": "^1.6.22", - "clsx": "^1.2.1", - "prism-react-renderer": "^1.3.5", - "react": "^17.0.2", - "react-dom": "^17.0.2" - }, - "devDependencies": { - "@docusaurus/module-type-aliases": "2.4.3" - }, - "browserslist": { - "production": [ - ">0.5%", - "not dead", - "not op_mini all" - ], - "development": [ - "last 1 chrome version", - "last 1 firefox version", - "last 1 safari version" - ] - }, - "engines": { - "node": ">=16.14" - } -} diff --git a/website/sidebars.js b/website/sidebars.js deleted file mode 100644 index 9ab54c2..0000000 --- a/website/sidebars.js +++ /dev/null @@ -1,33 +0,0 @@ -/** - * Creating a sidebar enables you to: - - create an ordered group of docs - - render a sidebar for each doc of that group - - provide next/previous navigation - - The sidebars can be generated from the filesystem, or explicitly defined here. - - Create as many sidebars as you want. - */ - -// @ts-check - -/** @type {import('@docusaurus/plugin-content-docs').SidebarsConfig} */ -const sidebars = { - // By default, Docusaurus generates a sidebar from the docs folder structure - tutorialSidebar: [{type: 'autogenerated', dirName: '.'}], - - // But you can create a sidebar manually - /* - tutorialSidebar: [ - 'intro', - 'hello', - { - type: 'category', - label: 'Tutorial', - items: ['tutorial-basics/create-a-document'], - }, - ], - */ -}; - -module.exports = sidebars; diff --git a/website/src/pages/buttons.js b/website/src/pages/buttons.js deleted file mode 100644 index 3cea9d0..0000000 --- a/website/src/pages/buttons.js +++ /dev/null @@ -1,128 +0,0 @@ -import React, { useEffect, useState } from 'react' - -const isArm = async () => { - // available on Chrome, Edge and Opera - if (typeof navigator.userAgentData?.getHighEntropyValues === 'function') { - const { architecture } = await navigator.userAgentData.getHighEntropyValues( - ['architecture'] - ) - return architecture === 'arm' - } - // for Firefox - const w = document.createElement('canvas').getContext('webgl') - const d = w.getExtension('WEBGL_debug_renderer_info') - const g = (d && w.getParameter(d.UNMASKED_RENDERER_WEBGL)) || '' - return Boolean(g.match(/Apple M[123]/)) // TODO: Linux -} - -const Button = ({ children, onClick, colored }) => { - const backgroundColor = colored - ? 'var(--ifm-color-primary-lightest)' - : 'var(--ifm-color-emphasis-200)' - return ( - - ) -} - -const Section = ({ children }) => ( -
{children}
-) - -const SpaceBetween = ({ children }) => ( -
- {children} -
-) - -export default function Buttons() { - const [binaryUrl, setBinaryUrl] = useState('') - const [downloadText, setDownloadText] = useState('Download binary') - - const fileURL = (filename) => - `https://install-latest-cli.arkdev.info/latest-release/${filename}` - - useEffect(async () => { - const nua = navigator.userAgent - const isMacOS = Boolean(nua.match(/OS X /)) - const isLinux = Boolean(nua.match(/Linux/)) - const isSafari = Boolean(nua.includes('Safari') && !nua.includes('Chrome')) - if (!isMacOS && !isLinux) return // no binaries available - if (isSafari) return // Safari hides the CPU architecture - const os = isMacOS ? 'darwin' : 'linux' - const arch = (await isArm()) ? 'arm64' : 'amd64' - const file = `ark-${os}-${arch}` - setBinaryUrl(fileURL(file)) - setDownloadText(`Download ${file}`) - }) - - const viewOnGithub = () => - window.open('https://github.com/ark-network/ark', '_blank') - - const downloadAlpha = () => { - // if we know user OS and architecture, start download immediately - if (!binaryUrl) window.open(binaryUrl, '_blank') - document.querySelector('#available-binaries').scrollIntoView({ - behavior: 'smooth', - }) - } - - return ( -
- - - - -
- ) -} diff --git a/website/src/pages/index.mdx b/website/src/pages/index.mdx deleted file mode 100644 index 6876562..0000000 --- a/website/src/pages/index.mdx +++ /dev/null @@ -1,148 +0,0 @@ -import Buttons from './buttons.js' - -# Welcome to Ark - -A second-layer solution designed to scale Bitcoin transactions - - - -## Why Ark? - -Bitcoin is the world's most secure and censorship-resistant blockchain. However, it's not the fastest or the cheapest. Ark is a second-layer solution designed to scale Bitcoin transactions. It uses a shared UTXO model for confidential and off-chain payments through an intermediary server that cannot access your funds. - -## Try it - -Start by downloading a compatible binary. - -### Available binaries - -- [ark-darwin-amd64](https://install-latest-cli.arkdev.info/latest-release/ark-darwin-amd64) -- [ark-darwin-arm64](https://install-latest-cli.arkdev.info/latest-release/ark-darwin-arm64) -- [ark-linux-amd64](https://install-latest-cli.arkdev.info/latest-release/ark-linux-amd64) -- [ark-linux-arm64](https://install-latest-cli.arkdev.info/latest-release/ark-linux-arm64) - -Move it to somewhere on your PATH: - -```bash -$ mv /usr/local/bin/ark -$ chmod +x /usr/local/bin/ark -``` - -### Configure the CLI - -The CLI requires an initial setup to initialize the wallet and connect to the ASP: - -```bash -$ ark init --password --ark-url https://asp.arkdev.info -``` - -You can also restore a wallet by specifying the hex encoded private key with the `--prvkey` flag. - -### View balance - -You can see both the onchain and offchain balance of the wallet with: - -```bash -$ ark balance -``` - -To see your balance with your VTXOs expiration details use `--expiry-details`: - -```bash -$ ark balance --expiry-details -``` - -### Receive funds - -You can print your onchain and offchain receiving addresses with: - -```bash -$ ark receive -``` - -#### Add funds to the ark wallet: - -Fund the `onchain_address` from previous command with https://liquidtestnet.com/faucet. - -### Onboard the ark - -``` -$ ark onboard --amount -``` - -This command will send funds from your onchain balance to your offchain balance. - -After confirmation, your ark wallet will be funded and ready to spend offchain. - -:::danger Use sats -Amount is always specified in _sats_ unit. -::: - -### Make payments - -You can make a payment by sending to either one or many receivers: - -```bash -$ ark send --to
--amount -$ ark send --receivers '[{"to": "
", "amount": }, ...]' -``` - -:::tip -You can send funds to onchain or offchain addresses: - -- funds to onchain addresses will come from your onchain balance -- funds to offchain addresses will come from your offchain balance - -::: - -### Collaborative redemption - -You can redeem your funds onchain collaborating with the ASP: - -```bash -$ ark redeem --address --amount -``` - -This command will send funds from your offchain balance to your onchain balance. - -:::info -Any change produced with this operation goes to your offchain address. -::: - -### Unilateral redemption - -If the ASP is unresponsive you can redeem all your offchain funds unilaterally: - -```bash -$ ark redeem --address --force -``` - -:::danger -The tag `--force` will make ark ignore `--amount` and redeem all funds. -::: - -### Help - -You can see all available commands with `help`: - -``` -$ ark help -``` - -### Create a second CLI - -To create a second CLI, on a different terminal use a different datadir by exporting the env var `ARK_WALLET_DATADIR`: - -```bash -$ export ARK_WALLET_DATADIR=path/to/custom -$ ark init --password --ark-url https://asp.arkdev.info -``` - -:::info -By default the CLI uses the following datadir: - -- POSIX (Linux/BSD): ~/.Ark-cli -- Mac OS: $HOME/Library/Application Support/Ark-cli -- Windows: %LOCALAPPDATA%\Ark-cli -- Plan 9: $home/Ark-cli - ::: diff --git a/website/static/.nojekyll b/website/static/.nojekyll deleted file mode 100644 index e69de29..0000000 diff --git a/website/static/img/ark-agora.png b/website/static/img/ark-agora.png deleted file mode 100644 index 6c7ab3a..0000000 Binary files a/website/static/img/ark-agora.png and /dev/null differ diff --git a/website/static/img/ark-banner.png b/website/static/img/ark-banner.png deleted file mode 100644 index 5e514df..0000000 Binary files a/website/static/img/ark-banner.png and /dev/null differ diff --git a/website/static/img/ark-logo.png b/website/static/img/ark-logo.png deleted file mode 100644 index 4bef5e0..0000000 Binary files a/website/static/img/ark-logo.png and /dev/null differ diff --git a/website/static/img/ark-og-image.png b/website/static/img/ark-og-image.png deleted file mode 100644 index 4bef5e0..0000000 Binary files a/website/static/img/ark-og-image.png and /dev/null differ diff --git a/website/static/img/shared_output.png b/website/static/img/shared_output.png deleted file mode 100644 index 3fb6f5b..0000000 Binary files a/website/static/img/shared_output.png and /dev/null differ diff --git a/website/static/liquidity-simulator/decimal.js b/website/static/liquidity-simulator/decimal.js deleted file mode 100644 index 4075ff6..0000000 --- a/website/static/liquidity-simulator/decimal.js +++ /dev/null @@ -1,4896 +0,0 @@ -;(function (globalScope) { - 'use strict' - - /*! - * decimal.js v10.4.3 - * An arbitrary-precision Decimal type for JavaScript. - * https://github.com/MikeMcl/decimal.js - * Copyright (c) 2022 Michael Mclaughlin - * MIT Licence - */ - - // ----------------------------------- EDITABLE DEFAULTS ------------------------------------ // - - // The maximum exponent magnitude. - // The limit on the value of `toExpNeg`, `toExpPos`, `minE` and `maxE`. - var EXP_LIMIT = 9e15, // 0 to 9e15 - // The limit on the value of `precision`, and on the value of the first argument to - // `toDecimalPlaces`, `toExponential`, `toFixed`, `toPrecision` and `toSignificantDigits`. - MAX_DIGITS = 1e9, // 0 to 1e9 - // Base conversion alphabet. - NUMERALS = '0123456789abcdef', - // The natural logarithm of 10 (1025 digits). - LN10 = - '2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862486334095254650828067566662873690987816894829072083255546808437998948262331985283935053089653777326288461633662222876982198867465436674744042432743651550489343149393914796194044002221051017141748003688084012647080685567743216228355220114804663715659121373450747856947683463616792101806445070648000277502684916746550586856935673420670581136429224554405758925724208241314695689016758940256776311356919292033376587141660230105703089634572075440370847469940168269282808481184289314848524948644871927809676271275775397027668605952496716674183485704422507197965004714951050492214776567636938662976979522110718264549734772662425709429322582798502585509785265383207606726317164309505995087807523710333101197857547331541421808427543863591778117054309827482385045648019095610299291824318237525357709750539565187697510374970888692180205189339507238539205144634197265287286965110862571492198849978748873771345686209167058', - // Pi (1025 digits). - PI = - '3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632789', - // The initial configuration properties of the Decimal constructor. - DEFAULTS = { - // These values must be integers within the stated ranges (inclusive). - // Most of these values can be changed at run-time using the `Decimal.config` method. - - // The maximum number of significant digits of the result of a calculation or base conversion. - // E.g. `Decimal.config({ precision: 20 });` - precision: 20, // 1 to MAX_DIGITS - - // The rounding mode used when rounding to `precision`. - // - // ROUND_UP 0 Away from zero. - // ROUND_DOWN 1 Towards zero. - // ROUND_CEIL 2 Towards +Infinity. - // ROUND_FLOOR 3 Towards -Infinity. - // ROUND_HALF_UP 4 Towards nearest neighbour. If equidistant, up. - // ROUND_HALF_DOWN 5 Towards nearest neighbour. If equidistant, down. - // ROUND_HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour. - // ROUND_HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity. - // ROUND_HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity. - // - // E.g. - // `Decimal.rounding = 4;` - // `Decimal.rounding = Decimal.ROUND_HALF_UP;` - rounding: 4, // 0 to 8 - - // The modulo mode used when calculating the modulus: a mod n. - // The quotient (q = a / n) is calculated according to the corresponding rounding mode. - // The remainder (r) is calculated as: r = a - n * q. - // - // UP 0 The remainder is positive if the dividend is negative, else is negative. - // DOWN 1 The remainder has the same sign as the dividend (JavaScript %). - // FLOOR 3 The remainder has the same sign as the divisor (Python %). - // HALF_EVEN 6 The IEEE 754 remainder function. - // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)). Always positive. - // - // Truncated division (1), floored division (3), the IEEE 754 remainder (6), and Euclidian - // division (9) are commonly used for the modulus operation. The other rounding modes can also - // be used, but they may not give useful results. - modulo: 1, // 0 to 9 - - // The exponent value at and beneath which `toString` returns exponential notation. - // JavaScript numbers: -7 - toExpNeg: -7, // 0 to -EXP_LIMIT - - // The exponent value at and above which `toString` returns exponential notation. - // JavaScript numbers: 21 - toExpPos: 21, // 0 to EXP_LIMIT - - // The minimum exponent value, beneath which underflow to zero occurs. - // JavaScript numbers: -324 (5e-324) - minE: -EXP_LIMIT, // -1 to -EXP_LIMIT - - // The maximum exponent value, above which overflow to Infinity occurs. - // JavaScript numbers: 308 (1.7976931348623157e+308) - maxE: EXP_LIMIT, // 1 to EXP_LIMIT - - // Whether to use cryptographically-secure random number generation, if available. - crypto: false, // true/false - }, - // ----------------------------------- END OF EDITABLE DEFAULTS ------------------------------- // - - Decimal, - inexact, - noConflict, - quadrant, - external = true, - decimalError = '[DecimalError] ', - invalidArgument = decimalError + 'Invalid argument: ', - precisionLimitExceeded = decimalError + 'Precision limit exceeded', - cryptoUnavailable = decimalError + 'crypto unavailable', - tag = '[object Decimal]', - mathfloor = Math.floor, - mathpow = Math.pow, - isBinary = /^0b([01]+(\.[01]*)?|\.[01]+)(p[+-]?\d+)?$/i, - isHex = /^0x([0-9a-f]+(\.[0-9a-f]*)?|\.[0-9a-f]+)(p[+-]?\d+)?$/i, - isOctal = /^0o([0-7]+(\.[0-7]*)?|\.[0-7]+)(p[+-]?\d+)?$/i, - isDecimal = /^(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i, - BASE = 1e7, - LOG_BASE = 7, - MAX_SAFE_INTEGER = 9007199254740991, - LN10_PRECISION = LN10.length - 1, - PI_PRECISION = PI.length - 1, - // Decimal.prototype object - P = { toStringTag: tag } - - // Decimal prototype methods - - /* - * absoluteValue abs - * ceil - * clampedTo clamp - * comparedTo cmp - * cosine cos - * cubeRoot cbrt - * decimalPlaces dp - * dividedBy div - * dividedToIntegerBy divToInt - * equals eq - * floor - * greaterThan gt - * greaterThanOrEqualTo gte - * hyperbolicCosine cosh - * hyperbolicSine sinh - * hyperbolicTangent tanh - * inverseCosine acos - * inverseHyperbolicCosine acosh - * inverseHyperbolicSine asinh - * inverseHyperbolicTangent atanh - * inverseSine asin - * inverseTangent atan - * isFinite - * isInteger isInt - * isNaN - * isNegative isNeg - * isPositive isPos - * isZero - * lessThan lt - * lessThanOrEqualTo lte - * logarithm log - * [maximum] [max] - * [minimum] [min] - * minus sub - * modulo mod - * naturalExponential exp - * naturalLogarithm ln - * negated neg - * plus add - * precision sd - * round - * sine sin - * squareRoot sqrt - * tangent tan - * times mul - * toBinary - * toDecimalPlaces toDP - * toExponential - * toFixed - * toFraction - * toHexadecimal toHex - * toNearest - * toNumber - * toOctal - * toPower pow - * toPrecision - * toSignificantDigits toSD - * toString - * truncated trunc - * valueOf toJSON - */ - - /* - * Return a new Decimal whose value is the absolute value of this Decimal. - * - */ - P.absoluteValue = P.abs = function () { - var x = new this.constructor(this) - if (x.s < 0) x.s = 1 - return finalise(x) - } - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of positive Infinity. - * - */ - P.ceil = function () { - return finalise(new this.constructor(this), this.e + 1, 2) - } - - /* - * Return a new Decimal whose value is the value of this Decimal clamped to the range - * delineated by `min` and `max`. - * - * min {number|string|Decimal} - * max {number|string|Decimal} - * - */ - P.clampedTo = P.clamp = function (min, max) { - var k, - x = this, - Ctor = x.constructor - min = new Ctor(min) - max = new Ctor(max) - if (!min.s || !max.s) return new Ctor(NaN) - if (min.gt(max)) throw Error(invalidArgument + max) - k = x.cmp(min) - return k < 0 ? min : x.cmp(max) > 0 ? max : new Ctor(x) - } - - /* - * Return - * 1 if the value of this Decimal is greater than the value of `y`, - * -1 if the value of this Decimal is less than the value of `y`, - * 0 if they have the same value, - * NaN if the value of either Decimal is NaN. - * - */ - P.comparedTo = P.cmp = function (y) { - var i, - j, - xdL, - ydL, - x = this, - xd = x.d, - yd = (y = new x.constructor(y)).d, - xs = x.s, - ys = y.s - - // Either NaN or ±Infinity? - if (!xd || !yd) { - return !xs || !ys ? NaN : xs !== ys ? xs : xd === yd ? 0 : !xd ^ (xs < 0) ? 1 : -1 - } - - // Either zero? - if (!xd[0] || !yd[0]) return xd[0] ? xs : yd[0] ? -ys : 0 - - // Signs differ? - if (xs !