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Howey Test and Cryptocurrencies: 'Every ICO Is a Security'
What Is the Howey Test?
To determine whether a transaction qualifies as a "investment contract" and thus qualifies as a security, the Howey Test refers to the U.S. Supreme Court cass: the Securities Act of 1933 and the Securities Exchange Act of 1934. According to the Howey Test, an investment contract exists when "money is invested in a common enterprise with a reasonable expectation of profits from others' efforts."
The test applies to any contract, scheme, or transaction. The Howey Test helps investors and project backers understand blockchain and digital currency projects. ICOs and certain cryptocurrencies may be found to be "investment contracts" under the test.
Understanding the Howey Test
The Howey Test comes from the 1946 Supreme Court case SEC v. W.J. Howey Co. The Howey Company sold citrus groves to Florida buyers who leased them back to Howey. The company would maintain the groves and sell the fruit for the owners. Both parties benefited. Most buyers had no farming experience and were not required to farm the land.
The SEC intervened because Howey failed to register the transactions. The court ruled that the leaseback agreements were investment contracts.
This established four criteria for determining an investment contract. Investing contract:
- An investment of money
- n a common enterprise
- With the expectation of profit
- To be derived from the efforts of others
In the case of Howey, the buyers saw the transactions as valuable because others provided the labor and expertise. An income stream was obtained by only investing capital. As a result of the Howey Test, the transaction had to be registered with the SEC.
Howey Test and Cryptocurrencies
Bitcoin is notoriously difficult to categorize. Decentralized, they evade regulation in many ways. Regardless, the SEC is looking into digital assets and determining when their sale qualifies as an investment contract.
The SEC claims that selling digital assets meets the "investment of money" test because fiat money or other digital assets are being exchanged. Like the "common enterprise" test.
Whether a digital asset qualifies as an investment contract depends on whether there is a "expectation of profit from others' efforts."
For example, buyers of digital assets may be relying on others' efforts if they expect the project's backers to build and maintain the digital network, rather than a dispersed community of unaffiliated users. Also, if the project's backers create scarcity by burning tokens, the test is met. Another way the "efforts of others" test is met is if the project's backers continue to act in a managerial role.
These are just a few examples given by the SEC. If a project's success is dependent on ongoing support from backers, the buyer of the digital asset is likely relying on "others' efforts."
Special Considerations
If the SEC determines a cryptocurrency token is a security, many issues arise. It means the SEC can decide whether a token can be sold to US investors and forces the project to register.
In 2017, the SEC ruled that selling DAO tokens for Ether violated federal securities laws. Instead of enforcing securities laws, the SEC issued a warning to the cryptocurrency industry.
Due to the Howey Test, most ICOs today are likely inaccessible to US investors. After a year of ICOs, then-SEC Chair Jay Clayton declared them all securities.
SEC Chairman Gensler Agrees With Predecessor: 'Every ICO Is a Security'
Howey Test FAQs
How Do You Determine If Something Is a Security?
The Howey Test determines whether certain transactions are "investment contracts." Securities are transactions that qualify as "investment contracts" under the Securities Act of 1933 and the Securities Exchange Act of 1934.
The Howey Test looks for a "investment of money in a common enterprise with a reasonable expectation of profits from others' efforts." If so, the Securities Act of 1933 and the Securities Exchange Act of 1934 require disclosure and registration.
Why Is Bitcoin Not a Security?
Former SEC Chair Jay Clayton clarified in June 2018 that bitcoin is not a security: "Cryptocurrencies: Replace the dollar, euro, and yen with bitcoin. That type of currency is not a security," said Clayton.
Bitcoin, which has never sought public funding to develop its technology, fails the SEC's Howey Test. However, according to Clayton, ICO tokens are securities.
A Security Defined by the SEC
In the public and private markets, securities are fungible and tradeable financial instruments. The SEC regulates public securities sales.
The Supreme Court defined a security offering in SEC v. W.J. Howey Co. In its judgment, the court defines a security using four criteria:
- An investment contract's existence
- The formation of a common enterprise
- The issuer's profit promise
- Third-party promotion of the offering
Read original post.
More on Web3 & Crypto
Caleb Naysmith
3 years ago Draft
A Myth: Decentralization
It’s simply not conceivable, or at least not credible.
