What is the result of in Python

Question

What does the   in a calculation  I can t seem to work out what it does   Does it work out a percent of the calculation for example  4   2 is apparently equal to 0  How

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I have found that the easiest way to grasp the modulus operator     is through long division  It is the remainder and can be useful in determining a number to be even or  odd   4 2   0    2 2 4  -4   0   11 3   2    3 3 11  -9   2

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It is  as in many C-like languages  the remainder or modulo operation  See the documentation for numeric types     int  float  long  complex

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An expression like x   y evaluates to the remainder of x    y - well  technically it is  quot modulus quot  instead of  quot reminder quot  so results may be different if you are comparing with other languages where   is the remainder operator  There are some subtle differences  if you are interested in the practical consequences see also  quot Why Python s Integer Division Floors quot  bellow   Precedence is the same as operators    division  and    multiplication    gt  gt  gt  9   2 4  gt  gt  gt  9   2 1   9 divided by 2 is equal to 4  4 times 2 is 8 9 minus 8 is 1 - the remainder   Python gotcha  depending on the Python version you are using    is also the  deprecated  string interpolation operator  so watch out if you are coming from a language with automatic type casting  like PHP or JS  where an expression like  12    2   3 is legal  in Python it will result in TypeError  not all arguments converted during string formatting which probably will be pretty confusing for you   update for Python 3  User n00p comments   9 2 is 4 5 in python  You have to do integer division like so  9  2 if you want python to tell you how many whole objects is left after division 4    To be precise  integer division used to be the default in Python 2  mind you  this answer is older than my boy who is already in school and at the time 2 x were mainstream     python2 7 Python 2 7 10  default  Oct  6 2017  22 29 07   GCC 4 2 1 Compatible Apple LLVM 9 0 0  clang-900 0 31   on darwin Type  quot help quot    quot copyright quot    quot credits quot  or  quot license quot  for more information   gt  gt  gt  9   2 4  gt  gt  gt  9    2 4  gt  gt  gt  9   2 1  In modern Python 9   2 results 4 5 indeed    python3 6 Python 3 6 1  default  Apr 27 2017  00 15 59   GCC 4 2 1 Compatible Apple LLVM 8 1 0  clang-802 0 42   on darwin Type  quot help quot    quot copyright quot    quot credits quot  or  quot license quot  for more information   gt  gt  gt  9   2 4 5  gt  gt  gt  9    2 4  gt  gt  gt  9   2 1   update  User dahiya boy asked in the comment session   Q  Can you please explain why -11   5   4 - dahiya boy  This is weird  right  If you try this in JavaScript   gt  -11   5 -1  This is because in JavaScript   is the  quot remainder quot  operator while in Python it is the  quot modulus quot   clock math  operator  You can get the explanation directly from GvR    Edit - dahiya boy  In Java and iOS -11   5   -1 whereas in python and ruby -11   5   4  Well half of the reason is explained by the Paulo Scardine  and rest of the explanation is below here In Java and iOS    gives the remainder that means if you divide 11   5  gives Quotient   2 and remainder   1 and -11   5 gives Quotient   -2 and remainder   -1  Sample code in swift iOS   But when we talk about in python its gives clock modulus  And its work with below formula mod a n    a -  n   Floor a n   Thats means  mod 11 5    11 -  5   Floor 11 5     gt  11 -  5   2  So  mod 11 5    1 And mod -11 5    -11 - 5   Floor -11 5    gt  -11 -  5    -3   So  mod -11 5    4 Sample code in python 3 0     Why Python s Integer Division Floors I was asked  again  today to explain why integer division in Python returns the floor of the result instead of truncating towards zero like C  For positive numbers  there s no surprise    gt  gt  gt  5  2 2   But if one of the operands is negative  the result is floored  i e   rounded away from zero  towards negative infinity     gt  gt  gt  -5  2 -3  gt  gt  gt  5  -2 -3   This disturbs some people  but there is a good mathematical reason  The integer division operation      and its sibling  the modulo operation      go together and satisfy a nice mathematical relationship  all variables are integers    a b   q with remainder r   such that  b q   r   a and 0  lt   r  lt  b    assuming a and b are  gt   0   If you want the relationship to extend for negative a  keeping b positive   you have two choices  if you truncate q towards zero  r will become negative  so that the invariant changes to 0  lt   abs r   lt  otherwise  you can floor q towards negative infinity  and the invariant remains 0  lt   r  lt  b   update  fixed this para  In mathematical number theory  mathematicians always prefer the latter choice  see e g  Wikipedia   For Python  I made the same choice because there are some interesting applications of the modulo operation where the sign of a is uninteresting  Consider taking a POSIX timestamp  seconds since the start of 1970  and turning it into the time of day  Since there are 24 3600   86400 seconds in a day  this calculation is simply t   86400  But if we were to express times before 1970 using negative numbers  the  quot truncate towards zero quot  rule would give a meaningless result  Using the floor rule it all works out fine  Other applications I ve thought of are computations of pixel positions in computer graphics  I m sure there are more  For negative b  by the way  everything just flips  and the invariant becomes   0  gt   r  gt  b    So why doesn t C do it this way  Probably the hardware didn t do this at the time C was designed  And the hardware probably didn t do it this way because in the oldest hardware  negative numbers were represented as  quot sign   magnitude quot  rather than the two s complement representation used these days  at least for integers   My first computer was a Control Data mainframe and it used one s complement for integers as well as floats  A pattern of 60 ones meant negative zero  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  He s probably right  the truncate-towards-negative-infinity rule can cause precision loss for x 1 0 when x is a very small negative number  But that s not enough for me to break integer modulo  and    is tightly coupled to that  PS  Note that I am using    instead of   -- this is Python 3 syntax  and also allowed in Python 2 to emphasize that you know you are invoking integer division  The   operator in Python 2 is ambiguous  since it returns a different result for two integer operands than for an int and a float or two floats  But that s a totally separate story  see PEP 238  Posted by Guido van Rossum at 9 49 AM