== ys) return xs - - // Compare exponents. - if (x.e !== y.e) return (x.e > y.e) ^ (xs < 0) ? 1 : -1 - - xdL = xd.length - ydL = yd.length - - // Compare digit by digit. - for (i = 0, j = xdL < ydL ? xdL : ydL; i < j; ++i) { - if (xd[i] !== yd[i]) return (xd[i] > yd[i]) ^ (xs < 0) ? 1 : -1 - } - - // Compare lengths. - return xdL === ydL ? 0 : (xdL > ydL) ^ (xs < 0) ? 1 : -1 - } - - /* - * Return a new Decimal whose value is the cosine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * cos(0) = 1 - * cos(-0) = 1 - * cos(Infinity) = NaN - * cos(-Infinity) = NaN - * cos(NaN) = NaN - * - */ - P.cosine = P.cos = function () { - var pr, - rm, - x = this, - Ctor = x.constructor - - if (!x.d) return new Ctor(NaN) - - // cos(0) = cos(-0) = 1 - if (!x.d[0]) return new Ctor(1) - - pr = Ctor.precision - rm = Ctor.rounding - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE - Ctor.rounding = 1 - - x = cosine(Ctor, toLessThanHalfPi(Ctor, x)) - - Ctor.precision = pr - Ctor.rounding = rm - - return finalise(quadrant == 2 || quadrant == 3 ? x.neg() : x, pr, rm, true) - } - - /* - * - * Return a new Decimal whose value is the cube root of the value of this Decimal, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * cbrt(0) = 0 - * cbrt(-0) = -0 - * cbrt(1) = 1 - * cbrt(-1) = -1 - * cbrt(N) = N - * cbrt(-I) = -I - * cbrt(I) = I - * - * Math.cbrt(x) = (x < 0 ? -Math.pow(-x, 1/3) : Math.pow(x, 1/3)) - * - */ - P.cubeRoot = P.cbrt = function () { - var e, - m, - n, - r, - rep, - s, - sd, - t, - t3, - t3plusx, - x = this, - Ctor = x.constructor - - if (!x.isFinite() || x.isZero()) return new Ctor(x) - external = false - - // Initial estimate. - s = x.s * mathpow(x.s * x, 1 / 3) - - // Math.cbrt underflow/overflow? - // Pass x to Math.pow as integer, then adjust the exponent of the result. - if (!s || Math.abs(s) == 1 / 0) { - n = digitsToString(x.d) - e = x.e - - // Adjust n exponent so it is a multiple of 3 away from x exponent. - if ((s = (e - n.length + 1) % 3)) n += s == 1 || s == -2 ? '0' : '00' - s = mathpow(n, 1 / 3) - - // Rarely, e may be one less than the result exponent value. - e = mathfloor((e + 1) / 3) - (e % 3 == (e < 0 ? -1 : 2)) - - if (s == 1 / 0) { - n = '5e' + e - } else { - n = s.toExponential() - n = n.slice(0, n.indexOf('e') + 1) + e - } - - r = new Ctor(n) - r.s = x.s - } else { - r = new Ctor(s.toString()) - } - - sd = (e = Ctor.precision) + 3 - - // Halley's method. - // TODO? Compare Newton's method. - for (;;) { - t = r - t3 = t.times(t).times(t) - t3plusx = t3.plus(x) - r = divide(t3plusx.plus(x).times(t), t3plusx.plus(t3), sd + 2, 1) - - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1) - - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or 4999 - // , i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || (!rep && n == '4999')) { - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0) - - if (t.times(t).times(t).eq(x)) { - r = t - break - } - } - - sd += 4 - rep = 1 - } else { - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || (!+n.slice(1) && n.charAt(0) == '5')) { - // Truncate to the first rounding digit. - finalise(r, e + 1, 1) - m = !r.times(r).times(r).eq(x) - } - - break - } - } - } - - external = true - - return finalise(r, e, Ctor.rounding, m) - } - - /* - * Return the number of decimal places of the value of this Decimal. - * - */ - P.decimalPlaces = P.dp = function () { - var w, - d = this.d, - n = NaN - - if (d) { - w = d.length - 1 - n = (w - mathfloor(this.e / LOG_BASE)) * LOG_BASE - - // Subtract the number of trailing zeros of the last word. - w = d[w] - if (w) for (; w % 10 == 0; w /= 10) n-- - if (n < 0) n = 0 - } - - return n - } - - /* - * n / 0 = I - * n / N = N - * n / I = 0 - * 0 / n = 0 - * 0 / 0 = N - * 0 / N = N - * 0 / I = 0 - * N / n = N - * N / 0 = N - * N / N = N - * N / I = N - * I / n = I - * I / 0 = I - * I / N = N - * I / I = N - * - * Return a new Decimal whose value is the value of this Decimal divided by `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - */ - P.dividedBy = P.div = function (y) { - return divide(this, new this.constructor(y)) - } - - /* - * Return a new Decimal whose value is the integer part of dividing the value of this Decimal - * by the value of `y`, rounded to `precision` significant digits using rounding mode `rounding`. - * - */ - P.dividedToIntegerBy = P.divToInt = function (y) { - var x = this, - Ctor = x.constructor - return finalise(divide(x, new Ctor(y), 0, 1, 1), Ctor.precision, Ctor.rounding) - } - - /* - * Return true if the value of this Decimal is equal to the value of `y`, otherwise return false. - * - */ - P.equals = P.eq = function (y) { - return this.cmp(y) === 0 - } - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number in the - * direction of negative Infinity. - * - */ - P.floor = function () { - return finalise(new this.constructor(this), this.e + 1, 3) - } - - /* - * Return true if the value of this Decimal is greater than the value of `y`, otherwise return - * false. - * - */ - P.greaterThan = P.gt = function (y) { - return this.cmp(y) > 0 - } - - /* - * Return true if the value of this Decimal is greater than or equal to the value of `y`, - * otherwise return false. - * - */ - P.greaterThanOrEqualTo = P.gte = function (y) { - var k = this.cmp(y) - return k == 1 || k === 0 - } - - /* - * Return a new Decimal whose value is the hyperbolic cosine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [1, Infinity] - * - * cosh(x) = 1 + x^2/2! + x^4/4! + x^6/6! + ... - * - * cosh(0) = 1 - * cosh(-0) = 1 - * cosh(Infinity) = Infinity - * cosh(-Infinity) = Infinity - * cosh(NaN) = NaN - * - * x time taken (ms) result - * 1000 9 9.8503555700852349694e+433 - * 10000 25 4.4034091128314607936e+4342 - * 100000 171 1.4033316802130615897e+43429 - * 1000000 3817 1.5166076984010437725e+434294 - * 10000000 abandoned after 2 minute wait - * - * TODO? Compare performance of cosh(x) = 0.5 * (exp(x) + exp(-x)) - * - */ - P.hyperbolicCosine = P.cosh = function () { - var k, - n, - pr, - rm, - len, - x = this, - Ctor = x.constructor, - one = new Ctor(1) - - if (!x.isFinite()) return new Ctor(x.s ? 1 / 0 : NaN) - if (x.isZero()) return one - - pr = Ctor.precision - rm = Ctor.rounding - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4 - Ctor.rounding = 1 - len = x.d.length - - // Argument reduction: cos(4x) = 1 - 8cos^2(x) + 8cos^4(x) + 1 - // i.e. cos(x) = 1 - cos^2(x/4)(8 - 8cos^2(x/4)) - - // Estimate the optimum number of times to use the argument reduction. - // TODO? Estimation reused from cosine() and may not be optimal here. - if (len < 32) { - k = Math.ceil(len / 3) - n = (1 / tinyPow(4, k)).toString() - } else { - k = 16 - n = '2.3283064365386962890625e-10' - } - - x = taylorSeries(Ctor, 1, x.times(n), new Ctor(1), true) - - // Reverse argument reduction - var cosh2_x, - i = k, - d8 = new Ctor(8) - for (; i--; ) { - cosh2_x = x.times(x) - x = one.minus(cosh2_x.times(d8.minus(cosh2_x.times(d8)))) - } - - return finalise(x, (Ctor.precision = pr), (Ctor.rounding = rm), true) - } - - /* - * Return a new Decimal whose value is the hyperbolic sine of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * sinh(x) = x + x^3/3! + x^5/5! + x^7/7! + ... - * - * sinh(0) = 0 - * sinh(-0) = -0 - * sinh(Infinity) = Infinity - * sinh(-Infinity) = -Infinity - * sinh(NaN) = NaN - * - * x time taken (ms) - * 10 2 ms - * 100 5 ms - * 1000 14 ms - * 10000 82 ms - * 100000 886 ms 1.4033316802130615897e+43429 - * 200000 2613 ms - * 300000 5407 ms - * 400000 8824 ms - * 500000 13026 ms 8.7080643612718084129e+217146 - * 1000000 48543 ms - * - * TODO? Compare performance of sinh(x) = 0.5 * (exp(x) - exp(-x)) - * - */ - P.hyperbolicSine = P.sinh = function () { - var k, - pr, - rm, - len, - x = this, - Ctor = x.constructor - - if (!x.isFinite() || x.isZero()) return new Ctor(x) - - pr = Ctor.precision - rm = Ctor.rounding - Ctor.precision = pr + Math.max(x.e, x.sd()) + 4 - Ctor.rounding = 1 - len = x.d.length - - if (len < 3) { - x = taylorSeries(Ctor, 2, x, x, true) - } else { - // Alternative argument reduction: sinh(3x) = sinh(x)(3 + 4sinh^2(x)) - // i.e. sinh(x) = sinh(x/3)(3 + 4sinh^2(x/3)) - // 3 multiplications and 1 addition - - // Argument reduction: sinh(5x) = sinh(x)(5 + sinh^2(x)(20 + 16sinh^2(x))) - // i.e. sinh(x) = sinh(x/5)(5 + sinh^2(x/5)(20 + 16sinh^2(x/5))) - // 4 multiplications and 2 additions - - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len) - k = k > 16 ? 16 : k | 0 - - x = x.times(1 / tinyPow(5, k)) - x = taylorSeries(Ctor, 2, x, x, true) - - // Reverse argument reduction - var sinh2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20) - for (; k--; ) { - sinh2_x = x.times(x) - x = x.times(d5.plus(sinh2_x.times(d16.times(sinh2_x).plus(d20)))) - } - } - - Ctor.precision = pr - Ctor.rounding = rm - - return finalise(x, pr, rm, true) - } - - /* - * Return a new Decimal whose value is the hyperbolic tangent of the value in radians of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * tanh(x) = sinh(x) / cosh(x) - * - * tanh(0) = 0 - * tanh(-0) = -0 - * tanh(Infinity) = 1 - * tanh(-Infinity) = -1 - * tanh(NaN) = NaN - * - */ - P.hyperbolicTangent = P.tanh = function () { - var pr, - rm, - x = this, - Ctor = x.constructor - - if (!x.isFinite()) return new Ctor(x.s) - if (x.isZero()) return new Ctor(x) - - pr = Ctor.precision - rm = Ctor.rounding - Ctor.precision = pr + 7 - Ctor.rounding = 1 - - return divide(x.sinh(), x.cosh(), (Ctor.precision = pr), (Ctor.rounding = rm)) - } - - /* - * Return a new Decimal whose value is the arccosine (inverse cosine) in radians of the value of - * this Decimal. - * - * Domain: [-1, 1] - * Range: [0, pi] - * - * acos(x) = pi/2 - asin(x) - * - * acos(0) = pi/2 - * acos(-0) = pi/2 - * acos(1) = 0 - * acos(-1) = pi - * acos(1/2) = pi/3 - * acos(-1/2) = 2*pi/3 - * acos(|x| > 1) = NaN - * acos(NaN) = NaN - * - */ - P.inverseCosine = P.acos = function () { - var halfPi, - x = this, - Ctor = x.constructor, - k = x.abs().cmp(1), - pr = Ctor.precision, - rm = Ctor.rounding - - if (k !== -1) { - return k === 0 - ? // |x| is 1 - x.isNeg() - ? getPi(Ctor, pr, rm) - : new Ctor(0) - : // |x| > 1 or x is NaN - new Ctor(NaN) - } - - if (x.isZero()) return getPi(Ctor, pr + 4, rm).times(0.5) - - // TODO? Special case acos(0.5) = pi/3 and acos(-0.5) = 2*pi/3 - - Ctor.precision = pr + 6 - Ctor.rounding = 1 - - x = x.asin() - halfPi = getPi(Ctor, pr + 4, rm).times(0.5) - - Ctor.precision = pr - Ctor.rounding = rm - - return halfPi.minus(x) - } - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine in radians of the - * value of this Decimal. - * - * Domain: [1, Infinity] - * Range: [0, Infinity] - * - * acosh(x) = ln(x + sqrt(x^2 - 1)) - * - * acosh(x < 1) = NaN - * acosh(NaN) = NaN - * acosh(Infinity) = Infinity - * acosh(-Infinity) = NaN - * acosh(0) = NaN - * acosh(-0) = NaN - * acosh(1) = 0 - * acosh(-1) = NaN - * - */ - P.inverseHyperbolicCosine = P.acosh = function () { - var pr, - rm, - x = this, - Ctor = x.constructor - - if (x.lte(1)) return new Ctor(x.eq(1) ? 0 : NaN) - if (!x.isFinite()) return new Ctor(x) - - pr = Ctor.precision - rm = Ctor.rounding - Ctor.precision = pr + Math.max(Math.abs(x.e), x.sd()) + 4 - Ctor.rounding = 1 - external = false - - x = x.times(x).minus(1).sqrt().plus(x) - - external = true - Ctor.precision = pr - Ctor.rounding = rm - - return x.ln() - } - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic sine in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * asinh(x) = ln(x + sqrt(x^2 + 1)) - * - * asinh(NaN) = NaN - * asinh(Infinity) = Infinity - * asinh(-Infinity) = -Infinity - * asinh(0) = 0 - * asinh(-0) = -0 - * - */ - P.inverseHyperbolicSine = P.asinh = function () { - var pr, - rm, - x = this, - Ctor = x.constructor - - if (!x.isFinite() || x.isZero()) return new Ctor(x) - - pr = Ctor.precision - rm = Ctor.rounding - Ctor.precision = pr + 2 * Math.max(Math.abs(x.e), x.sd()) + 6 - Ctor.rounding = 1 - external = false - - x = x.times(x).plus(1).sqrt().plus(x) - - external = true - Ctor.precision = pr - Ctor.rounding = rm - - return x.ln() - } - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent in radians of the - * value of this Decimal. - * - * Domain: [-1, 1] - * Range: [-Infinity, Infinity] - * - * atanh(x) = 0.5 * ln((1 + x) / (1 - x)) - * - * atanh(|x| > 1) = NaN - * atanh(NaN) = NaN - * atanh(Infinity) = NaN - * atanh(-Infinity) = NaN - * atanh(0) = 0 - * atanh(-0) = -0 - * atanh(1) = Infinity - * atanh(-1) = -Infinity - * - */ - P.inverseHyperbolicTangent = P.atanh = function () { - var pr, - rm, - wpr, - xsd, - x = this, - Ctor = x.constructor - - if (!x.isFinite()) return new Ctor(NaN) - if (x.e >= 0) return new Ctor(x.abs().eq(1) ? x.s / 0 : x.isZero() ? x : NaN) - - pr = Ctor.precision - rm = Ctor.rounding - xsd = x.sd() - - if (Math.max(xsd, pr) < 2 * -x.e - 1) return finalise(new Ctor(x), pr, rm, true) - - Ctor.precision = wpr = xsd - x.e - - x = divide(x.plus(1), new Ctor(1).minus(x), wpr + pr, 1) - - Ctor.precision = pr + 4 - Ctor.rounding = 1 - - x = x.ln() - - Ctor.precision = pr - Ctor.rounding = rm - - return x.times(0.5) - } - - /* - * Return a new Decimal whose value is the arcsine (inverse sine) in radians of the value of this - * Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * asin(x) = 2*atan(x/(1 + sqrt(1 - x^2))) - * - * asin(0) = 0 - * asin(-0) = -0 - * asin(1/2) = pi/6 - * asin(-1/2) = -pi/6 - * asin(1) = pi/2 - * asin(-1) = -pi/2 - * asin(|x| > 1) = NaN - * asin(NaN) = NaN - * - * TODO? Compare performance of Taylor series. - * - */ - P.inverseSine = P.asin = function () { - var halfPi, - k, - pr, - rm, - x = this, - Ctor = x.constructor - - if (x.isZero()) return new Ctor(x) - - k = x.abs().cmp(1) - pr = Ctor.precision - rm = Ctor.rounding - - if (k !== -1) { - // |x| is 1 - if (k === 0) { - halfPi = getPi(Ctor, pr + 4, rm).times(0.5) - halfPi.s = x.s - return halfPi - } - - // |x| > 1 or x is NaN - return new Ctor(NaN) - } - - // TODO? Special case asin(1/2) = pi/6 and asin(-1/2) = -pi/6 - - Ctor.precision = pr + 6 - Ctor.rounding = 1 - - x = x.div(new Ctor(1).minus(x.times(x)).sqrt().plus(1)).atan() - - Ctor.precision = pr - Ctor.rounding = rm - - return x.times(2) - } - - /* - * Return a new Decimal whose value is the arctangent (inverse tangent) in radians of the value - * of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi/2, pi/2] - * - * atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - * - * atan(0) = 0 - * atan(-0) = -0 - * atan(1) = pi/4 - * atan(-1) = -pi/4 - * atan(Infinity) = pi/2 - * atan(-Infinity) = -pi/2 - * atan(NaN) = NaN - * - */ - P.inverseTangent = P.atan = function () { - var i, - j, - k, - n, - px, - t, - r, - wpr, - x2, - x = this, - Ctor = x.constructor, - pr = Ctor.precision, - rm = Ctor.rounding - - if (!x.isFinite()) { - if (!x.s) return new Ctor(NaN) - if (pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.5) - r.s = x.s - return r - } - } else if (x.isZero()) { - return new Ctor(x) - } else if (x.abs().eq(1) && pr + 4 <= PI_PRECISION) { - r = getPi(Ctor, pr + 4, rm).times(0.25) - r.s = x.s - return r - } - - Ctor.precision = wpr = pr + 10 - Ctor.rounding = 1 - - // TODO? if (x >= 1 && pr <= PI_PRECISION) atan(x) = halfPi * x.s - atan(1 / x); - - // Argument reduction - // Ensure |x| < 0.42 - // atan(x) = 2 * atan(x / (1 + sqrt(1 + x^2))) - - k = Math.min(28, (wpr / LOG_BASE + 2) | 0) - - for (i = k; i; --i) x = x.div(x.times(x).plus(1).sqrt().plus(1)) - - external = false - - j = Math.ceil(wpr / LOG_BASE) - n = 1 - x2 = x.times(x) - r = new Ctor(x) - px = x - - // atan(x) = x - x^3/3 + x^5/5 - x^7/7 + ... - for (; i !== -1; ) { - px = px.times(x2) - t = r.minus(px.div((n += 2))) - - px = px.times(x2) - r = t.plus(px.div((n += 2))) - - if (r.d[j] !