One of the most touted selling points of Crypto has always been this grandiose idea of decentralization. Bitcoin first arose in 2009 after the housing crisis and subsequent crash that came with it. It aimed to solve this supposed issue of centralization. Nobody “owns” Bitcoin in theory, so the idea then goes that it won’t be subject to the same downfalls that led to the 2008 crash or similarly speculative events that led to the 2008 disaster. The issue is the banks, not the human nature associated with the greedy individuals running them.
Subsequent blockchains have attempted to fix many of the issues of Bitcoin by increasing capacity, decreasing the costs and processing times associated with Bitcoin, and expanding what can be done with their blockchains. Since nobody owns Bitcoin, it hasn’t really been able to be expanded on. You have people like Vitalk Buterin, however, that actively work on Ethereum though.
The leap from Bitcoin to Ethereum was a massive leap toward centralization, and the trend has only gotten worse. In fact, crypto has since become almost exclusively centralized in recent years.
Decentralization is only good in theory
It’s a good idea. In fact, it’s a wonderful idea. However, like other utopian societies, individuals misjudge human nature and greed. In a perfect world, decentralization would certainly be a wonderful idea because sure, people may function as their own banks, move payments immediately, remain anonymous, and so on. However, underneath this are a couple issues:
You can already send money instantaneously today.
They are not decentralized.
Decentralization is a bad idea.
Being your own bank is a stupid move.
Let’s break these down. Some are quite simple, but lets have a look.
Sending money right away
One thing with crypto is the idea that you can send payments instantly. This has pretty much been entirely solved in current times. You can transmit significant sums of money instantly for a nominal cost and it’s instantaneously cleared. Venmo was launched in 2009 and has since increased to prominence, and currently is on most people's phones. I can directly send ANY amount of money quickly from my bank to another person's Venmo account.
Comparing that with ETH and Bitcoin, Venmo wins all around. I can send money to someone for free instantly in dollars and the only fee paid is optional depending on when you want it.
Both Bitcoin and Ethereum are subject to demand. If the blockchains have a lot of people trying to process transactions fee’s go up, and the time that it takes to receive your crypto takes longer. When Ethereum gets bad, people have reported spending several thousand of dollars on just 1 transaction.
These transactions take place via “miners” bundling and confirming transactions, then recording them on the blockchain to confirm that the transaction did indeed happen. They charge fees to do this and are also paid in Bitcoin/ETH. When a transaction is confirmed, it's then sent to the other users wallet. This within itself is subject to lots of controversy because each transaction needs to be confirmed 6 times, this takes massive amounts of power, and most of the power is wasted because this is an adversarial system in which the person that mines the transaction gets paid, and everyone else is out of luck. Also, these could theoretically be subject to a “51% attack” in which anyone with over 51% of the mining hash rate could effectively control all of the transactions, and reverse transactions while keeping the BTC resulting in “double spending”.
There are tons of other issues with this, but essentially it means: They rely on these third parties to confirm the transactions. Without people confirming these transactions, Bitcoin stalls completely, and if anyone becomes too dominant they can effectively control bitcoin.
Not to mention, these transactions are in Bitcoin and ETH, not dollars. So, you need to convert them to dollars still, and that's several more transactions, and likely to take several days anyway as the centralized exchange needs to send you the money by traditional methods.
They are not distributed
That takes me to the following point. This isn’t decentralized, at all. Bitcoin is the closest it gets because Satoshi basically closed it to new upgrades, although its still subject to:
Whales
Miners
It’s vital to realize that these are often the same folks. While whales aren’t centralized entities typically, they can considerably effect the price and outcome of Bitcoin. If the largest wallets holding as much as 1 million BTC were to sell, it’d effectively collapse the price perhaps beyond repair. However, Bitcoin can and is pretty much controlled by the miners. Further, Bitcoin is more like an oligarchy than decentralized. It’s been effectively used to make the rich richer, and both the mining and price is impacted by the rich. The overwhelming minority of those actually using it are retail investors. The retail investors are basically never the ones generating money from it either.
As far as ETH and other cryptos go, there is realistically 0 case for them being decentralized. Vitalik could not only kill it but even walking away from it would likely lead to a significant decline. It has tons of issues right now that Vitalik has promised to fix with the eventual Ethereum 2.0., and stepping away from it wouldn’t help.
