Christmas is a time of cheer, of merriment, and of brotherly love, right? Well, that includes love between consoles. We might be a Nintendo website, but we can enjoy good work when we see it, and these gorgeous Christmas cards come courtesy of the PlayStation blog, where they’re featured a selection from a few of the best studios in the biz.

Quite a few of them are also on Switch, so we’re featuring our personal faves for you to enjoy, too, with the likes of Cuphead, Grindstone, and Wargroove making an appearance.

Awww, isn’t that lovely. Which studio would you love to get a Christmas card from? Let us know in the comments!

Starting today, Fortnite has issued a bunch of “Wakanda Forever Challenges” to all players, and the prize is the badass Wakanda Forever emote – a tribute to the actor who played the Wakandan King, Chadwick Boseman, who died earlier this year.

Players who complete the challenges before January 12th will receive the emote for free. Fortnite Insider has the scoop on what the challenges will involve:

– Play Matches (10)
– Outlast Opponents (500)
– Play Duo or Squad Matches (5)

The emote might not be the only Black Panther-related goodie that Fortnite players receive. In a cryptic emoji tweet, the Fortnite Twitter account hinted at what could be the addition of some new characters, including a black cat:

Which characters do you think these emojis correspond to? Let us know in the comments below!

Exponents are superscript numbers that describe how many times you want to multiply a number by itself. Calculating a value raised to the power of another value is a fundamental operation in applied mathematics such as finance, machine learning, statistics, and data science. This tutorial shows you how to do it in Python!

Definition

For pow(x, y), the pow() function returns the value of x raised to the power y. It performs the same function as the power operator ** , i.e. x**y, but differs in that it comes with an optional argument called mod.

Examples without mod

>>> pow(5, 2)

25

>>> pow(-3, 3)

-27

>>> pow(2, -2)

0.25

Parameters and Syntax

pow(base, exp, mod=None)

The pow() function includes two compulsory arguments, base and exp, and one optional argument, mod, whose default value is None. All arguments must be of numeric data type.

Parameter	Description
exp	A number that represents the base of the function, whose power is to be calculated.
base	A number that represents the exponent of the function, to which the base will be raised.
mod	A number with which the modulo will be computed.

Return value: The output of base raised to the power exp and will be a numeric data type, int, float or complex, depending on what you input.

Using the pow() function without the mod argument

When using the pow(x, y) function without the optional mod argument, it will perform the same operation as the power operator x**y, raising x to the power y.

Comparison of the two methods

>>> pow(6, 4)

1296

>>> 6 ** 4

1296

The pow() function accepts all numeric data types, i.e. int, float and even complex numbers. In general the return value will depend on what data types you input. The example above shows that both arguments are type int, therefore, an int type is returned. However, if you were to instead use a float number as one or both of the arguments, the function will automatically return a float type.

Examples using float types

>>> pow(3.0, 4)

81.0

>>> pow(4.5, 2.3)

31.7971929089206

As with float type inputs leading to float outputs, the same reasoning applies to complex numbers. If you enter a complex number as one or both of the arguments, a complex number will be returned.

Example using complex numbers

>>> pow(4+2j, 3)

(16+88j)

The return type will also depend on whether your arguments are non-negative or negative, as is shown in the below table.

base	exp	Return type
Non-negative	Non-negative	int
Non-negative	Negative	foat
Negative	Non-negative	int
Negative	Negative	float

Examples of return values with different input types

>>> pow(7, 2)

49

>>> pow(4, -5)

0.0009765625

>>> pow(-6, 3)

-216

>>> pow(-9, -4)

0.00015241579027587258

Using the pow() function with a mod argument

What sets the pow() function apart from the ** operator is its third optional argument, mod, which gives you the ability to do a modulo operation within the function. 

The process of operations when using the mod argument is as follows:

If we have pow(x, y, z), the function first performs the task of raising x to the power y and then that result is used to perform the modulo task with respect to z. It would be the equivalent of (x**y) % z .