== void 0) for (i = j; r.d[i] === t.d[i] && i--; ); - } - - if (k) r = r.times(2 << (k - 1)) - - external = true - - return finalise(r, (Ctor.precision = pr), (Ctor.rounding = rm), true) - } - - /* - * Return true if the value of this Decimal is a finite number, otherwise return false. - * - */ - P.isFinite = function () { - return !!this.d - } - - /* - * Return true if the value of this Decimal is an integer, otherwise return false. - * - */ - P.isInteger = P.isInt = function () { - return !!this.d && mathfloor(this.e / LOG_BASE) > this.d.length - 2 - } - - /* - * Return true if the value of this Decimal is NaN, otherwise return false. - * - */ - P.isNaN = function () { - return !this.s - } - - /* - * Return true if the value of this Decimal is negative, otherwise return false. - * - */ - P.isNegative = P.isNeg = function () { - return this.s < 0 - } - - /* - * Return true if the value of this Decimal is positive, otherwise return false. - * - */ - P.isPositive = P.isPos = function () { - return this.s > 0 - } - - /* - * Return true if the value of this Decimal is 0 or -0, otherwise return false. - * - */ - P.isZero = function () { - return !!this.d && this.d[0] === 0 - } - - /* - * Return true if the value of this Decimal is less than `y`, otherwise return false. - * - */ - P.lessThan = P.lt = function (y) { - return this.cmp(y) < 0 - } - - /* - * Return true if the value of this Decimal is less than or equal to `y`, otherwise return false. - * - */ - P.lessThanOrEqualTo = P.lte = function (y) { - return this.cmp(y) < 1 - } - - /* - * Return the logarithm of the value of this Decimal to the specified base, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * If no base is specified, return log[10](arg). - * - * log[base](arg) = ln(arg) / ln(base) - * - * The result will always be correctly rounded if the base of the log is 10, and 'almost always' - * otherwise: - * - * Depending on the rounding mode, the result may be incorrectly rounded if the first fifteen - * rounding digits are [49]99999999999999 or [50]00000000000000. In that case, the maximum error - * between the result and the correctly rounded result will be one ulp (unit in the last place). - * - * log[-b](a) = NaN - * log[0](a) = NaN - * log[1](a) = NaN - * log[NaN](a) = NaN - * log[Infinity](a) = NaN - * log[b](0) = -Infinity - * log[b](-0) = -Infinity - * log[b](-a) = NaN - * log[b](1) = 0 - * log[b](Infinity) = Infinity - * log[b](NaN) = NaN - * - * [base] {number|string|Decimal} The base of the logarithm. - * - */ - P.logarithm = P.log = function (base) { - var isBase10, - d, - denominator, - k, - inf, - num, - sd, - r, - arg = this, - Ctor = arg.constructor, - pr = Ctor.precision, - rm = Ctor.rounding, - guard = 5 - - // Default base is 10. - if (base == null) { - base = new Ctor(10) - isBase10 = true - } else { - base = new Ctor(base) - d = base.d - - // Return NaN if base is negative, or non-finite, or is 0 or 1. - if (base.s < 0 || !d || !d[0] || base.eq(1)) return new Ctor(NaN) - - isBase10 = base.eq(10) - } - - d = arg.d - - // Is arg negative, non-finite, 0 or 1? - if (arg.s < 0 || !d || !d[0] || arg.eq(1)) { - return new Ctor(d && !d[0] ? -1 / 0 : arg.s != 1 ? NaN : d ? 0 : 1 / 0) - } - - // The result will have a non-terminating decimal expansion if base is 10 and arg is not an - // integer power of 10. - if (isBase10) { - if (d.length > 1) { - inf = true - } else { - for (k = d[0]; k % 10 === 0; ) k /= 10 - inf = k !== 1 - } - } - - external = false - sd = pr + guard - num = naturalLogarithm(arg, sd) - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd) - - // The result will have 5 rounding digits. - r = divide(num, denominator, sd, 1) - - // If at a rounding boundary, i.e. the result's rounding digits are [49]9999 or [50]0000, - // calculate 10 further digits. - // - // If the result is known to have an infinite decimal expansion, repeat this until it is clear - // that the result is above or below the boundary. Otherwise, if after calculating the 10 - // further digits, the last 14 are nines, round up and assume the result is exact. - // Also assume the result is exact if the last 14 are zero. - // - // Example of a result that will be incorrectly rounded: - // log[1048576](4503599627370502) = 2.60000000000000009610279511444746... - // The above result correctly rounded using ROUND_CEIL to 1 decimal place should be 2.7, but it - // will be given as 2.6 as there are 15 zeros immediately after the requested decimal place, so - // the exact result would be assumed to be 2.6, which rounded using ROUND_CEIL to 1 decimal - // place is still 2.6. - if (checkRoundingDigits(r.d, (k = pr), rm)) { - do { - sd += 10 - num = naturalLogarithm(arg, sd) - denominator = isBase10 ? getLn10(Ctor, sd + 10) : naturalLogarithm(base, sd) - r = divide(num, denominator, sd, 1) - - if (!inf) { - // Check for 14 nines from the 2nd rounding digit, as the first may be 4. - if (+digitsToString(r.d).slice(k + 1, k + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0) - } - - break - } - } while (checkRoundingDigits(r.d, (k += 10), rm)) - } - - external = true - - return finalise(r, pr, rm) - } - - /* - * Return a new Decimal whose value is the maximum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * - P.max = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'lt'); - }; - */ - - /* - * Return a new Decimal whose value is the minimum of the arguments and the value of this Decimal. - * - * arguments {number|string|Decimal} - * - P.min = function () { - Array.prototype.push.call(arguments, this); - return maxOrMin(this.constructor, arguments, 'gt'); - }; - */ - - /* - * n - 0 = n - * n - N = N - * n - I = -I - * 0 - n = -n - * 0 - 0 = 0 - * 0 - N = N - * 0 - I = -I - * N - n = N - * N - 0 = N - * N - N = N - * N - I = N - * I - n = I - * I - 0 = I - * I - N = N - * I - I = N - * - * Return a new Decimal whose value is the value of this Decimal minus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.minus = P.sub = function (y) { - var d, - e, - i, - j, - k, - len, - pr, - rm, - xd, - xe, - xLTy, - yd, - x = this, - Ctor = x.constructor - - y = new Ctor(y) - - // If either is not finite... - if (!x.d || !y.d) { - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN) - // Return y negated if x is finite and y is ±Infinity. - else if (x.d) y.s = -y.s - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with different signs. - // Return NaN if both are ±Infinity with the same sign. - else y = new Ctor(y.d || x.s !== y.s ? x : NaN) - - return y - } - - // If signs differ... - if (x.s != y.s) { - y.s = -y.s - return x.plus(y) - } - - xd = x.d - yd = y.d - pr = Ctor.precision - rm = Ctor.rounding - - // If either is zero... - if (!xd[0] || !yd[0]) { - // Return y negated if x is zero and y is non-zero. - if (yd[0]) y.s = -y.s - // Return x if y is zero and x is non-zero. - else if (xd[0]) y = new Ctor(x) - // Return zero if both are zero. - // From IEEE 754 (2008) 6.3: 0 - 0 = -0 - -0 = -0 when rounding to -Infinity. - else return new Ctor(rm === 3 ? -0 : 0) - - return external ? finalise(y, pr, rm) : y - } - - // x and y are finite, non-zero numbers with the same sign. - - // Calculate base 1e7 exponents. - e = mathfloor(y.e / LOG_BASE) - xe = mathfloor(x.e / LOG_BASE) - - xd = xd.slice() - k = xe - e - - // If base 1e7 exponents differ... - if (k) { - xLTy = k < 0 - - if (xLTy) { - d = xd - k = -k - len = yd.length - } else { - d = yd - e = xe - len = xd.length - } - - // Numbers with massively different exponents would result in a very high number of - // zeros needing to be prepended, but this can be avoided while still ensuring correct - // rounding by limiting the number of zeros to `Math.ceil(pr / LOG_BASE) + 2`. - i = Math.max(Math.ceil(pr / LOG_BASE), len) + 2 - - if (k > i) { - k = i - d.length = 1 - } - - // Prepend zeros to equalise exponents. - d.reverse() - for (i = k; i--; ) d.push(0) - d.reverse() - - // Base 1e7 exponents equal. - } else { - // Check digits to determine which is the bigger number. - - i = xd.length - len = yd.length - xLTy = i < len - if (xLTy) len = i - - for (i = 0; i < len; i++) { - if (xd[i] != yd[i]) { - xLTy = xd[i] < yd[i] - break - } - } - - k = 0 - } - - if (xLTy) { - d = xd - xd = yd - yd = d - y.s = -y.s - } - - len = xd.length - - // Append zeros to `xd` if shorter. - // Don't add zeros to `yd` if shorter as subtraction only needs to start at `yd` length. - for (i = yd.length - len; i > 0; --i) xd[len++] = 0 - - // Subtract yd from xd. - for (i = yd.length; i > k; ) { - if (xd[--i] < yd[i]) { - for (j = i; j && xd[--j] === 0; ) xd[j] = BASE - 1 - --xd[j] - xd[i] += BASE - } - - xd[i] -= yd[i] - } - - // Remove trailing zeros. - for (; xd[--len] === 0; ) xd.pop() - - // Remove leading zeros and adjust exponent accordingly. - for (; xd[0] === 0; xd.shift()) --e - - // Zero? - if (!xd[0]) return new Ctor(rm === 3 ? -0 : 0) - - y.d = xd - y.e = getBase10Exponent(xd, e) - - return external ? finalise(y, pr, rm) : y - } - - /* - * n % 0 = N - * n % N = N - * n % I = n - * 0 % n = 0 - * -0 % n = -0 - * 0 % 0 = N - * 0 % N = N - * 0 % I = 0 - * N % n = N - * N % 0 = N - * N % N = N - * N % I = N - * I % n = N - * I % 0 = N - * I % N = N - * I % I = N - * - * Return a new Decimal whose value is the value of this Decimal modulo `y`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * The result depends on the modulo mode. - * - */ - P.modulo = P.mod = function (y) { - var q, - x = this, - Ctor = x.constructor - - y = new Ctor(y) - - // Return NaN if x is ±Infinity or NaN, or y is NaN or ±0. - if (!x.d || !y.s || (y.d && !y.d[0])) return new Ctor(NaN) - - // Return x if y is ±Infinity or x is ±0. - if (!y.d || (x.d && !x.d[0])) { - return finalise(new Ctor(x), Ctor.precision, Ctor.rounding) - } - - // Prevent rounding of intermediate calculations. - external = false - - if (Ctor.modulo == 9) { - // Euclidian division: q = sign(y) * floor(x / abs(y)) - // result = x - q * y where 0 <= result < abs(y) - q = divide(x, y.abs(), 0, 3, 1) - q.s *= y.s - } else { - q = divide(x, y, 0, Ctor.modulo, 1) - } - - q = q.times(y) - - external = true - - return x.minus(q) - } - - /* - * Return a new Decimal whose value is the natural exponential of the value of this Decimal, - * i.e. the base e raised to the power the value of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.naturalExponential = P.exp = function () { - return naturalExponential(this) - } - - /* - * Return a new Decimal whose value is the natural logarithm of the value of this Decimal, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - */ - P.naturalLogarithm = P.ln = function () { - return naturalLogarithm(this) - } - - /* - * Return a new Decimal whose value is the value of this Decimal negated, i.e. as if multiplied by - * -1. - * - */ - P.negated = P.neg = function () { - var x = new this.constructor(this) - x.s = -x.s - return finalise(x) - } - - /* - * n + 0 = n - * n + N = N - * n + I = I - * 0 + n = n - * 0 + 0 = 0 - * 0 + N = N - * 0 + I = I - * N + n = N - * N + 0 = N - * N + N = N - * N + I = N - * I + n = I - * I + 0 = I - * I + N = N - * I + I = I - * - * Return a new Decimal whose value is the value of this Decimal plus `y`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - */ - P.plus = P.add = function (y) { - var carry, - d, - e, - i, - k, - len, - pr, - rm, - xd, - yd, - x = this, - Ctor = x.constructor - - y = new Ctor(y) - - // If either is not finite... - if (!x.d || !y.d) { - // Return NaN if either is NaN. - if (!x.s || !y.s) y = new Ctor(NaN) - // Return x if y is finite and x is ±Infinity. - // Return x if both are ±Infinity with the same sign. - // Return NaN if both are ±Infinity with different signs. - // Return y if x is finite and y is ±Infinity. - else if (!x.d) y = new Ctor(y.d || x.s === y.s ? x : NaN) - - return y - } - - // If signs differ... - if (x.s != y.s) { - y.s = -y.s - return x.minus(y) - } - - xd = x.d - yd = y.d - pr = Ctor.precision - rm = Ctor.rounding - - // If either is zero... - if (!xd[0] || !yd[0]) { - // Return x if y is zero. - // Return y if y is non-zero. - if (!yd[0]) y = new Ctor(x) - - return external ? finalise(y, pr, rm) : y - } - - // x and y are finite, non-zero numbers with the same sign. - - // Calculate base 1e7 exponents. - k = mathfloor(x.e / LOG_BASE) - e = mathfloor(y.e / LOG_BASE) - - xd = xd.slice() - i = k - e - - // If base 1e7 exponents differ... - if (i) { - if (i < 0) { - d = xd - i = -i - len = yd.length - } else { - d = yd - e = k - len = xd.length - } - - // Limit number of zeros prepended to max(ceil(pr / LOG_BASE), len) + 1. - k = Math.ceil(pr / LOG_BASE) - len = k > len ? k + 1 : len + 1 - - if (i > len) { - i = len - d.length = 1 - } - - // Prepend zeros to equalise exponents. Note: Faster to use reverse then do unshifts. - d.reverse() - for (; i--; ) d.push(0) - d.reverse() - } - - len = xd.length - i = yd.length - - // If yd is longer than xd, swap xd and yd so xd points to the longer array. - if (len - i < 0) { - i = len - d = yd - yd = xd - xd = d - } - - // Only start adding at yd.length - 1 as the further digits of xd can be left as they are. - for (carry = 0; i; ) { - carry = ((xd[--i] = xd[i] + yd[i] + carry) / BASE) | 0 - xd[i] %= BASE - } - - if (carry) { - xd.unshift(carry) - ++e - } - - // Remove trailing zeros. - // No need to check for zero, as +x + +y != 0 && -x + -y != 0 - for (len = xd.length; xd[--len] == 0; ) xd.pop() - - y.d = xd - y.e = getBase10Exponent(xd, e) - - return external ? finalise(y, pr, rm) : y - } - - /* - * Return the number of significant digits of the value of this Decimal. - * - * [z] {boolean|number} Whether to count integer-part trailing zeros: true, false, 1 or 0. - * - */ - P.precision = P.sd = function (z) { - var k, - x = this - - if (z !== void 0 && z !== !!z && z !== 1 && z !== 0) throw Error(invalidArgument + z) - - if (x.d) { - k = getPrecision(x.d) - if (z && x.e + 1 > k) k = x.e + 1 - } else { - k = NaN - } - - return k - } - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a whole number using - * rounding mode `rounding`. - * - */ - P.round = function () { - var x = this, - Ctor = x.constructor - - return finalise(new Ctor(x), x.e + 1, Ctor.rounding) - } - - /* - * Return a new Decimal whose value is the sine of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-1, 1] - * - * sin(x) = x - x^3/3! + x^5/5! - ... - * - * sin(0) = 0 - * sin(-0) = -0 - * sin(Infinity) = NaN - * sin(-Infinity) = NaN - * sin(NaN) = NaN - * - */ - P.sine = P.sin = function () { - var pr, - rm, - x = this, - Ctor = x.constructor - - if (!x.isFinite()) return new Ctor(NaN) - if (x.isZero()) return new Ctor(x) - - pr = Ctor.precision - rm = Ctor.rounding - Ctor.precision = pr + Math.max(x.e, x.sd()) + LOG_BASE - Ctor.rounding = 1 - - x = sine(Ctor, toLessThanHalfPi(Ctor, x)) - - Ctor.precision = pr - Ctor.rounding = rm - - return finalise(quadrant > 2 ? x.neg() : x, pr, rm, true) - } - - /* - * Return a new Decimal whose value is the square root of this Decimal, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * sqrt(-n) = N - * sqrt(N) = N - * sqrt(-I) = N - * sqrt(I) = I - * sqrt(0) = 0 - * sqrt(-0) = -0 - * - */ - P.squareRoot = P.sqrt = function () { - var m, - n, - sd, - r, - rep, - t, - x = this, - d = x.d, - e = x.e, - s = x.s, - Ctor = x.constructor - - // Negative/NaN/Infinity/zero? - if (s !== 1 || !d || !d[0]) { - return new Ctor(!s || (s < 0 && (!d || d[0])) ? NaN : d ? x : 1 / 0) - } - - external = false - - // Initial estimate. - s = Math.sqrt(+x) - - // Math.sqrt underflow/overflow? - // Pass x to Math.sqrt as integer, then adjust the exponent of the result. - if (s == 0 || s == 1 / 0) { - n = digitsToString(d) - - if ((n.length + e) % 2 == 0) n += '0' - s = Math.sqrt(n) - e = mathfloor((e + 1) / 2) - (e < 0 || e % 2) - - if (s == 1 / 0) { - n = '5e' + e - } else { - n = s.toExponential() - n = n.slice(0, n.indexOf('e') + 1) + e - } - - r = new Ctor(n) - } else { - r = new Ctor(s.toString()) - } - - sd = (e = Ctor.precision) + 3 - - // Newton-Raphson iteration. - for (;;) { - t = r - r = t.plus(divide(x, t, sd + 2, 1)).times(0.5) - - // TODO? Replace with for-loop and checkRoundingDigits. - if (digitsToString(t.d).slice(0, sd) === (n = digitsToString(r.d)).slice(0, sd)) { - n = n.slice(sd - 3, sd + 1) - - // The 4th rounding digit may be in error by -1 so if the 4 rounding digits are 9999 or - // 4999, i.e. approaching a rounding boundary, continue the iteration. - if (n == '9999' || (!rep && n == '4999')) { - // On the first iteration only, check to see if rounding up gives the exact result as the - // nines may infinitely repeat. - if (!rep) { - finalise(t, e + 1, 0) - - if (t.times(t).eq(x)) { - r = t - break - } - } - - sd += 4 - rep = 1 - } else { - // If the rounding digits are null, 0{0,4} or 50{0,3}, check for an exact result. - // If not, then there are further digits and m will be truthy. - if (!+n || (!