Most tokens as well are generally tied to some promise of future developments and creators. The same is true for most NFT projects. The reason 99% of crypto and NFT projects fail is because they failed to deliver on various promises or bad dev teams, or poor innovation, or the founders just straight up stole from everyone. I could go more in-depth than this but go find any project and if there is a dev team, company, or person tied to it then it's likely, not decentralized. The success of that project is directly tied to the dev team, and if they wanted to, most hold large wallets and could sell it all off effectively killing the project. Not to mention, any crypto project that doesn’t have a locked contract can 100% be completely rugged and they can run off with all of the money.
Decentralization is undesirable
Even if they were decentralized then it would not be a good thing. The graphic above indicates this is effectively a rich person’s unregulated playground… so it’s exactly like… the very issue it tried to solve?
Not to mention, it’s supposedly meant to prevent things like 2008, but is regularly subjected to 50–90% drawdowns in value? Back when Bitcoin was only known in niche parts of the dark web and illegal markets, it would regularly drop as much as 90% and has a long history of massive drawdowns.
The majority of crypto is blatant scams, and ALL of crypto is a “zero” or “negative” sum game in that it relies on the next person buying for people to make money. This is not a good thing. This has yet to solve any issues around what caused the 2008 crisis. Rather, it seemingly amplified all of the bad parts of it actually. Crypto is the ultimate speculative asset and realistically has no valuation metric. People invest in Apple because it has revenue and cash on hand. People invest in crypto purely for speculation. The lack of regulation or accountability means this is amplified to the most extreme degree where anything goes: Fraud, deception, pump and dumps, scams, etc. This results in a pure speculative madhouse where, unsurprisingly, only the rich win. Not only that but the deck is massively stacked in against the everyday investor because you can’t do a pump and dump without money.
At the heart of all of this is still the same issues: greed and human nature. However, in setting out to solve the issues that allowed 2008 to happen, they made something that literally took all of the bad parts of 2008 and then amplified it. 2008, similarly, was due to greed and human nature but was allowed to happen due to lack of oversite, rich people's excessive leverage over the poor, and excessive speculation. Crypto trades SOLELY on human emotion, has 0 oversite, is pure speculation, and the power dynamic is just as bad or worse.
Why should each individual be their own bank?
This is the last one, and it's short and basic. Why do we want people functioning as their own bank? Everything we do relies on another person. Without the internet, and internet providers there is no crypto. We don’t have people functioning as their own home and car manufacturers or internet service providers. Sure, you might specialize in some of these things, but masquerading as your own bank is a horrible idea.
I am not in the banking industry so I don’t know all the issues with banking. Most people aren’t in banking or crypto, so they don’t know the ENDLESS scams associated with it, and they are bound to lose their money eventually.
If you appreciate this article and want to read more from me and authors like me, without any limits, consider buying me a coffee: buymeacoffee.com/calebnaysmith
mbvissers.eth
3 years ago
Why does every smart contract seem to implement ERC165?
ERC165 (or EIP-165) is a standard utilized by various open-source smart contracts like Open Zeppelin or Aavegotchi.
What's it? You must implement? Why do we need it? I'll describe the standard and answer any queries.
What is ERC165
ERC165 detects and publishes smart contract interfaces. Meaning? It standardizes how interfaces are recognized, how to detect if they implement ERC165, and how a contract publishes the interfaces it implements. How does it work?
Why use ERC165? Sometimes it's useful to know which interfaces a contract implements, and which version.
Identifying interfaces
An interface function's selector. This verifies an ABI function. XORing all function selectors defines an interface in this standard. The following code demonstrates.
// SPDX-License-Identifier: UNLICENCED
pragma solidity >=0.8.0 <0.9.0;
interface Solidity101 {
function hello() external pure;
function world(int) external pure;
}
contract Selector {
function calculateSelector() public pure returns (bytes4) {
Solidity101 i;
return i.hello.selector ^ i.world.selector;
// Returns 0xc6be8b58
}
function getHelloSelector() public pure returns (bytes4) {
Solidity101 i;
return i.hello.selector;
// Returns 0x19ff1d21
}
function getWorldSelector() public pure returns (bytes4) {
Solidity101 i;
return i.world.selector;
// Returns 0xdf419679
}
}This code isn't necessary to understand function selectors and how an interface's selector can be determined from the functions it implements.