Examples using mod

>>> pow(14, 7, 5)

4

>>> pow(-8, 3, 5)

3

>>> pow(2, 4, -3)

-2

The general rule for using the mod argument is that all values must be of integer type, the exp argument must be non-negative and the mod argument must be non-zero. However, Python 3.8 now comes with the functionality of computing modular inverses. In this case, the exp argument may be negative, on the condition that base is relatively prime to mod, i.e, the only common integer divisor of base and mod is 1.

So, when using the pow() function with negative exp, the function will perform as follows:

pow(inv_base, -exp, mod)

In other words, the function will compute the modular inverse of base and mod first and then that result will be used in the pow() function as base to be computed as normal with the  exp argument being converted to its non-negative counterpart.

Example of modular inverse

>>> pow(87, -1, 25)

23

In this example, the straight modular inverse is calculated because inv_base will be raised to the power 1.

Example of modular inverse when exp is not -1

>>> pow(34, -5, 19)

10

# The modular inverse of 34 mod 19 is 14, therefore, we end up with the function pow(14, 5, 19)

>>> pow(14, 5, 19)

10

Calculating the nth root of a number using pow()

Unfortunately, Python does not have a built-in function to calculate the nth root of a number. The math module only has a function to calculate square roots, math.sqrt(), therefore, we have to get creative in order to calculate nth roots.

We know that nx is equivalent to x1n. Thus, using this knowledge we can calculate the nth root in Python by using either pow(x, (1/n)) or x**(1/n). 

Examples of calculating nth roots

>>> pow(625, (1/4))

4.0

>>> 729**(1/3)

8.999999999999998

Note that performing an nth root calculation will always return a float when not using complex numbers. Since Python’s float type works on approximations, it will often return the approximation rather than the exact number, even when an exact answer is possible. This is demonstrated in the second example above.

When calculating the nth root of a negative number, the return value will be a complex number whether an integer number is possible or not.

Examples of calculating nth roots of negative bases

>>> pow(-16, (1/2))

(2.4492935982947064e-16+4j)

>>> pow(-27, (1/3))

(1.5000000000000004+2.598076211353316j)

We would expect the second example above, the cubed root of -27, to result in -3, but instead we get a complex number. This is because Python returns the principal root rather than the real root. For an explanation of these different types of roots, you can look up the Fundamental theorem of algebra.

math.pow() Function

In the math module of Python, there is a similar function called math.pow(). To use this we first need to import the math function, thus, the built-in pow() function will be very slightly faster. The main differences between the two functions is that math.pow() does not allow for the optional mod argument and it will always return a float. So if you want to ensure that you get a float result, math.pow() is a better option.

Example of using math.pow()

>>> import math

>>> math.pow(9, 5)

59049.0

When to use the pow() function vs when to use the ** operator

When deciding between using the pow() function or the ** operator, the most important factor to consider would be the efficiency of your code. We can use the timeit.timeit() function from the timeit module to find out how fast Python executes our code.

Examples of using timeit with simple numbers

>>> import timeit

>>> timeit.timeit('pow(5, 2)')

0.25059129999863217

>>> timeit.timeit('5**2')

0.008814800001346157

When performing a simple power computation, the ** operator appears to be much faster.

Examples using modulo

>>> timeit.timeit('pow(52, 2, 4)')

0.7482693000001746

>>> timeit.timeit('52**2 % 4')

0.012026999998852261

The same is true even when we include a modulo operation.

However, when we want to perform power operations with very large numbers, the pow() function is much quicker, showing that the power of the pow() function lies in executing longer computations.

Examples using large numbers

>>> timeit.timeit('pow(5234, 2341, 124)')

0.9020593000004737

>>> timeit.timeit('5234**2341 % 124')

152.56075580000106

Here the pow() function is extremely fast compared to the ** operator. Therefore, we can generalize these findings by saying that when you want to perform short, simple calculations, the ** operator is the better option, however, if your operations involve very large numbers, the pow() function is much more efficient.

The post A Guide to Python’s pow() Function first appeared on Finxter.