+n.slice(1) && n.charAt(0) == '5')) { - // Truncate to the first rounding digit. - finalise(r, e + 1, 1) - m = !r.times(r).eq(x) - } - - break - } - } - } - - external = true - - return finalise(r, e, Ctor.rounding, m) - } - - /* - * Return a new Decimal whose value is the tangent of the value in radians of this Decimal. - * - * Domain: [-Infinity, Infinity] - * Range: [-Infinity, Infinity] - * - * tan(0) = 0 - * tan(-0) = -0 - * tan(Infinity) = NaN - * tan(-Infinity) = NaN - * tan(NaN) = NaN - * - */ - P.tangent = P.tan = function () { - var pr, - rm, - x = this, - Ctor = x.constructor - - if (!x.isFinite()) return new Ctor(NaN) - if (x.isZero()) return new Ctor(x) - - pr = Ctor.precision - rm = Ctor.rounding - Ctor.precision = pr + 10 - Ctor.rounding = 1 - - x = x.sin() - x.s = 1 - x = divide(x, new Ctor(1).minus(x.times(x)).sqrt(), pr + 10, 0) - - Ctor.precision = pr - Ctor.rounding = rm - - return finalise(quadrant == 2 || quadrant == 4 ? x.neg() : x, pr, rm, true) - } - - /* - * n * 0 = 0 - * n * N = N - * n * I = I - * 0 * n = 0 - * 0 * 0 = 0 - * 0 * N = N - * 0 * I = N - * N * n = N - * N * 0 = N - * N * N = N - * N * I = N - * I * n = I - * I * 0 = N - * I * N = N - * I * I = I - * - * Return a new Decimal whose value is this Decimal times `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - */ - P.times = P.mul = function (y) { - var carry, - e, - i, - k, - r, - rL, - t, - xdL, - ydL, - x = this, - Ctor = x.constructor, - xd = x.d, - yd = (y = new Ctor(y)).d - - y.s *= x.s - - // If either is NaN, ±Infinity or ±0... - if (!xd || !xd[0] || !yd || !yd[0]) { - return new Ctor( - !y.s || (xd && !xd[0] && !yd) || (yd && !yd[0] && !xd) - ? // Return NaN if either is NaN. - // Return NaN if x is ±0 and y is ±Infinity, or y is ±0 and x is ±Infinity. - NaN - : // Return ±Infinity if either is ±Infinity. - // Return ±0 if either is ±0. - !xd || !yd - ? y.s / 0 - : y.s * 0 - ) - } - - e = mathfloor(x.e / LOG_BASE) + mathfloor(y.e / LOG_BASE) - xdL = xd.length - ydL = yd.length - - // Ensure xd points to the longer array. - if (xdL < ydL) { - r = xd - xd = yd - yd = r - rL = xdL - xdL = ydL - ydL = rL - } - - // Initialise the result array with zeros. - r = [] - rL = xdL + ydL - for (i = rL; i--; ) r.push(0) - - // Multiply! - for (i = ydL; --i >= 0; ) { - carry = 0 - for (k = xdL + i; k > i; ) { - t = r[k] + yd[i] * xd[k - i - 1] + carry - r[k--] = t % BASE | 0 - carry = (t / BASE) | 0 - } - - r[k] = (r[k] + carry) % BASE | 0 - } - - // Remove trailing zeros. - for (; !r[--rL]; ) r.pop() - - if (carry) ++e - else r.shift() - - y.d = r - y.e = getBase10Exponent(r, e) - - return external ? finalise(y, Ctor.precision, Ctor.rounding) : y - } - - /* - * Return a string representing the value of this Decimal in base 2, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toBinary = function (sd, rm) { - return toStringBinary(this, 2, sd, rm) - } - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `dp` - * decimal places using rounding mode `rm` or `rounding` if `rm` is omitted. - * - * If `dp` is omitted, return a new Decimal whose value is the value of this Decimal. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toDecimalPlaces = P.toDP = function (dp, rm) { - var x = this, - Ctor = x.constructor - - x = new Ctor(x) - if (dp === void 0) return x - - checkInt32(dp, 0, MAX_DIGITS) - - if (rm === void 0) rm = Ctor.rounding - else checkInt32(rm, 0, 8) - - return finalise(x, dp + x.e + 1, rm) - } - - /* - * Return a string representing the value of this Decimal in exponential notation rounded to - * `dp` fixed decimal places using rounding mode `rounding`. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toExponential = function (dp, rm) { - var str, - x = this, - Ctor = x.constructor - - if (dp === void 0) { - str = finiteToString(x, true) - } else { - checkInt32(dp, 0, MAX_DIGITS) - - if (rm === void 0) rm = Ctor.rounding - else checkInt32(rm, 0, 8) - - x = finalise(new Ctor(x), dp + 1, rm) - str = finiteToString(x, true, dp + 1) - } - - return x.isNeg() && !x.isZero() ? '-' + str : str - } - - /* - * Return a string representing the value of this Decimal in normal (fixed-point) notation to - * `dp` fixed decimal places and rounded using rounding mode `rm` or `rounding` if `rm` is - * omitted. - * - * As with JavaScript numbers, (-0).toFixed(0) is '0', but e.g. (-0.00001).toFixed(0) is '-0'. - * - * [dp] {number} Decimal places. Integer, 0 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'. - * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'. - * (-0).toFixed(3) is '0.000'. - * (-0.5).toFixed(0) is '-0'. - * - */ - P.toFixed = function (dp, rm) { - var str, - y, - x = this, - Ctor = x.constructor - - if (dp === void 0) { - str = finiteToString(x) - } else { - checkInt32(dp, 0, MAX_DIGITS) - - if (rm === void 0) rm = Ctor.rounding - else checkInt32(rm, 0, 8) - - y = finalise(new Ctor(x), dp + x.e + 1, rm) - str = finiteToString(y, false, dp + y.e + 1) - } - - // To determine whether to add the minus sign look at the value before it was rounded, - // i.e. look at `x` rather than `y`. - return x.isNeg() && !x.isZero() ? '-' + str : str - } - - /* - * Return an array representing the value of this Decimal as a simple fraction with an integer - * numerator and an integer denominator. - * - * The denominator will be a positive non-zero value less than or equal to the specified maximum - * denominator. If a maximum denominator is not specified, the denominator will be the lowest - * value necessary to represent the number exactly. - * - * [maxD] {number|string|Decimal} Maximum denominator. Integer >= 1 and < Infinity. - * - */ - P.toFraction = function (maxD) { - var d, - d0, - d1, - d2, - e, - k, - n, - n0, - n1, - pr, - q, - r, - x = this, - xd = x.d, - Ctor = x.constructor - - if (!xd) return new Ctor(x) - - n1 = d0 = new Ctor(1) - d1 = n0 = new Ctor(0) - - d = new Ctor(d1) - e = d.e = getPrecision(xd) - x.e - 1 - k = e % LOG_BASE - d.d[0] = mathpow(10, k < 0 ? LOG_BASE + k : k) - - if (maxD == null) { - // d is 10**e, the minimum max-denominator needed. - maxD = e > 0 ? d : n1 - } else { - n = new Ctor(maxD) - if (!n.isInt() || n.lt(n1)) throw Error(invalidArgument + n) - maxD = n.gt(d) ? (e > 0 ? d : n1) : n - } - - external = false - n = new Ctor(digitsToString(xd)) - pr = Ctor.precision - Ctor.precision = e = xd.length * LOG_BASE * 2 - - for (;;) { - q = divide(n, d, 0, 1, 1) - d2 = d0.plus(q.times(d1)) - if (d2.cmp(maxD) == 1) break - d0 = d1 - d1 = d2 - d2 = n1 - n1 = n0.plus(q.times(d2)) - n0 = d2 - d2 = d - d = n.minus(q.times(d2)) - n = d2 - } - - d2 = divide(maxD.minus(d0), d1, 0, 1, 1) - n0 = n0.plus(d2.times(n1)) - d0 = d0.plus(d2.times(d1)) - n0.s = n1.s = x.s - - // Determine which fraction is closer to x, n0/d0 or n1/d1? - r = divide(n1, d1, e, 1).minus(x).abs().cmp(divide(n0, d0, e, 1).minus(x).abs()) < 1 ? [n1, d1] : [n0, d0] - - Ctor.precision = pr - external = true - - return r - } - - /* - * Return a string representing the value of this Decimal in base 16, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toHexadecimal = P.toHex = function (sd, rm) { - return toStringBinary(this, 16, sd, rm) - } - - /* - * Returns a new Decimal whose value is the nearest multiple of `y` in the direction of rounding - * mode `rm`, or `Decimal.rounding` if `rm` is omitted, to the value of this Decimal. - * - * The return value will always have the same sign as this Decimal, unless either this Decimal - * or `y` is NaN, in which case the return value will be also be NaN. - * - * The return value is not affected by the value of `precision`. - * - * y {number|string|Decimal} The magnitude to round to a multiple of. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * 'toNearest() rounding mode not an integer: {rm}' - * 'toNearest() rounding mode out of range: {rm}' - * - */ - P.toNearest = function (y, rm) { - var x = this, - Ctor = x.constructor - - x = new Ctor(x) - - if (y == null) { - // If x is not finite, return x. - if (!x.d) return x - - y = new Ctor(1) - rm = Ctor.rounding - } else { - y = new Ctor(y) - if (rm === void 0) { - rm = Ctor.rounding - } else { - checkInt32(rm, 0, 8) - } - - // If x is not finite, return x if y is not NaN, else NaN. - if (!x.d) return y.s ? x : y - - // If y is not finite, return Infinity with the sign of x if y is Infinity, else NaN. - if (!y.d) { - if (y.s) y.s = x.s - return y - } - } - - // If y is not zero, calculate the nearest multiple of y to x. - if (y.d[0]) { - external = false - x = divide(x, y, 0, rm, 1).times(y) - external = true - finalise(x) - - // If y is zero, return zero with the sign of x. - } else { - y.s = x.s - x = y - } - - return x - } - - /* - * Return the value of this Decimal converted to a number primitive. - * Zero keeps its sign. - * - */ - P.toNumber = function () { - return +this - } - - /* - * Return a string representing the value of this Decimal in base 8, round to `sd` significant - * digits using rounding mode `rm`. - * - * If the optional `sd` argument is present then return binary exponential notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toOctal = function (sd, rm) { - return toStringBinary(this, 8, sd, rm) - } - - /* - * Return a new Decimal whose value is the value of this Decimal raised to the power `y`, rounded - * to `precision` significant digits using rounding mode `rounding`. - * - * ECMAScript compliant. - * - * pow(x, NaN) = NaN - * pow(x, ±0) = 1 - - * pow(NaN, non-zero) = NaN - * pow(abs(x) > 1, +Infinity) = +Infinity - * pow(abs(x) > 1, -Infinity) = +0 - * pow(abs(x) == 1, ±Infinity) = NaN - * pow(abs(x) < 1, +Infinity) = +0 - * pow(abs(x) < 1, -Infinity) = +Infinity - * pow(+Infinity, y > 0) = +Infinity - * pow(+Infinity, y < 0) = +0 - * pow(-Infinity, odd integer > 0) = -Infinity - * pow(-Infinity, even integer > 0) = +Infinity - * pow(-Infinity, odd integer < 0) = -0 - * pow(-Infinity, even integer < 0) = +0 - * pow(+0, y > 0) = +0 - * pow(+0, y < 0) = +Infinity - * pow(-0, odd integer > 0) = -0 - * pow(-0, even integer > 0) = +0 - * pow(-0, odd integer < 0) = -Infinity - * pow(-0, even integer < 0) = +Infinity - * pow(finite x < 0, finite non-integer) = NaN - * - * For non-integer or very large exponents pow(x, y) is calculated using - * - * x^y = exp(y*ln(x)) - * - * Assuming the first 15 rounding digits are each equally likely to be any digit 0-9, the - * probability of an incorrectly rounded result - * P([49]9{14} | [50]0{14}) = 2 * 0.2 * 10^-14 = 4e-15 = 1/2.5e+14 - * i.e. 1 in 250,000,000,000,000 - * - * If a result is incorrectly rounded the maximum error will be 1 ulp (unit in last place). - * - * y {number|string|Decimal} The power to which to raise this Decimal. - * - */ - P.toPower = P.pow = function (y) { - var e, - k, - pr, - r, - rm, - s, - x = this, - Ctor = x.constructor, - yn = +(y = new Ctor(y)) - - // Either ±Infinity, NaN or ±0? - if (!x.d || !y.d || !x.d[0] || !y.d[0]) return new Ctor(mathpow(+x, yn)) - - x = new Ctor(x) - - if (x.eq(1)) return x - - pr = Ctor.precision - rm = Ctor.rounding - - if (y.eq(1)) return finalise(x, pr, rm) - - // y exponent - e = mathfloor(y.e / LOG_BASE) - - // If y is a small integer use the 'exponentiation by squaring' algorithm. - if (e >= y.d.length - 1 && (k = yn < 0 ? -yn : yn) <= MAX_SAFE_INTEGER) { - r = intPow(Ctor, x, k, pr) - return y.s < 0 ? new Ctor(1).div(r) : finalise(r, pr, rm) - } - - s = x.s - - // if x is negative - if (s < 0) { - // if y is not an integer - if (e < y.d.length - 1) return new Ctor(NaN) - - // Result is positive if x is negative and the last digit of integer y is even. - if ((y.d[e] & 1) == 0) s = 1 - - // if x.eq(-1) - if (x.e == 0 && x.d[0] == 1 && x.d.length == 1) { - x.s = s - return x - } - } - - // Estimate result exponent. - // x^y = 10^e, where e = y * log10(x) - // log10(x) = log10(x_significand) + x_exponent - // log10(x_significand) = ln(x_significand) / ln(10) - k = mathpow(+x, yn) - e = - k == 0 || !isFinite(k) - ? mathfloor(yn * (Math.log('0.' + digitsToString(x.d)) / Math.LN10 + x.e + 1)) - : new Ctor(k + '').e - - // Exponent estimate may be incorrect e.g. x: 0.999999999999999999, y: 2.29, e: 0, r.e: -1. - - // Overflow/underflow? - if (e > Ctor.maxE + 1 || e < Ctor.minE - 1) return new Ctor(e > 0 ? s / 0 : 0) - - external = false - Ctor.rounding = x.s = 1 - - // Estimate the extra guard digits needed to ensure five correct rounding digits from - // naturalLogarithm(x). Example of failure without these extra digits (precision: 10): - // new Decimal(2.32456).pow('2087987436534566.46411') - // should be 1.162377823e+764914905173815, but is 1.162355823e+764914905173815 - k = Math.min(12, (e + '').length) - - // r = x^y = exp(y*ln(x)) - r = naturalExponential(y.times(naturalLogarithm(x, pr + k)), pr) - - // r may be Infinity, e.g. (0.9999999999999999).pow(-1e+40) - if (r.d) { - // Truncate to the required precision plus five rounding digits. - r = finalise(r, pr + 5, 1) - - // If the rounding digits are [49]9999 or [50]0000 increase the precision by 10 and recalculate - // the result. - if (checkRoundingDigits(r.d, pr, rm)) { - e = pr + 10 - - // Truncate to the increased precision plus five rounding digits. - r = finalise(naturalExponential(y.times(naturalLogarithm(x, e + k)), e), e + 5, 1) - - // Check for 14 nines from the 2nd rounding digit (the first rounding digit may be 4 or 9). - if (+digitsToString(r.d).slice(pr + 1, pr + 15) + 1 == 1e14) { - r = finalise(r, pr + 1, 0) - } - } - } - - r.s = s - external = true - Ctor.rounding = rm - - return finalise(r, pr, rm) - } - - /* - * Return a string representing the value of this Decimal rounded to `sd` significant digits - * using rounding mode `rounding`. - * - * Return exponential notation if `sd` is less than the number of digits necessary to represent - * the integer part of the value in normal notation. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - */ - P.toPrecision = function (sd, rm) { - var str, - x = this, - Ctor = x.constructor - - if (sd === void 0) { - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos) - } else { - checkInt32(sd, 1, MAX_DIGITS) - - if (rm === void 0) rm = Ctor.rounding - else checkInt32(rm, 0, 8) - - x = finalise(new Ctor(x), sd, rm) - str = finiteToString(x, sd <= x.e || x.e <= Ctor.toExpNeg, sd) - } - - return x.isNeg() && !x.isZero() ? '-' + str : str - } - - /* - * Return a new Decimal whose value is the value of this Decimal rounded to a maximum of `sd` - * significant digits using rounding mode `rm`, or to `precision` and `rounding` respectively if - * omitted. - * - * [sd] {number} Significant digits. Integer, 1 to MAX_DIGITS inclusive. - * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive. - * - * 'toSD() digits out of range: {sd}' - * 'toSD() digits not an integer: {sd}' - * 'toSD() rounding mode not an integer: {rm}' - * 'toSD() rounding mode out of range: {rm}' - * - */ - P.toSignificantDigits = P.toSD = function (sd, rm) { - var x = this, - Ctor = x.constructor - - if (sd === void 0) { - sd = Ctor.precision - rm = Ctor.rounding - } else { - checkInt32(sd, 1, MAX_DIGITS) - - if (rm === void 0) rm = Ctor.rounding - else checkInt32(rm, 0, 8) - } - - return finalise(new Ctor(x), sd, rm) - } - - /* - * Return a string representing the value of this Decimal. - * - * Return exponential notation if this Decimal has a positive exponent equal to or greater than - * `toExpPos`, or a negative exponent equal to or less than `toExpNeg`. - * - */ - P.toString = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos) - - return x.isNeg() && !x.isZero() ? '-' + str : str - } - - /* - * Return a new Decimal whose value is the value of this Decimal truncated to a whole number. - * - */ - P.truncated = P.trunc = function () { - return finalise(new this.constructor(this), this.e + 1, 1) - } - - /* - * Return a string representing the value of this Decimal. - * Unlike `toString`, negative zero will include the minus sign. - * - */ - P.valueOf = P.toJSON = function () { - var x = this, - Ctor = x.constructor, - str = finiteToString(x, x.e <= Ctor.toExpNeg || x.e >= Ctor.toExpPos) - - return x.isNeg() ? '-' + str : str - } - - // Helper functions for Decimal.prototype (P) and/or Decimal methods, and their callers. - - /* - * digitsToString P.cubeRoot, P.logarithm, P.squareRoot, P.toFraction, P.toPower, - * finiteToString, naturalExponential, naturalLogarithm - * checkInt32 P.toDecimalPlaces, P.toExponential, P.toFixed, P.toNearest, - * P.toPrecision, P.toSignificantDigits, toStringBinary, random - * checkRoundingDigits P.logarithm, P.toPower, naturalExponential, naturalLogarithm - * convertBase toStringBinary, parseOther - * cos P.cos - * divide P.atanh, P.cubeRoot, P.dividedBy, P.dividedToIntegerBy, - * P.logarithm, P.modulo, P.squareRoot, P.tan, P.tanh, P.toFraction, - * P.toNearest, toStringBinary, naturalExponential, naturalLogarithm, - * taylorSeries, atan2, parseOther - * finalise P.absoluteValue, P.atan, P.atanh, P.ceil, P.cos, P.cosh, - * P.cubeRoot, P.dividedToIntegerBy, P.floor, P.logarithm, P.minus, - * P.modulo, P.negated, P.plus, P.round, P.sin, P.sinh, P.squareRoot, - * P.tan, P.times, P.toDecimalPlaces, P.toExponential, P.toFixed, - * P.toNearest, P.toPower, P.toPrecision, P.toSignificantDigits, - * P.truncated, divide, getLn10, getPi, naturalExponential, - * naturalLogarithm, ceil, floor, round, trunc - * finiteToString P.toExponential, P.toFixed, P.toPrecision, P.toString, P.valueOf, - * toStringBinary - * getBase10Exponent P.minus, P.plus, P.times, parseOther - * getLn10 P.logarithm, naturalLogarithm - * getPi P.acos, P.asin, P.atan, toLessThanHalfPi, atan2 - * getPrecision P.precision, P.toFraction - * getZeroString digitsToString, finiteToString - * intPow P.toPower, parseOther - * isOdd toLessThanHalfPi - * maxOrMin max, min - * naturalExponential P.naturalExponential, P.toPower - * naturalLogarithm P.acosh, P.asinh, P.atanh, P.logarithm, P.naturalLogarithm, - * P.toPower, naturalExponential - * nonFiniteToString finiteToString, toStringBinary - * parseDecimal Decimal - * parseOther Decimal - * sin P.sin - * taylorSeries P.cosh, P.sinh, cos, sin - * toLessThanHalfPi P.cos, P.sin - * toStringBinary P.toBinary, P.toHexadecimal, P.toOctal - * truncate intPow - * - * Throws: P.logarithm, P.precision, P.toFraction, checkInt32, getLn10, getPi, - * naturalLogarithm, config, parseOther, random, Decimal - */ - - function digitsToString(d) { - var i, - k, - ws, - indexOfLastWord = d.length - 1, - str = '', - w = d[0] - - if (indexOfLastWord > 0) { - str += w - for (i = 1; i < indexOfLastWord; i++) { - ws = d[i] + '' - k = LOG_BASE - ws.length - if (k) str += getZeroString(k) - str += ws - } - - w = d[i] - ws = w + '' - k = LOG_BASE - ws.length - if (k) str += getZeroString(k) - } else if (w === 0) { - return '0' - } - - // Remove trailing zeros of last w. - for (; w % 10 === 0; ) w /= 10 - - return str + w - } - - function checkInt32(i, min, max) { - if (i !