Run that sample in Remix to see how interface function modifications affect contract function output.
Contracts publish their implemented interfaces.
We can identify interfaces. Now we must disclose the interfaces we're implementing. First, import IERC165 like so.
pragma solidity ^0.4.20;
interface ERC165 {
/// @notice Query if a contract implements an interface
/// @param interfaceID The interface identifier, as specified in ERC-165
/// @dev Interface identification is specified in ERC-165.
/// @return `true` if the contract implements `interfaceID` and
/// `interfaceID` is not 0xffffffff, `false` otherwise
function supportsInterface(bytes4 interfaceID) external view returns (bool);
}We still need to build this interface in our smart contract. ERC721 from OpenZeppelin is a good example.
// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (token/ERC721/ERC721.sol)
pragma solidity ^0.8.0;
import "./IERC721.sol";
import "./extensions/IERC721Metadata.sol";
import "../../utils/introspection/ERC165.sol";
// ...
contract ERC721 is Context, ERC165, IERC721, IERC721Metadata {
// ...
function supportsInterface(bytes4 interfaceId) public view virtual override(ERC165, IERC165) returns (bool) {
return
interfaceId == type(IERC721).interfaceId ||
interfaceId == type(IERC721Metadata).interfaceId ||
super.supportsInterface(interfaceId);
}
// ...
}I deleted unnecessary code. The smart contract imports ERC165, IERC721 and IERC721Metadata. The is keyword at smart contract declaration implements all three.
Kind (interface).
Note that type(interface).interfaceId returns the same as the interface selector.
We override supportsInterface in the smart contract to return a boolean that checks if interfaceId is the same as one of the implemented contracts.
Super.supportsInterface() calls ERC165 code. Checks if interfaceId is IERC165.
function supportsInterface(bytes4 interfaceId) public view virtual override returns (bool) {
return interfaceId == type(IERC165).interfaceId;
}So, if we run supportsInterface with an interfaceId, our contract function returns true if it's implemented and false otherwise. True for IERC721, IERC721Metadata, andIERC165.
Conclusion
I hope this post has helped you understand and use ERC165 and why it's employed.
Have a great day, thanks for reading!
Ashraful Islam
4 years ago
Clean API Call With React Hooks
| Photo by Juanjo Jaramillo on Unsplash |
Calling APIs is the most common thing to do in any modern web application. When it comes to talking with an API then most of the time we need to do a lot of repetitive things like getting data from an API call, handling the success or error case, and so on.
When calling tens of hundreds of API calls we always have to do those tedious tasks. We can handle those things efficiently by putting a higher level of abstraction over those barebone API calls, whereas in some small applications, sometimes we don’t even care.
The problem comes when we start adding new features on top of the existing features without handling the API calls in an efficient and reusable manner. In that case for all of those API calls related repetitions, we end up with a lot of repetitive code across the whole application.
In React, we have different approaches for calling an API. Nowadays mostly we use React hooks. With React hooks, it’s possible to handle API calls in a very clean and consistent way throughout the application in spite of whatever the application size is. So let’s see how we can make a clean and reusable API calling layer using React hooks for a simple web application.
I’m using a code sandbox for this blog which you can get here.
import "./styles.css";
import React, { useEffect, useState } from "react";
import axios from "axios";
export default function App() {
const [posts, setPosts] = useState(null);
const [error, setError] = useState("");
const [loading, setLoading] = useState(false);
useEffect(() => {
handlePosts();
}, []);
const handlePosts = async () => {
setLoading(true);
try {
const result = await axios.get(
"https://jsonplaceholder.typicode.com/posts"
);
setPosts(result.data);
} catch (err) {
setError(err.message || "Unexpected Error!");
} finally {
setLoading(false);
}
};
return (
<div className="App">
<div>
<h1>Posts</h1>
{loading && <p>Posts are loading!</p>}
{error && <p>{error}</p>}
<ul>
{posts?.map((post) => (
<li key={post.id}>{post.title}</li>
))}
</ul>
</div>
</div>
);
}
I know the example above isn’t the best code but at least it’s working and it’s valid code. I will try to improve that later. For now, we can just focus on the bare minimum things for calling an API.