It’s been a rough week for one of the most anticipated triple-A games of the year. Microsoft has now pledged to offer full refunds to Xbox players that feel let down by Cyberpunk 2077‘s console version, following in the footsteps of a similar decision from Sony yesterday as well as developer CD Projekt Red’s own advice to unhappy players.

Specifically, Microsoft is offering full refunds to those that bought Cyberpunk 2077 digitally through the Microsoft Store but, unlike PlayStation, isn’t delisting the infamously buggy console game.

“To ensure that every player can get the experience they expect on Xbox, we will be expanding our existing refund policy to offer full refunds to anyone who purchased Cyberpunk 2077 digitally from the Microsoft Store, until further notice,” reads a tweet from the Xbox Support team.

“While we know the developers at CD Projekt Red have worked hard to ship Cyberpunk 2077 in extremely challenging circumstances, we also realize that some players have been unhappy with the current experience on older consoles.”

Cyberpunk 2077 launched last week to much acclaim from game reviewers, but it was later discovered that the experience on the PC version of the game reviewers saw didn’t line up with its console counterpart, especially on older PlayStation 4 or Xbox One systems. CD Projekt later admitted in a conference call that it didn’t give performance on last-generation consoles the attention it needed, leading to console versions that, at best, regularly crash and, at worst, are borderline unplayable.

“We ignored the signals about the need for additional time to refine the game on the base last-gen consoles,” CD Projekt CEO Adam Kicinski later explained in a call with investors. “It was the wrong approach and against our business philosophy. On top of that, during the campaign, we showed the game mostly on PCs.”

CD Projekt has, in a statement shared to Twitter shortly after launch, pledged to “fix bugs and crashes, and improve the overall experience” through updates but suggested those currently unhappy with Cyberpunk 2077‘s console performance seek refunds through the storefronts they purchased the game from.

This led to a bit of a scramble at first as digital stores like the PlayStation Store typically don’t allow for games to be returned once they’ve been downloaded and played. In the days since, PlayStation announced that it would put a special refund policy in place to allow for Cyberpunk 2077 refunds, but also, in a landmark move, completely delisted the game from the PlayStation Store until further notice.

In a note to investors, CD Projekt explained that the delisting was the result of a conversation between it and Sony, and assured investors that copies will remain for sale physically in the meantime.

But despite today’s refund policy extension on Xbox, Kicinski said earlier today that delisting on Xbox doesn’t appear to be on the table as its discussions with Microsoft haven’t taken a turn toward removal quite yet.

On the retail front, CD Projekt recently promised to help players refund physical or digital copies bought through retail stores itself.

Both Microsoft and Sony have launched special refund initiatives for Cyberpunk 2077, and CD Projekt Red now says it is looking at other ways to help players outside of those purchasing platforms to receive refunds for the game if they so choose.

Building on its original refund pledge from earlier in the week, CD Projekt Red now says that it intends for “every owner of a physical copy, or a digital copy bought at retail” to receive a refund for their purchase of Cyberpunk 2077 following widespread complaints of bugs and performance issues, particularly on older consoles.

In many cases, store refund policies don’t allow video games to be returned if they’ve been opened or, in the case of digital copies, redeemed. For those that aren’t covered under the expanded return policies for Cyberpunk 2077 on Xbox and PlayStation, CD Projekt now says they’ll pay out of pocket if necessary to help

“We’d like you to know that our intention is for every owner of a physical copy, or a digital copy bought at retail, who has valid proof of purchase (and sends us an email at [email protected] within the time window) to receive a refund. We will do this out of our own pocket if necessary.”

“If you are unable to obtain a refund for the game from the store where you bought it, please contact us via e-mail until December 21. As this is a one-time initiative, we will provide everyone with next steps only after the refund request window closes.”

Ryan can list the first 151 Pokémon all in order off by heart – a feat he calls his ‘party trick’ despite being such an introvert that he’d never be found anywhere near a party. He’d much rather just have a night in with Mario Kart and a pizza, and we can’t say we blame him.