== ~~i || i < min || i > max) { - throw Error(invalidArgument + i) - } - } - - /* - * Check 5 rounding digits if `repeating` is null, 4 otherwise. - * `repeating == null` if caller is `log` or `pow`, - * `repeating != null` if caller is `naturalLogarithm` or `naturalExponential`. - */ - function checkRoundingDigits(d, i, rm, repeating) { - var di, k, r, rd - - // Get the length of the first word of the array d. - for (k = d[0]; k >= 10; k /= 10) --i - - // Is the rounding digit in the first word of d? - if (--i < 0) { - i += LOG_BASE - di = 0 - } else { - di = Math.ceil((i + 1) / LOG_BASE) - i %= LOG_BASE - } - - // i is the index (0 - 6) of the rounding digit. - // E.g. if within the word 3487563 the first rounding digit is 5, - // then i = 4, k = 1000, rd = 3487563 % 1000 = 563 - k = mathpow(10, LOG_BASE - i) - rd = d[di] % k | 0 - - if (repeating == null) { - if (i < 3) { - if (i == 0) rd = (rd / 100) | 0 - else if (i == 1) rd = (rd / 10) | 0 - r = (rm < 4 && rd == 99999) || (rm > 3 && rd == 49999) || rd == 50000 || rd == 0 - } else { - r = - (((rm < 4 && rd + 1 == k) || (rm > 3 && rd + 1 == k / 2)) && - ((d[di + 1] / k / 100) | 0) == mathpow(10, i - 2) - 1) || - ((rd == k / 2 || rd == 0) && ((d[di + 1] / k / 100) | 0) == 0) - } - } else { - if (i < 4) { - if (i == 0) rd = (rd / 1000) | 0 - else if (i == 1) rd = (rd / 100) | 0 - else if (i == 2) rd = (rd / 10) | 0 - r = ((repeating || rm < 4) && rd == 9999) || (!repeating && rm > 3 && rd == 4999) - } else { - r = - (((repeating || rm < 4) && rd + 1 == k) || (!repeating && rm > 3 && rd + 1 == k / 2)) && - ((d[di + 1] / k / 1000) | 0) == mathpow(10, i - 3) - 1 - } - } - - return r - } - - // Convert string of `baseIn` to an array of numbers of `baseOut`. - // Eg. convertBase('255', 10, 16) returns [15, 15]. - // Eg. convertBase('ff', 16, 10) returns [2, 5, 5]. - function convertBase(str, baseIn, baseOut) { - var j, - arr = [0], - arrL, - i = 0, - strL = str.length - - for (; i < strL; ) { - for (arrL = arr.length; arrL--; ) arr[arrL] *= baseIn - arr[0] += NUMERALS.indexOf(str.charAt(i++)) - for (j = 0; j < arr.length; j++) { - if (arr[j] > baseOut - 1) { - if (arr[j + 1] === void 0) arr[j + 1] = 0 - arr[j + 1] += (arr[j] / baseOut) | 0 - arr[j] %= baseOut - } - } - } - - return arr.reverse() - } - - /* - * cos(x) = 1 - x^2/2! + x^4/4! - ... - * |x| < pi/2 - * - */ - function cosine(Ctor, x) { - var k, len, y - - if (x.isZero()) return x - - // Argument reduction: cos(4x) = 8*(cos^4(x) - cos^2(x)) + 1 - // i.e. cos(x) = 8*(cos^4(x/4) - cos^2(x/4)) + 1 - - // Estimate the optimum number of times to use the argument reduction. - len = x.d.length - if (len < 32) { - k = Math.ceil(len / 3) - y = (1 / tinyPow(4, k)).toString() - } else { - k = 16 - y = '2.3283064365386962890625e-10' - } - - Ctor.precision += k - - x = taylorSeries(Ctor, 1, x.times(y), new Ctor(1)) - - // Reverse argument reduction - for (var i = k; i--; ) { - var cos2x = x.times(x) - x = cos2x.times(cos2x).minus(cos2x).times(8).plus(1) - } - - Ctor.precision -= k - - return x - } - - /* - * Perform division in the specified base. - */ - var divide = (function () { - // Assumes non-zero x and k, and hence non-zero result. - function multiplyInteger(x, k, base) { - var temp, - carry = 0, - i = x.length - - for (x = x.slice(); i--; ) { - temp = x[i] * k + carry - x[i] = temp % base | 0 - carry = (temp / base) | 0 - } - - if (carry) x.unshift(carry) - - return x - } - - function compare(a, b, aL, bL) { - var i, r - - if (aL != bL) { - r = aL > bL ? 1 : -1 - } else { - for (i = r = 0; i < aL; i++) { - if (a[i] != b[i]) { - r = a[i] > b[i] ? 1 : -1 - break - } - } - } - - return r - } - - function subtract(a, b, aL, base) { - var i = 0 - - // Subtract b from a. - for (; aL--; ) { - a[aL] -= i - i = a[aL] < b[aL] ? 1 : 0 - a[aL] = i * base + a[aL] - b[aL] - } - - // Remove leading zeros. - for (; !a[0] && a.length > 1; ) a.shift() - } - - return function (x, y, pr, rm, dp, base) { - var cmp, - e, - i, - k, - logBase, - more, - prod, - prodL, - q, - qd, - rem, - remL, - rem0, - sd, - t, - xi, - xL, - yd0, - yL, - yz, - Ctor = x.constructor, - sign = x.s == y.s ? 1 : -1, - xd = x.d, - yd = y.d - - // Either NaN, Infinity or 0? - if (!xd || !xd[0] || !yd || !yd[0]) { - return new Ctor( // Return NaN if either NaN, or both Infinity or 0. - !x.s || !y.s || (xd ? yd && xd[0] == yd[0] : !yd) - ? NaN - : // Return ±0 if x is 0 or y is ±Infinity, or return ±Infinity as y is 0. - (xd && xd[0] == 0) || !yd - ? sign * 0 - : sign / 0 - ) - } - - if (base) { - logBase = 1 - e = x.e - y.e - } else { - base = BASE - logBase = LOG_BASE - e = mathfloor(x.e / logBase) - mathfloor(y.e / logBase) - } - - yL = yd.length - xL = xd.length - q = new Ctor(sign) - qd = q.d = [] - - // Result exponent may be one less than e. - // The digit array of a Decimal from toStringBinary may have trailing zeros. - for (i = 0; yd[i] == (xd[i] || 0); i++); - - if (yd[i] > (xd[i] || 0)) e-- - - if (pr == null) { - sd = pr = Ctor.precision - rm = Ctor.rounding - } else if (dp) { - sd = pr + (x.e - y.e) + 1 - } else { - sd = pr - } - - if (sd < 0) { - qd.push(1) - more = true - } else { - // Convert precision in number of base 10 digits to base 1e7 digits. - sd = (sd / logBase + 2) | 0 - i = 0 - - // divisor < 1e7 - if (yL == 1) { - k = 0 - yd = yd[0] - sd++ - - // k is the carry. - for (; (i < xL || k) && sd--; i++) { - t = k * base + (xd[i] || 0) - qd[i] = (t / yd) | 0 - k = t % yd | 0 - } - - more = k || i < xL - - // divisor >= 1e7 - } else { - // Normalise xd and yd so highest order digit of yd is >= base/2 - k = (base / (yd[0] + 1)) | 0 - - if (k > 1) { - yd = multiplyInteger(yd, k, base) - xd = multiplyInteger(xd, k, base) - yL = yd.length - xL = xd.length - } - - xi = yL - rem = xd.slice(0, yL) - remL = rem.length - - // Add zeros to make remainder as long as divisor. - for (; remL < yL; ) rem[remL++] = 0 - - yz = yd.slice() - yz.unshift(0) - yd0 = yd[0] - - if (yd[1] >= base / 2) ++yd0 - - do { - k = 0 - - // Compare divisor and remainder. - cmp = compare(yd, rem, yL, remL) - - // If divisor < remainder. - if (cmp < 0) { - // Calculate trial digit, k. - rem0 = rem[0] - if (yL != remL) rem0 = rem0 * base + (rem[1] || 0) - - // k will be how many times the divisor goes into the current remainder. - k = (rem0 / yd0) | 0 - - // Algorithm: - // 1. product = divisor * trial digit (k) - // 2. if product > remainder: product -= divisor, k-- - // 3. remainder -= product - // 4. if product was < remainder at 2: - // 5. compare new remainder and divisor - // 6. If remainder > divisor: remainder -= divisor, k++ - - if (k > 1) { - if (k >= base) k = base - 1 - - // product = divisor * trial digit. - prod = multiplyInteger(yd, k, base) - prodL = prod.length - remL = rem.length - - // Compare product and remainder. - cmp = compare(prod, rem, prodL, remL) - - // product > remainder. - if (cmp == 1) { - k-- - - // Subtract divisor from product. - subtract(prod, yL < prodL ? yz : yd, prodL, base) - } - } else { - // cmp is -1. - // If k is 0, there is no need to compare yd and rem again below, so change cmp to 1 - // to avoid it. If k is 1 there is a need to compare yd and rem again below. - if (k == 0) cmp = k = 1 - prod = yd.slice() - } - - prodL = prod.length - if (prodL < remL) prod.unshift(0) - - // Subtract product from remainder. - subtract(rem, prod, remL, base) - - // If product was < previous remainder. - if (cmp == -1) { - remL = rem.length - - // Compare divisor and new remainder. - cmp = compare(yd, rem, yL, remL) - - // If divisor < new remainder, subtract divisor from remainder. - if (cmp < 1) { - k++ - - // Subtract divisor from remainder. - subtract(rem, yL < remL ? yz : yd, remL, base) - } - } - - remL = rem.length - } else if (cmp === 0) { - k++ - rem = [0] - } // if cmp === 1, k will be 0 - - // Add the next digit, k, to the result array. - qd[i++] = k - - // Update the remainder. - if (cmp && rem[0]) { - rem[remL++] = xd[xi] || 0 - } else { - rem = [xd[xi]] - remL = 1 - } - } while ((xi++ < xL || rem[0] !== void 0) && sd--) - - more = rem[0] !== void 0 - } - - // Leading zero? - if (!qd[0]) qd.shift() - } - - // logBase is 1 when divide is being used for base conversion. - if (logBase == 1) { - q.e = e - inexact = more - } else { - // To calculate q.e, first get the number of digits of qd[0]. - for (i = 1, k = qd[0]; k >= 10; k /= 10) i++ - q.e = i + e * logBase - 1 - - finalise(q, dp ? pr + q.e + 1 : pr, rm, more) - } - - return q - } - })() - - /* - * Round `x` to `sd` significant digits using rounding mode `rm`. - * Check for over/under-flow. - */ - function finalise(x, sd, rm, isTruncated) { - var digits, - i, - j, - k, - rd, - roundUp, - w, - xd, - xdi, - Ctor = x.constructor - - // Don't round if sd is null or undefined. - out: if (sd != null) { - xd = x.d - - // Infinity/NaN. - if (!xd) return x - - // rd: the rounding digit, i.e. the digit after the digit that may be rounded up. - // w: the word of xd containing rd, a base 1e7 number. - // xdi: the index of w within xd. - // digits: the number of digits of w. - // i: what would be the index of rd within w if all the numbers were 7 digits long (i.e. if - // they had leading zeros) - // j: if > 0, the actual index of rd within w (if < 0, rd is a leading zero). - - // Get the length of the first word of the digits array xd. - for (digits = 1, k = xd[0]; k >= 10; k /= 10) digits++ - i = sd - digits - - // Is the rounding digit in the first word of xd? - if (i < 0) { - i += LOG_BASE - j = sd - w = xd[(xdi = 0)] - - // Get the rounding digit at index j of w. - rd = (w / mathpow(10, digits - j - 1)) % 10 | 0 - } else { - xdi = Math.ceil((i + 1) / LOG_BASE) - k = xd.length - if (xdi >= k) { - if (isTruncated) { - // Needed by `naturalExponential`, `naturalLogarithm` and `squareRoot`. - for (; k++ <= xdi; ) xd.push(0) - w = rd = 0 - digits = 1 - i %= LOG_BASE - j = i - LOG_BASE + 1 - } else { - break out - } - } else { - w = k = xd[xdi] - - // Get the number of digits of w. - for (digits = 1; k >= 10; k /= 10) digits++ - - // Get the index of rd within w. - i %= LOG_BASE - - // Get the index of rd within w, adjusted for leading zeros. - // The number of leading zeros of w is given by LOG_BASE - digits. - j = i - LOG_BASE + digits - - // Get the rounding digit at index j of w. - rd = j < 0 ? 0 : (w / mathpow(10, digits - j - 1)) % 10 | 0 - } - } - - // Are there any non-zero digits after the rounding digit? - isTruncated = isTruncated || sd < 0 || xd[xdi + 1] !== void 0 || (j < 0 ? w : w % mathpow(10, digits - j - 1)) - - // The expression `w % mathpow(10, digits - j - 1)` returns all the digits of w to the right - // of the digit at (left-to-right) index j, e.g. if w is 908714 and j is 2, the expression - // will give 714. - - roundUp = - rm < 4 - ? (rd || isTruncated) && (rm == 0 || rm == (x.s < 0 ? 3 : 2)) - : rd > 5 || - (rd == 5 && - (rm == 4 || - isTruncated || - (rm == 6 && - // Check whether the digit to the left of the rounding digit is odd. - (i > 0 ? (j > 0 ? w / mathpow(10, digits - j) : 0) : xd[xdi - 1]) % 10 & 1) || - rm == (x.s < 0 ? 8 : 7))) - - if (sd < 1 || !xd[0]) { - xd.length = 0 - if (roundUp) { - // Convert sd to decimal places. - sd -= x.e + 1 - - // 1, 0.1, 0.01, 0.001, 0.0001 etc. - xd[0] = mathpow(10, (LOG_BASE - (sd % LOG_BASE)) % LOG_BASE) - x.e = -sd || 0 - } else { - // Zero. - xd[0] = x.e = 0 - } - - return x - } - - // Remove excess digits. - if (i == 0) { - xd.length = xdi - k = 1 - xdi-- - } else { - xd.length = xdi + 1 - k = mathpow(10, LOG_BASE - i) - - // E.g. 56700 becomes 56000 if 7 is the rounding digit. - // j > 0 means i > number of leading zeros of w. - xd[xdi] = j > 0 ? ((w / mathpow(10, digits - j)) % mathpow(10, j) | 0) * k : 0 - } - - if (roundUp) { - for (;;) { - // Is the digit to be rounded up in the first word of xd? - if (xdi == 0) { - // i will be the length of xd[0] before k is added. - for (i = 1, j = xd[0]; j >= 10; j /= 10) i++ - j = xd[0] += k - for (k = 1; j >= 10; j /= 10) k++ - - // if i != k the length has increased. - if (i != k) { - x.e++ - if (xd[0] == BASE) xd[0] = 1 - } - - break - } else { - xd[xdi] += k - if (xd[xdi] != BASE) break - xd[xdi--] = 0 - k = 1 - } - } - } - - // Remove trailing zeros. - for (i = xd.length; xd[--i] === 0; ) xd.pop() - } - - if (external) { - // Overflow? - if (x.e > Ctor.maxE) { - // Infinity. - x.d = null - x.e = NaN - - // Underflow? - } else if (x.e < Ctor.minE) { - // Zero. - x.e = 0 - x.d = [0] - // Ctor.underflow = true; - } // else Ctor.underflow = false; - } - - return x - } - - function finiteToString(x, isExp, sd) { - if (!x.isFinite()) return nonFiniteToString(x) - var k, - e = x.e, - str = digitsToString(x.d), - len = str.length - - if (isExp) { - if (sd && (k = sd - len) > 0) { - str = str.charAt(0) + '.' + str.slice(1) + getZeroString(k) - } else if (len > 1) { - str = str.charAt(0) + '.' + str.slice(1) - } - - str = str + (x.e < 0 ? 'e' : 'e+') + x.e - } else if (e < 0) { - str = '0.' + getZeroString(-e - 1) + str - if (sd && (k = sd - len) > 0) str += getZeroString(k) - } else if (e >= len) { - str += getZeroString(e + 1 - len) - if (sd && (k = sd - e - 1) > 0) str = str + '.' + getZeroString(k) - } else { - if ((k = e + 1) < len) str = str.slice(0, k) + '.' + str.slice(k) - if (sd && (k = sd - len) > 0) { - if (e + 1 === len) str += '.' - str += getZeroString(k) - } - } - - return str - } - - // Calculate the base 10 exponent from the base 1e7 exponent. - function getBase10Exponent(digits, e) { - var w = digits[0] - - // Add the number of digits of the first word of the digits array. - for (e *= LOG_BASE; w >= 10; w /= 10) e++ - return e - } - - function getLn10(Ctor, sd, pr) { - if (sd > LN10_PRECISION) { - // Reset global state in case the exception is caught. - external = true - if (pr) Ctor.precision = pr - throw Error(precisionLimitExceeded) - } - return finalise(new Ctor(LN10), sd, 1, true) - } - - function getPi(Ctor, sd, rm) { - if (sd > PI_PRECISION) throw Error(precisionLimitExceeded) - return finalise(new Ctor(PI), sd, rm, true) - } - - function getPrecision(digits) { - var w = digits.length - 1, - len = w * LOG_BASE + 1 - - w = digits[w] - - // If non-zero... - if (w) { - // Subtract the number of trailing zeros of the last word. - for (; w % 10 == 0; w /= 10) len-- - - // Add the number of digits of the first word. - for (w = digits[0]; w >= 10; w /= 10) len++ - } - - return len - } - - function getZeroString(k) { - var zs = '' - for (; k--; ) zs += '0' - return zs - } - - /* - * Return a new Decimal whose value is the value of Decimal `x` to the power `n`, where `n` is an - * integer of type number. - * - * Implements 'exponentiation by squaring'. Called by `pow` and `parseOther`. - * - */ - function intPow(Ctor, x, n, pr) { - var isTruncated, - r = new Ctor(1), - // Max n of 9007199254740991 takes 53 loop iterations. - // Maximum digits array length; leaves [28, 34] guard digits. - k = Math.ceil(pr / LOG_BASE + 4) - - external = false - - for (;;) { - if (n % 2) { - r = r.times(x) - if (truncate(r.d, k)) isTruncated = true - } - - n = mathfloor(n / 2) - if (n === 0) { - // To ensure correct rounding when r.d is truncated, increment the last word if it is zero. - n = r.d.length - 1 - if (isTruncated && r.d[n] === 0) ++r.d[n] - break - } - - x = x.times(x) - truncate(x.d, k) - } - - external = true - - return r - } - - function isOdd(n) { - return n.d[n.d.length - 1] & 1 - } - - /* - * Handle `max` and `min`. `ltgt` is 'lt' or 'gt'. - */ - function maxOrMin(Ctor, args, ltgt) { - var y, - x = new Ctor(args[0]), - i = 0 - - for (; ++i < args.length; ) { - y = new Ctor(args[i]) - if (!y.s) { - x = y - break - } else if (x[ltgt](y)) { - x = y - } - } - - return x - } - - /* - * Return a new Decimal whose value is the natural exponential of `x` rounded to `sd` significant - * digits. - * - * Taylor/Maclaurin series. - * - * exp(x) = x^0/0! + x^1/1! + x^2/2! + x^3/3! + ... - * - * Argument reduction: - * Repeat x = x / 32, k += 5, until |x| < 0.1 - * exp(x) = exp(x / 2^k)^(2^k) - * - * Previously, the argument was initially reduced by - * exp(x) = exp(r) * 10^k where r = x - k * ln10, k = floor(x / ln10) - * to first put r in the range [0, ln10], before dividing by 32 until |x| < 0.1, but this was - * found to be slower than just dividing repeatedly by 32 as above. - * - * Max integer argument: exp('20723265836946413') = 6.3e+9000000000000000 - * Min integer argument: exp('-20723265836946411') = 1.2e-9000000000000000 - * (Math object integer min/max: Math.exp(709) = 8.2e+307, Math.exp(-745) = 5e-324) - * - * exp(Infinity) = Infinity - * exp(-Infinity) = 0 - * exp(NaN) = NaN - * exp(±0) = 1 - * - * exp(x) is non-terminating for any finite, non-zero x. - * - * The result will always be correctly rounded. - * - */ - function naturalExponential(x, sd) { - var denominator, - guard, - j, - pow, - sum, - t, - wpr, - rep = 0, - i = 0, - k = 0, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision - - // 0/NaN/Infinity? - if (!x.d || !x.d[0] || x.e > 17) { - return new Ctor(x.d ? (!x.d[0] ? 