Here “a” is dividend and “b” is the divisor. The sibling of the modulo operator is known as the integer division operation (//), where the fractional part (i.e. Ask Question Asked 2 years, 5 months ago. Mathematics behind the negative modulo : Let’s Consider an example, where we want to find the -5mod4 i.e. With modulo division, only the remainder is returned. A weekly newsletter sent every Friday with the best articles we published that week. Decoupling Capacitor Loop Length vs Loop Area. It's worth noting that the formal mathematical definition states that b is a positive integer. The syntax of modulo operator is a % b. Python Modulo Negative Numbers. Why -1%26 = -1 in Java and C, and why it is 25 in Python? Why did flying boats in the '30s and '40s have a longer range than land based aircraft? For example, -22%12 will give us 2 and -19/12 will give us 5. Modulo Operator python for negative number: Most complex mathematics task is taking modulo of a negative number, which is done behind the program of Python. If we don’t understand the mathematics behind the modulo of negative number than it will become a huge blender. This gives negative numbers a seamless behavior, especially when used in combination with the // integer-divide operator, as % modulo often is (as in math.divmod): for n in range(-8,8): print n, n//4, n%4 Produces: the remainder) is discarded. but in C, if N ≥ 3, we get a negative number which is an invalid number, and we need to manually fix it up by adding 7: (See http://en.wikipedia.org/wiki/Modulo_operator for how the sign of result is determined for different languages.). I've found some strange behaviour in Python regarding negative numbers: Unlike C or C++, Python's modulo operator (%) always return a number having the same sign as the denominator (divisor). In python, modulo operator works like this. The followings are valid integer literals in Python. Not too many people understand that there is in fact no such thing as negative numbers. How can a monster infested dungeon keep out hazardous gases? So why does floor(-3.1) return -4? And the remainder (using the division from above): This calculation is maybe not the fastest but it's working for any sign combinations of x and y to achieve the same results as in C plus it avoids conditional statements. Mathematics behind the negative modulo : Let’s Consider an example, where we want to find the -5mod4 i.e. The solution here is using the modulo operator with negative numbers. Calculate a number divisible by 5 and “greater” than -12. ... we have learned the basics of working with numbers in python. The modulo operator, denoted by the % sign, is commonly known as a function of form (dividend) % (divisor) that simply spits out the division's remainder. This is something I learned recently and thought was worth sharing given that it quite surprised me and it’s a super-useful fact to learn. Below screenshot python modulo with negative numbers. Here, the remainder will have the same sign as the divisor, so my divisor is positive that’s why the remainder is also positive vice versa. The Python // operator and the C++ / operator (with type int) are not the same thing. For Python it's -2 because it will always return the value of the divisor and it's because 5*5 = 25 and when you divide 23 by 25 in Python you obtain a remainder of -2 (since it must be negative because the divisor was negative) so we have 25 - 2 = 23. Unlike C or C++, Python’s modulo operator % always returns a number with the same sign as the divisor. It returns the remainder of dividing the left hand operand by right hand operand. Python Modulo. Does Python have a ternary conditional operator? Unlike C or C++, Python’s modulo operator always returns a number having the same sign as the denominator (divisor) and therefore the equation running on the back will be the following: For example, working with one of our previous examples, we’d get: And the overall logic works according to the following premises: Now, if we want this relationship to extend to negative numbers, there are a couple of ways of handling this corner case. rev 2021.1.18.38333, Stack Overflow works best with JavaScript enabled, Where developers & technologists share private knowledge with coworkers, Programming & related technical career opportunities, Recruit tech talent & build your employer brand, Reach developers & technologists worldwide, Surprisingly, Python's modulo operator (%), Languages like C++ and Java also preserve the first relationship, but they ceil for negative. https://blog.tecladocode.com/pythons-modulo-operator-and-floor-division There is no one best way to handle integer division and mods with negative numbers. 