Here, you can try to get posts data from JsonPlaceholer. Those are the most common steps we follow for calling an API like requesting data, handling loading, success, and error cases.
If we try to call another API from the same component then how that would gonna look? Let’s see.
500: Internal Server Error
Now it’s going insane! For calling two simple APIs we’ve done a lot of duplication. On a top-level view, the component is doing nothing but just making two GET requests and handling the success and error cases. For each request, it’s maintaining three states which will periodically increase later if we’ve more calls.
Let’s refactor to make the code more reusable with fewer repetitions.
Step 1: Create a Hook for the Redundant API Request Codes
Most of the repetitions we have done so far are about requesting data, handing the async things, handling errors, success, and loading states. How about encapsulating those things inside a hook?
The only unique things we are doing inside handleComments and handlePosts are calling different endpoints. The rest of the things are pretty much the same. So we can create a hook that will handle the redundant works for us and from outside we’ll let it know which API to call.
500: Internal Server Error
Here, this request function is identical to what we were doing on the handlePosts and handleComments. The only difference is, it’s calling an async function apiFunc which we will provide as a parameter with this hook. This apiFunc is the only independent thing among any of the API calls we need.
With hooks in action, let’s change our old codes in App component, like this:
500: Internal Server Error
How about the current code? Isn’t it beautiful without any repetitions and duplicate API call handling things?
Let’s continue our journey from the current code. We can make App component more elegant. Now it knows a lot of details about the underlying library for the API call. It shouldn’t know that. So, here’s the next step…
Step 2: One Component Should Take Just One Responsibility
Our App component knows too much about the API calling mechanism. Its responsibility should just request the data. How the data will be requested under the hood, it shouldn’t care about that.
We will extract the API client-related codes from the App component. Also, we will group all the API request-related codes based on the API resource. Now, this is our API client:
import axios from "axios";
const apiClient = axios.create({
// Later read this URL from an environment variable
baseURL: "https://jsonplaceholder.typicode.com"
});
export default apiClient;
All API calls for comments resource will be in the following file:
import client from "./client";
const getComments = () => client.get("/comments");
export default {
getComments
};
All API calls for posts resource are placed in the following file:
import client from "./client";
const getPosts = () => client.get("/posts");
export default {
getPosts
};
Finally, the App component looks like the following:
import "./styles.css";
import React, { useEffect } from "react";
import commentsApi from "./api/comments";
import postsApi from "./api/posts";
import useApi from "./hooks/useApi";
export default function App() {
const getPostsApi = useApi(postsApi.getPosts);
const getCommentsApi = useApi(commentsApi.getComments);
useEffect(() => {
getPostsApi.request();
getCommentsApi.request();
}, []);
return (
<div className="App">
{/* Post List */}
<div>
<h1>Posts</h1>
{getPostsApi.loading && <p>Posts are loading!</p>}
{getPostsApi.error && <p>{getPostsApi.error}</p>}
<ul>
{getPostsApi.data?.map((post) => (
<li key={post.id}>{post.title}</li>
))}
</ul>
</div>
{/* Comment List */}
<div>
<h1>Comments</h1>
{getCommentsApi.loading && <p>Comments are loading!</p>}
{getCommentsApi.error && <p>{getCommentsApi.error}</p>}
<ul>
{getCommentsApi.data?.map((comment) => (
<li key={comment.id}>{comment.name}</li>
))}
</ul>
</div>
</div>
);
}
Now it doesn’t know anything about how the APIs get called. Tomorrow if we want to change the API calling library from axios to fetch or anything else, our App component code will not get affected. We can just change the codes form client.js This is the beauty of abstraction.
Apart from the abstraction of API calls, Appcomponent isn’t right the place to show the list of the posts and comments. It’s a high-level component. It shouldn’t handle such low-level data interpolation things.
So we should move this data display-related things to another low-level component. Here I placed those directly in the App component just for the demonstration purpose and not to distract with component composition-related things.
Final Thoughts
The React library gives the flexibility for using any kind of third-party library based on the application’s needs. As it doesn’t have any predefined architecture so different teams/developers adopted different approaches to developing applications with React. There’s nothing good or bad. We choose the development practice based on our needs/choices. One thing that is there beyond any choices is writing clean and maintainable codes.