1 : x.s < 0 ? 0 : 1 / 0) : x.s ? (x.s < 0 ? 0 : x) : 0 / 0) - } - - if (sd == null) { - external = false - wpr = pr - } else { - wpr = sd - } - - t = new Ctor(0.03125) - - // while abs(x) >= 0.1 - while (x.e > -2) { - // x = x / 2^5 - x = x.times(t) - k += 5 - } - - // Use 2 * log10(2^k) + 5 (empirically derived) to estimate the increase in precision - // necessary to ensure the first 4 rounding digits are correct. - guard = ((Math.log(mathpow(2, k)) / Math.LN10) * 2 + 5) | 0 - wpr += guard - denominator = pow = sum = new Ctor(1) - Ctor.precision = wpr - - for (;;) { - pow = finalise(pow.times(x), wpr, 1) - denominator = denominator.times(++i) - t = sum.plus(divide(pow, denominator, wpr, 1)) - - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - j = k - while (j--) sum = finalise(sum.times(sum), wpr, 1) - - // Check to see if the first 4 rounding digits are [49]999. - // If so, repeat the summation with a higher precision, otherwise - // e.g. with precision: 18, rounding: 1 - // exp(18.404272462595034083567793919843761) = 98372560.1229999999 (should be 98372560.123) - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { - if (rep < 3 && checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += 10 - denominator = pow = t = new Ctor(1) - i = 0 - rep++ - } else { - return finalise(sum, (Ctor.precision = pr), rm, (external = true)) - } - } else { - Ctor.precision = pr - return sum - } - } - - sum = t - } - } - - /* - * Return a new Decimal whose value is the natural logarithm of `x` rounded to `sd` significant - * digits. - * - * ln(-n) = NaN - * ln(0) = -Infinity - * ln(-0) = -Infinity - * ln(1) = 0 - * ln(Infinity) = Infinity - * ln(-Infinity) = NaN - * ln(NaN) = NaN - * - * ln(n) (n != 1) is non-terminating. - * - */ - function naturalLogarithm(y, sd) { - var c, - c0, - denominator, - e, - numerator, - rep, - sum, - t, - wpr, - x1, - x2, - n = 1, - guard = 10, - x = y, - xd = x.d, - Ctor = x.constructor, - rm = Ctor.rounding, - pr = Ctor.precision - - // Is x negative or Infinity, NaN, 0 or 1? - if (x.s < 0 || !xd || !xd[0] || (!x.e && xd[0] == 1 && xd.length == 1)) { - return new Ctor(xd && !xd[0] ? -1 / 0 : x.s != 1 ? NaN : xd ? 0 : x) - } - - if (sd == null) { - external = false - wpr = pr - } else { - wpr = sd - } - - Ctor.precision = wpr += guard - c = digitsToString(xd) - c0 = c.charAt(0) - - if (Math.abs((e = x.e)) < 1.5e15) { - // Argument reduction. - // The series converges faster the closer the argument is to 1, so using - // ln(a^b) = b * ln(a), ln(a) = ln(a^b) / b - // multiply the argument by itself until the leading digits of the significand are 7, 8, 9, - // 10, 11, 12 or 13, recording the number of multiplications so the sum of the series can - // later be divided by this number, then separate out the power of 10 using - // ln(a*10^b) = ln(a) + b*ln(10). - - // max n is 21 (gives 0.9, 1.0 or 1.1) (9e15 / 21 = 4.2e14). - //while (c0 < 9 && c0 != 1 || c0 == 1 && c.charAt(1) > 1) { - // max n is 6 (gives 0.7 - 1.3) - while ((c0 < 7 && c0 != 1) || (c0 == 1 && c.charAt(1) > 3)) { - x = x.times(y) - c = digitsToString(x.d) - c0 = c.charAt(0) - n++ - } - - e = x.e - - if (c0 > 1) { - x = new Ctor('0.' + c) - e++ - } else { - x = new Ctor(c0 + '.' + c.slice(1)) - } - } else { - // The argument reduction method above may result in overflow if the argument y is a massive - // number with exponent >= 1500000000000000 (9e15 / 6 = 1.5e15), so instead recall this - // function using ln(x*10^e) = ln(x) + e*ln(10). - t = getLn10(Ctor, wpr + 2, pr).times(e + '') - x = naturalLogarithm(new Ctor(c0 + '.' + c.slice(1)), wpr - guard).plus(t) - Ctor.precision = pr - - return sd == null ? finalise(x, pr, rm, (external = true)) : x - } - - // x1 is x reduced to a value near 1. - x1 = x - - // Taylor series. - // ln(y) = ln((1 + x)/(1 - x)) = 2(x + x^3/3 + x^5/5 + x^7/7 + ...) - // where x = (y - 1)/(y + 1) (|x| < 1) - sum = numerator = x = divide(x.minus(1), x.plus(1), wpr, 1) - x2 = finalise(x.times(x), wpr, 1) - denominator = 3 - - for (;;) { - numerator = finalise(numerator.times(x2), wpr, 1) - t = sum.plus(divide(numerator, new Ctor(denominator), wpr, 1)) - - if (digitsToString(t.d).slice(0, wpr) === digitsToString(sum.d).slice(0, wpr)) { - sum = sum.times(2) - - // Reverse the argument reduction. Check that e is not 0 because, besides preventing an - // unnecessary calculation, -0 + 0 = +0 and to ensure correct rounding -0 needs to stay -0. - if (e !== 0) sum = sum.plus(getLn10(Ctor, wpr + 2, pr).times(e + '')) - sum = divide(sum, new Ctor(n), wpr, 1) - - // Is rm > 3 and the first 4 rounding digits 4999, or rm < 4 (or the summation has - // been repeated previously) and the first 4 rounding digits 9999? - // If so, restart the summation with a higher precision, otherwise - // e.g. with precision: 12, rounding: 1 - // ln(135520028.6126091714265381533) = 18.7246299999 when it should be 18.72463. - // `wpr - guard` is the index of first rounding digit. - if (sd == null) { - if (checkRoundingDigits(sum.d, wpr - guard, rm, rep)) { - Ctor.precision = wpr += guard - t = numerator = x = divide(x1.minus(1), x1.plus(1), wpr, 1) - x2 = finalise(x.times(x), wpr, 1) - denominator = rep = 1 - } else { - return finalise(sum, (Ctor.precision = pr), rm, (external = true)) - } - } else { - Ctor.precision = pr - return sum - } - } - - sum = t - denominator += 2 - } - } - - // ±Infinity, NaN. - function nonFiniteToString(x) { - // Unsigned. - return String((x.s * x.s) / 0) - } - - /* - * Parse the value of a new Decimal `x` from string `str`. - */ - function parseDecimal(x, str) { - var e, i, len - - // Decimal point? - if ((e = str.indexOf('.')) > -1) str = str.replace('.', '') - - // Exponential form? - if ((i = str.search(/e/i)) > 0) { - // Determine exponent. - if (e < 0) e = i - e += +str.slice(i + 1) - str = str.substring(0, i) - } else if (e < 0) { - // Integer. - e = str.length - } - - // Determine leading zeros. - for (i = 0; str.charCodeAt(i) === 48; i++); - - // Determine trailing zeros. - for (len = str.length; str.charCodeAt(len - 1) === 48; --len); - str = str.slice(i, len) - - if (str) { - len -= i - x.e = e = e - i - 1 - x.d = [] - - // Transform base - - // e is the base 10 exponent. - // i is where to slice str to get the first word of the digits array. - i = (e + 1) % LOG_BASE - if (e < 0) i += LOG_BASE - - if (i < len) { - if (i) x.d.push(+str.slice(0, i)) - for (len -= LOG_BASE; i < len; ) x.d.push(+str.slice(i, (i += LOG_BASE))) - str = str.slice(i) - i = LOG_BASE - str.length - } else { - i -= len - } - - for (; i--; ) str += '0' - x.d.push(+str) - - if (external) { - // Overflow? - if (x.e > x.constructor.maxE) { - // Infinity. - x.d = null - x.e = NaN - - // Underflow? - } else if (x.e < x.constructor.minE) { - // Zero. - x.e = 0 - x.d = [0] - // x.constructor.underflow = true; - } // else x.constructor.underflow = false; - } - } else { - // Zero. - x.e = 0 - x.d = [0] - } - - return x - } - - /* - * Parse the value of a new Decimal `x` from a string `str`, which is not a decimal value. - */ - function parseOther(x, str) { - var base, Ctor, divisor, i, isFloat, len, p, xd, xe - - if (str.indexOf('_') > -1) { - str = str.replace(/(\d)_(?=\d)/g, '$1') - if (isDecimal.test(str)) return parseDecimal(x, str) - } else if (str === 'Infinity' || str === 'NaN') { - if (!+str) x.s = NaN - x.e = NaN - x.d = null - return x - } - - if (isHex.test(str)) { - base = 16 - str = str.toLowerCase() - } else if (isBinary.test(str)) { - base = 2 - } else if (isOctal.test(str)) { - base = 8 - } else { - throw Error(invalidArgument + str) - } - - // Is there a binary exponent part? - i = str.search(/p/i) - - if (i > 0) { - p = +str.slice(i + 1) - str = str.substring(2, i) - } else { - str = str.slice(2) - } - - // Convert `str` as an integer then divide the result by `base` raised to a power such that the - // fraction part will be restored. - i = str.indexOf('.') - isFloat = i >= 0 - Ctor = x.constructor - - if (isFloat) { - str = str.replace('.', '') - len = str.length - i = len - i - - // log[10](16) = 1.2041... , log[10](88) = 1.9444.... - divisor = intPow(Ctor, new Ctor(base), i, i * 2) - } - - xd = convertBase(str, base, BASE) - xe = xd.length - 1 - - // Remove trailing zeros. - for (i = xe; xd[i] === 0; --i) xd.pop() - if (i < 0) return new Ctor(x.s * 0) - x.e = getBase10Exponent(xd, xe) - x.d = xd - external = false - - // At what precision to perform the division to ensure exact conversion? - // maxDecimalIntegerPartDigitCount = ceil(log[10](b) * otherBaseIntegerPartDigitCount) - // log[10](2) = 0.30103, log[10](8) = 0.90309, log[10](16) = 1.20412 - // E.g. ceil(1.2 * 3) = 4, so up to 4 decimal digits are needed to represent 3 hex int digits. - // maxDecimalFractionPartDigitCount = {Hex:4|Oct:3|Bin:1} * otherBaseFractionPartDigitCount - // Therefore using 4 * the number of digits of str will always be enough. - if (isFloat) x = divide(x, divisor, len * 4) - - // Multiply by the binary exponent part if present. - if (p) x = x.times(Math.abs(p) < 54 ? mathpow(2, p) : Decimal.pow(2, p)) - external = true - - return x - } - - /* - * sin(x) = x - x^3/3! + x^5/5! - ... - * |x| < pi/2 - * - */ - function sine(Ctor, x) { - var k, - len = x.d.length - - if (len < 3) { - return x.isZero() ? x : taylorSeries(Ctor, 2, x, x) - } - - // Argument reduction: sin(5x) = 16*sin^5(x) - 20*sin^3(x) + 5*sin(x) - // i.e. sin(x) = 16*sin^5(x/5) - 20*sin^3(x/5) + 5*sin(x/5) - // and sin(x) = sin(x/5)(5 + sin^2(x/5)(16sin^2(x/5) - 20)) - - // Estimate the optimum number of times to use the argument reduction. - k = 1.4 * Math.sqrt(len) - k = k > 16 ? 16 : k | 0 - - x = x.times(1 / tinyPow(5, k)) - x = taylorSeries(Ctor, 2, x, x) - - // Reverse argument reduction - var sin2_x, - d5 = new Ctor(5), - d16 = new Ctor(16), - d20 = new Ctor(20) - for (; k--; ) { - sin2_x = x.times(x) - x = x.times(d5.plus(sin2_x.times(d16.times(sin2_x).minus(d20)))) - } - - return x - } - - // Calculate Taylor series for `cos`, `cosh`, `sin` and `sinh`. - function taylorSeries(Ctor, n, x, y, isHyperbolic) { - var j, - t, - u, - x2, - i = 1, - pr = Ctor.precision, - k = Math.ceil(pr / LOG_BASE) - - external = false - x2 = x.times(x) - u = new Ctor(y) - - for (;;) { - t = divide(u.times(x2), new Ctor(n++ * n++), pr, 1) - u = isHyperbolic ? y.plus(t) : y.minus(t) - y = divide(t.times(x2), new Ctor(n++ * n++), pr, 1) - t = u.plus(y) - - if (t.d[k] !== void 0) { - for (j = k; t.d[j] === u.d[j] && j--; ); - if (j == -1) break - } - - j = u - u = y - y = t - t = j - i++ - } - - external = true - t.d.length = k + 1 - - return t - } - - // Exponent e must be positive and non-zero. - function tinyPow(b, e) { - var n = b - while (--e) n *= b - return n - } - - // Return the absolute value of `x` reduced to less than or equal to half pi. - function toLessThanHalfPi(Ctor, x) { - var t, - isNeg = x.s < 0, - pi = getPi(Ctor, Ctor.precision, 1), - halfPi = pi.times(0.5) - - x = x.abs() - - if (x.lte(halfPi)) { - quadrant = isNeg ? 4 : 1 - return x - } - - t = x.divToInt(pi) - - if (t.isZero()) { - quadrant = isNeg ? 3 : 2 - } else { - x = x.minus(t.times(pi)) - - // 0 <= x < pi - if (x.lte(halfPi)) { - quadrant = isOdd(t) ? (isNeg ? 2 : 3) : isNeg ? 4 : 1 - return x - } - - quadrant = isOdd(t) ? (isNeg ? 1 : 4) : isNeg ? 3 : 2 - } - - return x.minus(pi).abs() - } - - /* - * Return the value of Decimal `x` as a string in base `baseOut`. - * - * If the optional `sd` argument is present include a binary exponent suffix. - */ - function toStringBinary(x, baseOut, sd, rm) { - var base, - e, - i, - k, - len, - roundUp, - str, - xd, - y, - Ctor = x.constructor, - isExp = sd !== void 0 - - if (isExp) { - checkInt32(sd, 1, MAX_DIGITS) - if (rm === void 0) rm = Ctor.rounding - else checkInt32(rm, 0, 8) - } else { - sd = Ctor.precision - rm = Ctor.rounding - } - - if (!x.isFinite()) { - str = nonFiniteToString(x) - } else { - str = finiteToString(x) - i = str.indexOf('.') - - // Use exponential notation according to `toExpPos` and `toExpNeg`? No, but if required: - // maxBinaryExponent = floor((decimalExponent + 1) * log[2](10)) - // minBinaryExponent = floor(decimalExponent * log[2](10)) - // log[2](10) = 3.321928094887362347870319429489390175864 - - if (isExp) { - base = 2 - if (baseOut == 16) { - sd = sd * 4 - 3 - } else if (baseOut == 8) { - sd = sd * 3 - 2 - } - } else { - base = baseOut - } - - // Convert the number as an integer then divide the result by its base raised to a power such - // that the fraction part will be restored. - - // Non-integer. - if (i >= 0) { - str = str.replace('.', '') - y = new Ctor(1) - y.e = str.length - i - y.d = convertBase(finiteToString(y), 10, base) - y.e = y.d.length - } - - xd = convertBase(str, 10, base) - e = len = xd.length - - // Remove trailing zeros. - for (; xd[--len] == 0; ) xd.pop() - - if (!xd[0]) { - str = isExp ? '0p+0' : '0' - } else { - if (i < 0) { - e-- - } else { - x = new Ctor(x) - x.d = xd - x.e = e - x = divide(x, y, sd, rm, 0, base) - xd = x.d - e = x.e - roundUp = inexact - } - - // The rounding digit, i.e. the digit after the digit that may be rounded up. - i = xd[sd] - k = base / 2 - roundUp = roundUp || xd[sd + 1] !== void 0 - - roundUp = - rm < 4 - ? (i !== void 0 || roundUp) && (rm === 0 || rm === (x.s < 0 ? 3 : 2)) - : i > k || (i === k && (rm === 4 || roundUp || (rm === 6 && xd[sd - 1] & 1) || rm === (x.s < 0 ? 8 : 7))) - - xd.length = sd - - if (roundUp) { - // Rounding up may mean the previous digit has to be rounded up and so on. - for (; ++xd[--sd] > base - 1; ) { - xd[sd] = 0 - if (!sd) { - ++e - xd.unshift(1) - } - } - } - - // Determine trailing zeros. - for (len = xd.length; !xd[len - 1]; --len); - - // E.g. [4, 11, 15] becomes 4bf. - for (i = 0, str = ''; i < len; i++) str += NUMERALS.charAt(xd[i]) - - // Add binary exponent suffix? - if (isExp) { - if (len > 1) { - if (baseOut == 16 || baseOut == 8) { - i = baseOut == 16 ? 4 : 3 - for (--len; len % i; len++) str += '0' - xd = convertBase(str, base, baseOut) - for (len = xd.length; !xd[len - 1]; --len); - - // xd[0] will always be be 1 - for (i = 1, str = '1.'; i < len; i++) str += NUMERALS.charAt(xd[i]) - } else { - str = str.charAt(0) + '.' + str.slice(1) - } - } - - str = str + (e < 0 ? 'p' : 'p+') + e - } else if (e < 0) { - for (; ++e; ) str = '0' + str - str = '0.' + str - } else { - if (++e > len) for (e -= len; e--; ) str += '0' - else if (e < len) str = str.slice(0, e) + '.' + str.slice(e) - } - } - - str = (baseOut == 16 ? '0x' : baseOut == 2 ? '0b' : baseOut == 8 ? '0o' : '') + str - } - - return x.s < 0 ? '-' + str : str - } - - // Does not strip trailing zeros. - function truncate(arr, len) { - if (arr.length > len) { - arr.length = len - return true - } - } - - // Decimal methods - - /* - * abs - * acos - * acosh - * add - * asin - * asinh - * atan - * atanh - * atan2 - * cbrt - * ceil - * clamp - * clone - * config - * cos - * cosh - * div - * exp - * floor - * hypot - * ln - * log - * log2 - * log10 - * max - * min - * mod - * mul - * pow - * random - * round - * set - * sign - * sin - * sinh - * sqrt - * sub - * sum - * tan - * tanh - * trunc - */ - - /* - * Return a new Decimal whose value is the absolute value of `x`. - * - * x {number|string|Decimal} - * - */ - function abs(x) { - return new this(x).abs() - } - - /* - * Return a new Decimal whose value is the arccosine in radians of `x`. - * - * x {number|string|Decimal} - * - */ - function acos(x) { - return new this(x).acos() - } - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic cosine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function acosh(x) { - return new this(x).acosh() - } - - /* - * Return a new Decimal whose value is the sum of `x` and `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function add(x, y) { - return new this(x).plus(y) - } - - /* - * Return a new Decimal whose value is the arcsine in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function asin(x) { - return new this(x).asin() - } - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic sine of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function asinh(x) { - return new this(x).asinh() - } - - /* - * Return a new Decimal whose value is the arctangent in radians of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function atan(x) { - return new this(x).atan() - } - - /* - * Return a new Decimal whose value is the inverse of the hyperbolic tangent of `x`, rounded to - * `precision` significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function atanh(x) { - return new this(x).atanh() - } - - /* - * Return a new Decimal whose value is the arctangent in radians of `y/x` in the range -pi to pi - * (inclusive), rounded to `precision` significant digits using rounding mode `rounding`. - * - * Domain: [-Infinity, Infinity] - * Range: [-pi, pi] - * - * y {number|string|Decimal} The y-coordinate. - * x {number|string|Decimal} The x-coordinate. - * - * atan2(±0, -0) = ±pi - * atan2(±0, +0) = ±0 - * atan2(±0, -x) = ±pi for x > 0 - * atan2(±0, x) = ±0 for x > 0 - * atan2(-y, ±0) = -pi/2 for y > 0 - * atan2(y, ±0) = pi/2 for y > 0 - * atan2(±y, -Infinity) = ±pi for finite y > 0 - * atan2(±y, +Infinity) = ±0 for finite y > 0 - * atan2(±Infinity, x) = ±pi/2 for finite x - * atan2(±Infinity, -Infinity) = ±3*pi/4 - * atan2(±Infinity, +Infinity) = ±pi/4 - * atan2(NaN, x) = NaN - * atan2(y, NaN) = NaN - * - */ - function atan2(y, x) { - y = new this(y) - x = new this(x) - var r, - pr = this.precision, - rm = this.rounding, - wpr = pr + 4 - - // Either NaN - if (!y.s || !x.s) { - r = new this(NaN) - - // Both ±Infinity - } else if (!y.d && !x.d) { - r = getPi(this, wpr, 1).times(x.s > 0 ? 