2 goes into 7 three times and there is 1 left over. Python modulo with negative numbers In python, the modulo operator will always give the remainder having the same sign as the divisor. Consider, and % is modulo - not the remainder! Would a vampire still be able to be a practicing Muslim? * [python] fixed modulo by negative number (closes #8845) * add comment RealyUniqueName added a commit that referenced this issue Sep 26, 2019 [python] align `-x % -y` with other targets ( #8845 ) I also thought it was a strange behavior of Python. When is that a desired behaviour? In Python, the modulo operator can be used on negative numbers also which gives the same remainder as with positive numbers but the negative sign … It would be nice if a/b was the same magnitude and opposite sign of (-a)/b. Therefore, you should always stick with the above equation. The modulo operator is considered an arithmetic operation, along with +, -, /, *, **, //. In Python we can compute with. Taking modulo of a negative number is a bit more complex mathematics which is done behind the program of Python. whereas other languages such as C, JAVA, JavaScript use truncation instead of floor. your coworkers to find and share information. (Yes, I googled it). So, let’s keep it short and sweet and get straight to it. Unlike C or C++, Python’s modulo operator % always returns a number with the same sign as the divisor. Why would one of Germany's leading publishers publish a novel by Jewish writer Stefan Zweig in 1939? C and C++ round integer division towards zero (so a/b == -((-a)/b)), and apparently Python doesn't. why is user 'nobody' listed as a user on my iMAC? In Python, integers are zero, positive or negative whole numbers without a fractional part and having unlimited precision, e.g. Python modulo operator (%) is used to get the remainder of a division. Modulo with Float. ... by testing for a remainder of 1. Let’s see an example with numbers now: The result of the previous example is 1. The basic syntax of Python Modulo is a % b.Here a is divided by b and the remainder of that division is returned. To get the remainder of two numbers, we use the modulus(%) operator. Your expression yields 3 because (-5) % 4 = (-2 × 4 + 3) % 4 = 3. Why do jet engine igniters require huge voltages? While x%y in C yields. Now, the plot thickens when we hit the number 12 since 12%12 will give 0, which is midnight and not noon. The modulo operator is shown. (x+y)mod z … Int. A ZeroDivisionError exception is raised if the right argument is zero. The arguments may be floating point numbers. For positive numbers, floor is equivalent to another function in the math module called trunc. But if we were to express times before 1970 using negative numbers, other criteria used would give a meaningless result, while using the floor rule works out fine. Why is it so hard to build crewed rockets/spacecraft able to reach escape velocity. If none of the conditions are satisfy, the result is prime number. In Python, the modulo ‘%’ operator works as follows: The numbers are first converted in the common type. Join Stack Overflow to learn, share knowledge, and build your career. "It would be nice if a/b was the same magnitude and opposite sign of (-a)/b." Finally, take into account the following when working with negative numbers: Finally, let’s see a quick example for a = -500 and b = 12: To end this article, let’s see an interesting application of the modulo operator with negative numbers: converting an hour written in the 24-hour clock into the 12-hour clock. For instance, 5 % 3 = 2, and 7 % 3 = 1. If we don’t understand the mathematics behind the modulo of negative number than it will become a huge blender. In Python, you can calculate the quotient with // and the remainder with %.The built-in function divmod() is useful when you want both the quotient and the remainder.Built-in Functions - divmod() — Python 3.7.4 documentation divmod(a, b) returns … Mathematically python is not giving correct output for integer division for negative number, e.g. A tutorial to understand modulo operation (especially in Python). Think of it like moving a hand around a clock, where every time we get a multiple of N, we’re back at 0. 0, 100, -10. >>> math.fmod(-7,3) -1.0 >>> math.fmod(7,-3) 1.0 Disclaimer:It's important to note that this post specifically applies to the Python pragramming language and its % notation. (-10 in this case). As pointed out, Python modulo makes a well-reasoned exception to the conventions of other languages. Stack Overflow for Teams is a private, secure spot for you and What's the word for someone who takes a conceited stance in stead of their bosses in order to appear important? As pointed out, Python modulo makes a well-reasoned exception to the conventions of other languages. Floor division and modulo are linked by the following identity, x = (x // y) * y + (x % y), which is why modulo also yields unexpected results for negative numbers, not just floor division. #Calculate exponents in the Python programming language. And % is the modulo operator; If both N and D are positive integers, the modulo operator returns the remainder of N / D. However, it’s not the case for the negative numbers. If you need more information about rounding