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INTΞGRITY team
3 years ago
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YOUR CALIFORNIA PRIVACY RIGHTS
The California Consumer Privacy Act, or "CCPA" (Cal. Civ. Code 1798.100 et seq. ), grants California residents some rights regarding their personal data. If you are a California resident, you are subject to this clause.
We have collected the following categories of personal information over the past year: identifiers, commercial information, internet or other electronic network activity information, and conclusions. Please refer to the section titled "Collection of Information" for specifics regarding the data points we gather and the sorts of sources from which we acquire them. We collect personal information for the business and marketing purposes outlined in the section on Use of Information. In the past 12 months, we have shared the following types of personal information to the following groups of recipients for business purposes:
Category of Personal Information: Identifiers
Categories of Recipients: Analytics Providers, Communication Providers, Custom Service Providers, Fraud Prevention and Security Providers, Infrastructure Providers, Marketing Providers, Payment Processors
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Categories of Recipients: Analytics Providers, Infrastructure Providers, Payment Processors
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Categories of Recipients: Analytics Providers, Infrastructure Providers
Category of Personal Information: Inferences
Categories of Recipients: Analytics Providers, Infrastructure Providers
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For people in the EEA, please visit https://edpb.europa.eu/about-edpb/board/members en.
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For people in Switzerland: https://www.edoeb.admin.ch/edoeb/en/home/the-fdpic/contact.html
CONTACT US
Please contact us at hello@int3grity.com if you have any queries regarding this Privacy Statement.
Luke Plunkett
3 years ago
Gran Turismo 7 Update Eases Up On The Grind After Fan Outrage
Polyphony Digital has changed the game after apologizing in March.
To make amends for some disastrous downtime, Gran Turismo 7 director Kazunori Yamauchi announced a credits handout and promised to “dramatically change GT7's car economy to help make amends” last month. The first of these has arrived.
The game's 1.11 update includes the following concessions to players frustrated by the economy and its subsequent grind:
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The last half of the World Circuits events have increased in-game credit rewards.
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Modified Arcade and Custom Race rewards
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Clearing all circuit layouts with Gold or Bronze now rewards In-game Credits. Exiting the Sector selection screen with the Exit button will award Credits if an event has already been cleared.
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Increased Credits Rewards in Lobby and Daily Races
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Increased the free in-game Credits cap from 20,000,000 to 100,000,000.
Additionally, “The Human Comedy” missions are one-hour endurance races that award “up to 1,200,000” credits per event.
This isn't everything Yamauchi promised last month; he said it would take several patches and updates to fully implement the changes. Here's a list of everything he said would happen, some of which have already happened (like the World Cup rewards and credit cap):
- Increase rewards in the latter half of the World Circuits by roughly 100%.
- Added high rewards for all Gold/Bronze results clearing the Circuit Experience.
- Online Races rewards increase.
- Add 8 new 1-hour Endurance Race events to Missions. So expect higher rewards.
- Increase the non-paid credit limit in player wallets from 20M to 100M.
- Expand the number of Used and Legend cars available at any time.
- With time, we will increase the payout value of limited time rewards.
- New World Circuit events.
- Missions now include 24-hour endurance races.
- Online Time Trials added, with rewards based on the player's time difference from the leader.
- Make cars sellable.
The full list of updates and changes can be found here.
Read the original post.
Shalitha Suranga
3 years ago
The Top 5 Mathematical Concepts Every Programmer Needs to Know
Using math to write efficient code in any language
Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.
A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.
We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.
Expressions in mathematics and built-in mathematical functions
A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.
When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.
Linux utilizes clear math expressions.
Inbuilt max and min functions can minimize verbose if statements.
How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.
import math as m
results = 102
items_per_page = 10
pages = m.ceil(results / items_per_page)
print(pages)Learn to write clear, concise math expressions.
Combinatorics in Algorithm Design
Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?
Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.
Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.
Logarithms and Geometry Understanding
Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.
GetWindowRect is a Windows GUI SDK geometric object.
High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.
How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):
Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.
Employing Mathematical Data Structures
Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.
Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.
Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.
Recognizing Applications of Recursion
A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.
Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:
Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.
Conclusion
Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.
Master the above math fundamentals to build clean, efficient code.