0.25 : 0.75) - r.s = y.s - - // x is ±Infinity or y is ±0 - } else if (!x.d || y.isZero()) { - r = x.s < 0 ? getPi(this, pr, rm) : new this(0) - r.s = y.s - - // y is ±Infinity or x is ±0 - } else if (!y.d || x.isZero()) { - r = getPi(this, wpr, 1).times(0.5) - r.s = y.s - - // Both non-zero and finite - } else if (x.s < 0) { - this.precision = wpr - this.rounding = 1 - r = this.atan(divide(y, x, wpr, 1)) - x = getPi(this, wpr, 1) - this.precision = pr - this.rounding = rm - r = y.s < 0 ? r.minus(x) : r.plus(x) - } else { - r = this.atan(divide(y, x, wpr, 1)) - } - - return r - } - - /* - * Return a new Decimal whose value is the cube root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function cbrt(x) { - return new this(x).cbrt() - } - - /* - * Return a new Decimal whose value is `x` rounded to an integer using `ROUND_CEIL`. - * - * x {number|string|Decimal} - * - */ - function ceil(x) { - return finalise((x = new this(x)), x.e + 1, 2) - } - - /* - * Return a new Decimal whose value is `x` clamped to the range delineated by `min` and `max`. - * - * x {number|string|Decimal} - * min {number|string|Decimal} - * max {number|string|Decimal} - * - */ - function clamp(x, min, max) { - return new this(x).clamp(min, max) - } - - /* - * Configure global settings for a Decimal constructor. - * - * `obj` is an object with one or more of the following properties, - * - * precision {number} - * rounding {number} - * toExpNeg {number} - * toExpPos {number} - * maxE {number} - * minE {number} - * modulo {number} - * crypto {boolean|number} - * defaults {true} - * - * E.g. Decimal.config({ precision: 20, rounding: 4 }) - * - */ - function config(obj) { - if (!obj || typeof obj !== 'object') throw Error(decimalError + 'Object expected') - var i, - p, - v, - useDefaults = obj.defaults === true, - ps = [ - 'precision', - 1, - MAX_DIGITS, - 'rounding', - 0, - 8, - 'toExpNeg', - -EXP_LIMIT, - 0, - 'toExpPos', - 0, - EXP_LIMIT, - 'maxE', - 0, - EXP_LIMIT, - 'minE', - -EXP_LIMIT, - 0, - 'modulo', - 0, - 9, - ] - - for (i = 0; i < ps.length; i += 3) { - if (((p = ps[i]), useDefaults)) this[p] = DEFAULTS[p] - if ((v = obj[p]) !== void 0) { - if (mathfloor(v) === v && v >= ps[i + 1] && v <= ps[i + 2]) this[p] = v - else throw Error(invalidArgument + p + ': ' + v) - } - } - - if (((p = 'crypto'), useDefaults)) this[p] = DEFAULTS[p] - if ((v = obj[p]) !== void 0) { - if (v === true || v === false || v === 0 || v === 1) { - if (v) { - if (typeof crypto != 'undefined' && crypto && (crypto.getRandomValues || crypto.randomBytes)) { - this[p] = true - } else { - throw Error(cryptoUnavailable) - } - } else { - this[p] = false - } - } else { - throw Error(invalidArgument + p + ': ' + v) - } - } - - return this - } - - /* - * Return a new Decimal whose value is the cosine of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function cos(x) { - return new this(x).cos() - } - - /* - * Return a new Decimal whose value is the hyperbolic cosine of `x`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function cosh(x) { - return new this(x).cosh() - } - - /* - * Create and return a Decimal constructor with the same configuration properties as this Decimal - * constructor. - * - */ - function clone(obj) { - var i, p, ps - - /* - * The Decimal constructor and exported function. - * Return a new Decimal instance. - * - * v {number|string|Decimal} A numeric value. - * - */ - function Decimal(v) { - var e, - i, - t, - x = this - - // Decimal called without new. - if (!(x instanceof Decimal)) return new Decimal(v) - - // Retain a reference to this Decimal constructor, and shadow Decimal.prototype.constructor - // which points to Object. - x.constructor = Decimal - - // Duplicate. - if (isDecimalInstance(v)) { - x.s = v.s - - if (external) { - if (!v.d || v.e > Decimal.maxE) { - // Infinity. - x.e = NaN - x.d = null - } else if (v.e < Decimal.minE) { - // Zero. - x.e = 0 - x.d = [0] - } else { - x.e = v.e - x.d = v.d.slice() - } - } else { - x.e = v.e - x.d = v.d ? v.d.slice() : v.d - } - - return - } - - t = typeof v - - if (t === 'number') { - if (v === 0) { - x.s = 1 / v < 0 ? -1 : 1 - x.e = 0 - x.d = [0] - return - } - - if (v < 0) { - v = -v - x.s = -1 - } else { - x.s = 1 - } - - // Fast path for small integers. - if (v === ~~v && v < 1e7) { - for (e = 0, i = v; i >= 10; i /= 10) e++ - - if (external) { - if (e > Decimal.maxE) { - x.e = NaN - x.d = null - } else if (e < Decimal.minE) { - x.e = 0 - x.d = [0] - } else { - x.e = e - x.d = [v] - } - } else { - x.e = e - x.d = [v] - } - - return - - // Infinity, NaN. - } else if (v * 0 !== 0) { - if (!v) x.s = NaN - x.e = NaN - x.d = null - return - } - - return parseDecimal(x, v.toString()) - } else if (t !== 'string') { - throw Error(invalidArgument + v) - } - - // Minus sign? - if ((i = v.charCodeAt(0)) === 45) { - v = v.slice(1) - x.s = -1 - } else { - // Plus sign? - if (i === 43) v = v.slice(1) - x.s = 1 - } - - return isDecimal.test(v) ? parseDecimal(x, v) : parseOther(x, v) - } - - Decimal.prototype = P - - Decimal.ROUND_UP = 0 - Decimal.ROUND_DOWN = 1 - Decimal.ROUND_CEIL = 2 - Decimal.ROUND_FLOOR = 3 - Decimal.ROUND_HALF_UP = 4 - Decimal.ROUND_HALF_DOWN = 5 - Decimal.ROUND_HALF_EVEN = 6 - Decimal.ROUND_HALF_CEIL = 7 - Decimal.ROUND_HALF_FLOOR = 8 - Decimal.EUCLID = 9 - - Decimal.config = Decimal.set = config - Decimal.clone = clone - Decimal.isDecimal = isDecimalInstance - - Decimal.abs = abs - Decimal.acos = acos - Decimal.acosh = acosh // ES6 - Decimal.add = add - Decimal.asin = asin - Decimal.asinh = asinh // ES6 - Decimal.atan = atan - Decimal.atanh = atanh // ES6 - Decimal.atan2 = atan2 - Decimal.cbrt = cbrt // ES6 - Decimal.ceil = ceil - Decimal.clamp = clamp - Decimal.cos = cos - Decimal.cosh = cosh // ES6 - Decimal.div = div - Decimal.exp = exp - Decimal.floor = floor - Decimal.hypot = hypot // ES6 - Decimal.ln = ln - Decimal.log = log - Decimal.log10 = log10 // ES6 - Decimal.log2 = log2 // ES6 - Decimal.max = max - Decimal.min = min - Decimal.mod = mod - Decimal.mul = mul - Decimal.pow = pow - Decimal.random = random - Decimal.round = round - Decimal.sign = sign // ES6 - Decimal.sin = sin - Decimal.sinh = sinh // ES6 - Decimal.sqrt = sqrt - Decimal.sub = sub - Decimal.sum = sum - Decimal.tan = tan - Decimal.tanh = tanh // ES6 - Decimal.trunc = trunc // ES6 - - if (obj === void 0) obj = {} - if (obj) { - if (obj.defaults !== true) { - ps = ['precision', 'rounding', 'toExpNeg', 'toExpPos', 'maxE', 'minE', 'modulo', 'crypto'] - for (i = 0; i < ps.length; ) if (!obj.hasOwnProperty((p = ps[i++]))) obj[p] = this[p] - } - } - - Decimal.config(obj) - - return Decimal - } - - /* - * Return a new Decimal whose value is `x` divided by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function div(x, y) { - return new this(x).div(y) - } - - /* - * Return a new Decimal whose value is the natural exponential of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The power to which to raise the base of the natural log. - * - */ - function exp(x) { - return new this(x).exp() - } - - /* - * Return a new Decimal whose value is `x` round to an integer using `ROUND_FLOOR`. - * - * x {number|string|Decimal} - * - */ - function floor(x) { - return finalise((x = new this(x)), x.e + 1, 3) - } - - /* - * Return a new Decimal whose value is the square root of the sum of the squares of the arguments, - * rounded to `precision` significant digits using rounding mode `rounding`. - * - * hypot(a, b, ...) = sqrt(a^2 + b^2 + ...) - * - * arguments {number|string|Decimal} - * - */ - function hypot() { - var i, - n, - t = new this(0) - - external = false - - for (i = 0; i < arguments.length; ) { - n = new this(arguments[i++]) - if (!n.d) { - if (n.s) { - external = true - return new this(1 / 0) - } - t = n - } else if (t.d) { - t = t.plus(n.times(n)) - } - } - - external = true - - return t.sqrt() - } - - /* - * Return true if object is a Decimal instance (where Decimal is any Decimal constructor), - * otherwise return false. - * - */ - function isDecimalInstance(obj) { - return obj instanceof Decimal || (obj && obj.toStringTag === tag) || false - } - - /* - * Return a new Decimal whose value is the natural logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function ln(x) { - return new this(x).ln() - } - - /* - * Return a new Decimal whose value is the log of `x` to the base `y`, or to base 10 if no base - * is specified, rounded to `precision` significant digits using rounding mode `rounding`. - * - * log[y](x) - * - * x {number|string|Decimal} The argument of the logarithm. - * y {number|string|Decimal} The base of the logarithm. - * - */ - function log(x, y) { - return new this(x).log(y) - } - - /* - * Return a new Decimal whose value is the base 2 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function log2(x) { - return new this(x).log(2) - } - - /* - * Return a new Decimal whose value is the base 10 logarithm of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function log10(x) { - return new this(x).log(10) - } - - /* - * Return a new Decimal whose value is the maximum of the arguments. - * - * arguments {number|string|Decimal} - * - */ - function max() { - return maxOrMin(this, arguments, 'lt') - } - - /* - * Return a new Decimal whose value is the minimum of the arguments. - * - * arguments {number|string|Decimal} - * - */ - function min() { - return maxOrMin(this, arguments, 'gt') - } - - /* - * Return a new Decimal whose value is `x` modulo `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function mod(x, y) { - return new this(x).mod(y) - } - - /* - * Return a new Decimal whose value is `x` multiplied by `y`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function mul(x, y) { - return new this(x).mul(y) - } - - /* - * Return a new Decimal whose value is `x` raised to the power `y`, rounded to precision - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} The base. - * y {number|string|Decimal} The exponent. - * - */ - function pow(x, y) { - return new this(x).pow(y) - } - - /* - * Returns a new Decimal with a random value equal to or greater than 0 and less than 1, and with - * `sd`, or `Decimal.precision` if `sd` is omitted, significant digits (or less if trailing zeros - * are produced). - * - * [sd] {number} Significant digits. Integer, 0 to MAX_DIGITS inclusive. - * - */ - function random(sd) { - var d, - e, - k, - n, - i = 0, - r = new this(1), - rd = [] - - if (sd === void 0) sd = this.precision - else checkInt32(sd, 1, MAX_DIGITS) - - k = Math.ceil(sd / LOG_BASE) - - if (!this.crypto) { - for (; i < k; ) rd[i++] = (Math.random() * 1e7) | 0 - - // Browsers supporting crypto.getRandomValues. - } else if (crypto.getRandomValues) { - d = crypto.getRandomValues(new Uint32Array(k)) - - for (; i < k; ) { - n = d[i] - - // 0 <= n < 4294967296 - // Probability n >= 4.29e9, is 4967296 / 4294967296 = 0.00116 (1 in 865). - if (n >= 4.29e9) { - d[i] = crypto.getRandomValues(new Uint32Array(1))[0] - } else { - // 0 <= n <= 4289999999 - // 0 <= (n % 1e7) <= 9999999 - rd[i++] = n % 1e7 - } - } - - // Node.js supporting crypto.randomBytes. - } else if (crypto.randomBytes) { - // buffer - d = crypto.randomBytes((k *= 4)) - - for (; i < k; ) { - // 0 <= n < 2147483648 - n = d[i] + (d[i + 1] << 8) + (d[i + 2] << 16) + ((d[i + 3] & 0x7f) << 24) - - // Probability n >= 2.14e9, is 7483648 / 2147483648 = 0.0035 (1 in 286). - if (n >= 2.14e9) { - crypto.randomBytes(4).copy(d, i) - } else { - // 0 <= n <= 2139999999 - // 0 <= (n % 1e7) <= 9999999 - rd.push(n % 1e7) - i += 4 - } - } - - i = k / 4 - } else { - throw Error(cryptoUnavailable) - } - - k = rd[--i] - sd %= LOG_BASE - - // Convert trailing digits to zeros according to sd. - if (k && sd) { - n = mathpow(10, LOG_BASE - sd) - rd[i] = ((k / n) | 0) * n - } - - // Remove trailing words which are zero. - for (; rd[i] === 0; i--) rd.pop() - - // Zero? - if (i < 0) { - e = 0 - rd = [0] - } else { - e = -1 - - // Remove leading words which are zero and adjust exponent accordingly. - for (; rd[0] === 0; e -= LOG_BASE) rd.shift() - - // Count the digits of the first word of rd to determine leading zeros. - for (k = 1, n = rd[0]; n >= 10; n /= 10) k++ - - // Adjust the exponent for leading zeros of the first word of rd. - if (k < LOG_BASE) e -= LOG_BASE - k - } - - r.e = e - r.d = rd - - return r - } - - /* - * Return a new Decimal whose value is `x` rounded to an integer using rounding mode `rounding`. - * - * To emulate `Math.round`, set rounding to 7 (ROUND_HALF_CEIL). - * - * x {number|string|Decimal} - * - */ - function round(x) { - return finalise((x = new this(x)), x.e + 1, this.rounding) - } - - /* - * Return - * 1 if x > 0, - * -1 if x < 0, - * 0 if x is 0, - * -0 if x is -0, - * NaN otherwise - * - * x {number|string|Decimal} - * - */ - function sign(x) { - x = new this(x) - return x.d ? (x.d[0] ? x.s : 0 * x.s) : x.s || NaN - } - - /* - * Return a new Decimal whose value is the sine of `x`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function sin(x) { - return new this(x).sin() - } - - /* - * Return a new Decimal whose value is the hyperbolic sine of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function sinh(x) { - return new this(x).sinh() - } - - /* - * Return a new Decimal whose value is the square root of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} - * - */ - function sqrt(x) { - return new this(x).sqrt() - } - - /* - * Return a new Decimal whose value is `x` minus `y`, rounded to `precision` significant digits - * using rounding mode `rounding`. - * - * x {number|string|Decimal} - * y {number|string|Decimal} - * - */ - function sub(x, y) { - return new this(x).sub(y) - } - - /* - * Return a new Decimal whose value is the sum of the arguments, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * Only the result is rounded, not the intermediate calculations. - * - * arguments {number|string|Decimal} - * - */ - function sum() { - var i = 0, - args = arguments, - x = new this(args[i]) - - external = false - for (; x.s && ++i < args.length; ) x = x.plus(args[i]) - external = true - - return finalise(x, this.precision, this.rounding) - } - - /* - * Return a new Decimal whose value is the tangent of `x`, rounded to `precision` significant - * digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function tan(x) { - return new this(x).tan() - } - - /* - * Return a new Decimal whose value is the hyperbolic tangent of `x`, rounded to `precision` - * significant digits using rounding mode `rounding`. - * - * x {number|string|Decimal} A value in radians. - * - */ - function tanh(x) { - return new this(x).tanh() - } - - /* - * Return a new Decimal whose value is `x` truncated to an integer. - * - * x {number|string|Decimal} - * - */ - function trunc(x) { - return finalise((x = new this(x)), x.e + 1, 1) - } - - // Create and configure initial Decimal constructor. - Decimal = clone(DEFAULTS) - Decimal.prototype.constructor = Decimal - Decimal['default'] = Decimal.Decimal = Decimal - - // Create the internal constants from their string values. - LN10 = new Decimal(LN10) - PI = new Decimal(PI) - - // Export. - - // AMD. - if (typeof define == 'function' && define.amd) { - define(function () { - return Decimal - }) - - // Node and other environments that support module.exports. - } else if (typeof module != 'undefined' && module.exports) { - if (typeof Symbol == 'function' && typeof Symbol.iterator == 'symbol') { - P[Symbol['for']('nodejs.util.inspect.custom')] = P.toString - P[Symbol.toStringTag] = 'Decimal' - } - - module.exports = Decimal - - // Browser. - } else { - if (!globalScope) { - globalScope = typeof self != 'undefined' && self && self.self == self ? self : window - } - - noConflict = globalScope.Decimal - Decimal.noConflict = function () { - globalScope.Decimal = noConflict - return Decimal - } - - globalScope.Decimal = Decimal - } -})(this) diff --git a/website/static/liquidity-simulator/index.html b/website/static/liquidity-simulator/index.html deleted file mode 100644 index 2651e4d..0000000 --- a/website/static/liquidity-simulator/index.html +++ /dev/null @@ -1,134 +0,0 @@ - - - Ark liquidity simulator - - - -
-
-