in python, read this. It is one of the things where Java and Python are fundamentally different. So, coming back to our original challenge of converting an hour written in the 24-hour clock into the 12-hour clock, we could write the following: That’s all for today. This gives negative numbers a seamless behavior, especially when used in combination with the // integer-divide operator, as % modulo often is (as in math.divmod): * ... as long as the right operand is positive. Code tutorials, advice, career opportunities, and more! That may not makes sense mathematically though. If you’re using a negative operand, then you may see different results between math.fmod (x, y) and x % y. Applying random luck scores to instances of people. It returns the remainder of dividing the left hand operand by right-hand operand. Since we really want a == (a/b)*b + a%b, the first two are incompatible. rounded away from 0 towards negative infinity), returning the largest integer less than or equal to x. With division, the result is stored in a single number. The challenge seems easy, right? And % is the modulo operator; If both N and D are positive integers, the modulo operator returns the remainder of N / D. However, it’s not the case for the negative numbers. (Although I assume that you have already resolved your concern a long time ago). Simple Python modulo operator examples Thanks. Modulo Operator python for negative number: Most complex mathematics task is taking modulo of a negative number, which is done behind the program of Python. However, the behaviour of floor and truncbegins to diverge when we pass in negative numbers as arguments. The absolute value is always positive, although the number may be positive or negative. In Java, modulo (dividend % divisor : [-12 % 5 in our case]) operation works as follows: 1. Thanks your example made me understand it :). Here's an explanation from Guido van Rossum: http://python-history.blogspot.com/2010/08/why-pythons-integer-division-floors.html. In this scenario the divisor is a floating-point number. ... function is used to generate the absolute value of a number. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. In Python, // is floor division. However, if one of the operands is negative, the result will be floored as well (i.e. What is __future__ in Python used for and how/when to use it, and how it works. Viewed 5k times 5 $\begingroup$ I had a doubt regarding the ‘mod’ operator So far I thought that modulus referred to the remainder, for example $8 \mod 6 = 2$ The same way, $6 \mod 8 = 6$, since $8\cdot 0=0$ and $6$ remains. Taking modulo of a negative number is a bit more complex mathematics which is done behind the program of Python. Take the following example: For positive numbers, there’s no surprise. Why would that be nice? According to Wikipedia, in mathematical number theory, mathematicians prefer to stick to flooring towards negative infinity as in the following example: Python follows the same logic. Since we really want a == (a/b)*b + a%b, the first two are incompatible. @NullUserException - yup, it was. For example: Now, there are several ways of performing this operation. -5%4. Basically Python modulo operation is used to get the reminder of a division. It would be nice if a % b was indeed a modulo b. Proper way to declare custom exceptions in modern Python? Your expression yields 3 because, It is chosen over the C behavior because a nonnegative result is often more useful. To what extent is the students' perspective on the lecturer credible? Modulus of negative numbers. Can you use the modulo operator % on negative numbers? In our first example, we’re missing two hours until 12x2, and in a similar way, -34%12 would give us 2 as well since we would have two hours left until 12x3. How do I install a Python package with a .whl file? Where is the antenna in this remote control board? There is no one best way to handle integer division and mods with negative numbers. It's used to get the remainder of a division problem. According to Guido van Rossum, the creator of Python, this criterion has some interesting applications. How Python's Modulo Operator Really Works. The basic syntax is: a % b Modulus. ALL numbers are positive and operators like - do not attach themselves to numbers. For example, 23%2 will give us 11 and 15%12 will give us 3… exactly what we want! Does Python have a string 'contains' substring method? Active 11 months ago. “The % symbol in Python is … The simplest way is using the exponentiation … If you want Python to behave like C or Java when dealing with negative numbers for getting the modulo result, there is a built-in function called math.fmod () that can be used. What is the origin and original meaning of "tonic", "supertonic", "mediant", etc.? See you around, and thanks for reading! The followings are valid integer literals in Python. “The % symbol in Python is called the Modulo Operator. Basically, Python modulo operation is used to get the remainder of a division. In the previous example, a is divided by b, and the r (i.e. Don’t forget to take a look to some of my other stories on Better Programming: And if you want to receive my latest articles directly on your email, just subscribe to my newsletter :). We usually express that operation as b n, where b is the base and n is the exponent or power. In Python, integers are zero, positive or negative whole numbers without a fractional part and having unlimited precision, e.g. Why? How does the modulo operation work with negative numbers and why? The modulo operation on negative numbers in Python, C,Python - different behaviour of the modulo (%) operation, http://en.wikipedia.org/wiki/Modulo_operator, Podcast 305: What does it mean to be a “senior” software engineer. Adding scripts to Processing toolbox via PyQGIS. When both the dividend and divisor are positive integers, the result is simply the positive remainder. If we don’t understand the mathematics behind the modulo of negative number than it will become a huge blender. The output is the remainder when a is divided by b. It would be nice if a/b was the same magnitude and opposite sign of (-a)/b. Example -2 is NOT negative … After writing the above code (python modulo with negative numbers), Ones you will print ” remainder “ then the output will appear as a “ 1 ”. How does Python handle the modulo operation with negative numbers? 0, 100, -10. Since there are 24*3600 = 86,400 seconds in a day, this calculation is simply t % 86,400. How does Python handle the modulo operation with negative numbers? Unlike C or C++, Python’s modulo operator (%) always return a number having the same sign as the denominator (divisor). Essentially, it's so that a/b = q with remainder r preserves the relationships b*q + r = a and 0 <= r < b. Tim Peters, who knows where all Python's floating point skeletons are buried, has expressed some worry about my desire to extend these rules to floating point modulo. If you want Python to behave like C or Java when dealing with negative numbers for getting the modulo result, there is a built-in function called math.fmod() that can be used. I forgot the geometric representation of integers numbers. (x+y)mod z … Python Number Types: int, float, complex. If today is Tuesday (day #2), what is the week day N days before? Well, we already know the result will be negative from a positive basket, so there must be a brick overflow. For example, consider taking a POSIX timestamp (seconds since the start of 1970) and turning it into the time of day. Next step is checking whether the number is divisible by another number in the range from 2 to number without any reminder. With negative numbers, the quotient will be rounded down towards $-\infty$, shifting the number left on the number … : -7//2= -3 but python is giving output -4. msg201716 - Author: Georg Brandl (georg.brandl) * Date: 2013-10-30 07:30 Which one to keep is a difficult question, and there are arguments for both sides. fixed. If the numerator is N and the denominator D, then this equation N = D * ( N // D) + (N % D) is always satisfied. In mathematics, an exponent of a number says how many times that number is repeatedly multiplied with itself (Wikipedia, 2019). By recalling the geometry of integers given by the number line, one can get the correct values for the quotient and the remainder, and check that Python's behavior is fine. ... Division and modulo division are related operations. How do I merge two dictionaries in a single expression in Python (taking union of dictionaries)? 176 / 14 ≈ 12.6 and 14 * 13 = 182, so the answer is 176 - 182 = -6. -5%4. Given two positive numbers, a and n, a modulo n (a % n, abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. Maximum useful resolution for scanning 35mm film. On the other hand 11 % -10 == -9. For example, -9%2 returns 1 because the divisor is positive, 9%-2 returns -1 because the divisor is negative, and -9%-2 returns -1 because the divisor is negative as … Use floor division operator // or the floor() function of the math module to get the floor division of two integers. Int. Taking modulo of a negative number is a bit more complex mathematics which is done behind the program of Python. Can anti-radiation missiles be used to target stealth fighter aircraft? Take a look, Writing a simple task Applet for Cinnamon Desktop, Developing a Serverless Backend API using Flask, 5 Reasons to Finally Start That Side Project You’ve Been Putting Off, Top 29 Useful Python Snippets That Save You Time, What Is Polymorphism — and How Do We Implement It in Python, Lessons From Steve McConnell’s “Code Complete”. As a rule of thumb, this kind of operation will always give us how many units we have left until the next multiple of our denominator. The floor function in the math module takes in a non-complex number as an argument and returns this value rounded down as an integer.
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