ASP

-

- -
- 1 - · - 10 - · - 100 -

-

- -
- 2 weeks - · - 1 month -

-

- -
- 1 - · - 10 - · - 100 -

-

- -

-

Users

-

- -
- 4 - · - 40 - · - 400 -

-

- -
- 0.01 - · - 0.1 - · - 1 -

-

- -
- 0.33 - · - 0.50 - · - 1 -

-

- -
- 1 - · - 10 - · - 100 -

-
-
-

Stats

-
-
-

Payments

-
-
-
-

VTXOs

-
-
-
-

Budget

-
-
-
-
-

Timeline

-

- - - -

-
-

- Each color tone represents a specific user
- Mouse over a circle to see a JSON representation of the payment -

-
-
-
- - - - diff --git a/website/static/liquidity-simulator/script.js b/website/static/liquidity-simulator/script.js deleted file mode 100644 index a6ccd60..0000000 --- a/website/static/liquidity-simulator/script.js +++ /dev/null @@ -1,261 +0,0 @@ -const dqs = (selector) => document.querySelector(selector) - -const clock = { - current: 0, - intervalId: '', - pause: () => clock.removeInterval(), - play() { - const maxDays = Number(dqs('#timelock').value) - // if already running, do nothing - if (clock.intervalId) return - // reset and play timeline if on the end of previous timeline - if (clock.current === maxDays) { - clock.reset() - clock.play() - return - } - // start clock - clock.intervalId = setInterval(() => { - clock.current += 1 - if (clock.current === maxDays) clock.removeInterval() - days.db.push(days.randomDay()) - ui.render() - }, 300) - }, - reset() { - clock.removeInterval() - clock.current = 0 - days.db = [] - ui.render() - }, - removeInterval: () => { - if (clock.intervalId) { - clearInterval(clock.intervalId) - clock.intervalId = '' - } - }, -} - -const days = { - db: [], - untilNow: () => { - const users = {} - let eachPayment = 0 - let eachVTXO = 0 - let numEvents = 0 - let numVTXOs = 0 - let sumPayments = 0 - let sumVTXOs = 0 - days.db.forEach((day) => { - if (!day) return - day.forEach((event) => { - if (!users[event.user]) users[event.user] = 0 - users[event.user] += 1 - eachVTXO = event.vtxos.each - eachPayment = event.payment.value - numEvents += 1 - numVTXOs = Decimal.add(numVTXOs, event.vtxos.num).toNumber() - sumPayments = Decimal.add(sumPayments, event.payment.value).toNumber() - sumVTXOs = Decimal.add(sumVTXOs, event.vtxos.sum).toNumber() - }) - }) - return { - eachPayment, - eachVTXO, - numEvents, - numUsers: Object.keys(users).length, - numVTXOs, - ratioVTXOsPayments: Decimal.div(sumVTXOs, sumPayments).toNumber(), - sumPayments, - sumVTXOs, - } - }, - randomDay: () => { - let day - const numberUsers = dqs('#numberUsers').value - const onboardAmount = dqs('#onboardAmount').value - const timelock = Number(dqs('#timelock').value) - const moneyVelocity = Decimal.div(timelock, 28) - .mul(dqs('#moneyVelocity').value) - .toNumber() - const numberPayments = Decimal.div(timelock, 28) - .mul(dqs('#numberPayments').value) - .toNumber() - const vtxoRatio = Number(dqs('#vtxoRatio').value) - const paymentValue = Decimal.mul(onboardAmount, moneyVelocity) - .div(numberPayments) - .toNumber() - const vtxoVal = Decimal.div(onboardAmount, vtxoRatio).toNumber() - const vtxoNum = Decimal.div(paymentValue, vtxoVal).ceil().toNumber() - const vtxoSum = Decimal.mul(vtxoNum, vtxoVal).toNumber() - const paymentChange = Decimal.sub(vtxoSum, paymentValue).toNumber() - for (let user = 0; user < numberUsers; user++) { - const rand = timelock * Math.random() - if (rand < numberPayments) { - if (!day) day = [] - day.push({ - user, - payment: { - value: paymentValue, - change: paymentChange, - }, - vtxos: { - each: vtxoVal, - num: vtxoNum, - sum: vtxoSum, - }, - }) - } - } - return day - }, -} - -const pretty = { - btc: (num) => pretty.num(num, 0, 8), - num: (num = 0, min = 0, max = 2) => { - if (num === 0) return '0' - return new Intl.NumberFormat('en-us', { - minimumFractionDigits: min, - maximumFractionDigits: max, - }).format(num) - }, -} - -const ui = { - theme: { - circle: { radius: 5 }, - colors: [ - 'indianred', - 'lightCoral', - 'red', - 'darkred', - 'pink', - 'hotpink', - 'mediumvioletred', - 'lightsalmon', - 'coral', - 'orangered', - 'darkorange', - 'orange', - 'gold', - 'moccasin', - 'khaki', - 'darkkhaki', - 'thistle', - 'plum', - ], - margin: 10, - vSpace: 20, - }, - renderStats: () => { - const dustLimit = Decimal.div( - dqs('#dustLimit').value, - 100_000_000 // from satoshis to btc - ) - const initialBudget = Number(dqs('#initialBudget').value) - const { - eachPayment, - eachVTXO, - numUsers, - numEvents, - numVTXOs, - ratioVTXOsPayments, - sumPayments, - sumVTXOs, - } = days.untilNow() - const connectorsValue = Decimal.mul(numVTXOs, dustLimit).toNumber() - const totalCost = Decimal.add(sumVTXOs, connectorsValue).toNumber() - const budget = { - initial: initialBudget, - payments: sumVTXOs, - connectors: connectorsValue, - available: Decimal.sub(initialBudget, totalCost).toNumber(), - } - const stats = ` -

Each: ${pretty.btc(eachPayment)} BTC

-

Number of users: ${numUsers}

-

Number of events: ${numEvents}

-

Total payments: ${pretty.btc(sumPayments)} BTC

- ` - const vtxos = ` -

Each: ${pretty.btc(eachVTXO)} BTC

-

VTXOs used: ${numVTXOs}

-

Total value: ${pretty.btc(sumVTXOs)} BTC

-

Ratio value / payments: ${pretty.num(ratioVTXOsPayments)}

- ` - const liquidity = ` -

Initial: ${pretty.btc(budget.initial)} BTC

-

Payments: ${pretty.btc(budget.payments)} BTC

-

Connectors: ${pretty.btc(budget.connectors)} BTC

-

Available: ${pretty.btc(budget.available)} BTC

- ` - dqs('#graph1').innerHTML = stats - dqs('#graph2').innerHTML = vtxos - dqs('#graph3').innerHTML = liquidity - }, - renderTimeline: () => { - const container = dqs('.timelineContainer') - const containerWidth = container.offsetWidth - ui.theme.margin * 2 - const steps = dqs('#timelock').value - const stepWidth = Decimal.div(containerWidth, steps).toNumber() - const height = container.offsetHeight - 2 - const width = clock.current * stepWidth + ui.theme.margin * 2 - const viewbox = `0 0 ${width} ${height}` - // render event inside timeline - const _event = (event, idx, index) => { - const r = ui.theme.circle.radius - const cx = index * stepWidth + r + ui.theme.margin - const cy = (idx + 2) * ui.theme.vSpace - const fill = ui.theme.colors[event.user % ui.theme.colors.length] - return ` - - ${JSON.stringify(event, null, 2)} - - ` - } - // render day inside timeline - const _day = (day, index) => { - if (!day) return - const cx = index * stepWidth + ui.theme.circle.radius + ui.theme.margin - const cy = ui.theme.vSpace - const idx = index + 1 - const num = `${idx}` - return num + day.map((event, idx) => _event(event, idx, index)).join() - } - // render days inside timeline - const _days = () => days.db.map((day, index) => _day(day, index)).join() - // timeline is a svg - const svg = ` - - - - ${_days()} - - ` - dqs('.timelineContainer').innerHTML = svg - }, - resizeTimeline: () => { - const container = dqs('.timelineContainer') - const numberUsers = Number(dqs('#numberUsers').value) - const height = (numberUsers + 2) * ui.theme.vSpace - // don't reduce size - if (container?.offsetHeight > height) return - container.style.height = `${height}px` - }, - render: () => { - ui.resizeTimeline() - ui.renderTimeline() - ui.renderStats() - }, -} - -window.onload = () => { - dqs('#pauseButton').onclick = () => clock.pause() - dqs('#playButton').onclick = () => clock.play() - dqs('#resetButton').onclick = () => clock.reset() -} diff --git a/website/static/liquidity-simulator/style.css b/website/static/liquidity-simulator/style.css deleted file mode 100644 index c4c2a86..0000000 --- a/website/static/liquidity-simulator/style.css +++ /dev/null @@ -1,30 +0,0 @@ -input { - margin: 0.21rem 0; - max-width: 90%; - width: 10rem; -} -a { - color: lightCoral; - cursor: pointer; -} -.flexed { - display: flex; - justify-content: space-between; -} -.graphContainer { - column-gap: 3rem; - display: grid; - grid-template-columns: repeat(3, 1fr); - margin-bottom: 3rem; -} -.graphContainer > div { - border: 1px solid grey; - height: 12rem; - padding: 0 1rem; -} -.timelineContainer { - border: 1px solid grey; - text-align: right; - height: 120px; - max-height: 60vh; -} diff --git a/website/yarn.lock b/website/yarn.lock deleted file mode 100644 index e867286..0000000 --- a/website/yarn.lock +++ /dev/null @@ -1,8134 +0,0 @@ -# THIS IS AN AUTOGENERATED FILE. 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