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In most languages   is used for modulus  Python is no exception

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It s a modulo operation http   en wikipedia org wiki Modulo operation  http   docs python org reference expressions html  So with order of operations  that works out to   3 2 1-5     4 2  -  1 4    6   1     0  -  0    6  7  The 1 4 0 because we re doing integer math here

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It was hard for me to readily find specific use cases for the use of   online  e g  why does doing fractional modulus division or negative modulus division result in the answer that it does  Hope this helps clarify questions like this   Modulus Division In General   Modulus division returns the remainder of a mathematical division operation  It is does it as follows   Say we have a dividend of 5 and divisor of 2  the following division operation would be  equated to x     dividend   5 divisor   2  x   5 2     The first step in the modulus calculation is to conduct integer division    x int   5    2   integer division in python uses double slash   x int    2 Next  the output of x int is multiplied by the divisor   x mult   x int   divisor  x mult   4 Lastly  the dividend is subtracted from the x mult  dividend - x mult   1  The modulus operation  therefore  returns 1   5   2   1   Application to apply the modulus to a fraction   Example  2   5    The calculation of the modulus when applied to a fraction is the same as above  however  it is important to note that the integer division will result in a value of zero when the divisor is larger than the dividend   dividend   2  divisor   5   The integer division results in 0 whereas the  therefore  when step 3 above is performed  the value of the dividend is carried through  subtracted from zero    dividend - 0   2      gt  2   5   2    Application to apply the modulus to a negative   Floor division occurs in which the value of the integer division is rounded down to the lowest integer value   import math   x   -1 1 math floor -1 1    -2   y   1 1 math floor   1   Therefore  when you do integer division you may get a different outcome than you expect   Applying the steps above on the following dividend and divisor illustrates the modulus concept   dividend  -5  divisor  2    Step 1  Apply integer division  x int   -5    2    -3   Step 2  Multiply the result of the integer division by the divisor  x mult   x int   2   -6   Step 3  Subtract the dividend from the multiplied variable  notice the double negative    dividend - x mult   -5 - -6    1   Therefore   -5   2   1

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x   y calculates the remainder of the division x divided by y where the quotient is an integer  The remainder has the sign of y     On Python 3 the calculation yields 6 75  this is because the   does a true division  not integer division like  by default  on Python 2  On Python 2 1   4 gives 0  as the result is rounded down   The integer division can be done on Python 3 too  with    operator  thus to get the 7 as a result  you can execute   3   2   1 - 5   4   2 - 1    4   6   Also  you can get the Python style division on Python 2  by just adding the line  from   future   import division   as the first source code line in each source file

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Modulus operator  it is used for remainder division on integers  typically  but in Python can be used for floating point numbers   http   docs python org reference expressions html     The    modulo  operator yields the remainder from the division of the first argument by the second  The numeric arguments are first converted to a common type  A zero right argument raises the ZeroDivisionError exception  The arguments may be floating point numbers  e g   3 14 0 7 equals 0 34  since 3 14 equals 4 0 7   0 34   The modulo operator always yields a result with the same sign as its second operand  or zero   the absolute value of the result is strictly smaller than the absolute value of the second operand  2

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Modulus - Divides left hand operand by right hand operand and returns remainder   If it helps   1 0 gt  2 6   gt  2 2 0 gt  8 6   gt  2 3 0 gt  2 6    8 6   gt  true       and so on

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The modulus is a mathematical operation  sometimes described as  clock arithmetic   I find that describing it as simply a remainder is misleading and confusing because it masks the real reason it is used so much in computer science  It really is used to wrap around cycles    Think of a clock  Suppose you look at a clock in  military  time  where the range of times goes from 0 00 - 23 59  Now if you wanted something to happen every day at midnight  you would want the current time mod 24 to be zero    if  hour   24    0     You can think of all hours in history wrapping around a circle of 24 hours over and over and the current hour of the day is that infinitely long number mod 24  It is a much more profound concept than just a remainder  it is a mathematical way to deal with cycles and it is very important in computer science  It is also used to wrap around arrays  allowing you to increase the index and use the modulus to wrap back to the beginning after you reach the end of the array

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Be aware that    3  2   1 - 5     4   2  -  1 4    6   even with the brackets results in 6 75 instead of 7 if calculated in Python 3 4     And the     operator is not that easy to understand  too  python2 7   try     - 1 4  1 - 1 4   This is a bit off-topic here  but should be considered when evaluating the above expression

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The    modulo  operator yields the remainder from the division of the first argument by the second  The numeric arguments are first converted to a common type  A zero right argument raises the ZeroDivisionError exception  The arguments may be floating point numbers  e g   3 14 0 7 equals 0 34  since 3 14 equals 4 0 7   0 34   The modulo operator always yields a result with the same sign as its second operand  or zero   the absolute value of the result is strictly smaller than the absolute value of the second operand  2     Taken from http   docs python org reference expressions html  Example 1   6 2 evaluates to 0 because there s no remainder if 6 is divided by 2   3 times     Example 2  7 2 evaluates to 1 because there s a remainder of 1 when 7 is divided by 2   3 times     So to summarise that  it returns the remainder of a division operation  or 0 if there is no remainder   So 6 2 means find the remainder of 6 divided by 2

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Somewhat off topic  the   is also used in string formatting operations like    to substitute values into a string    gt  gt  gt  x    abc   key s    gt  gt  gt  x      key   value    gt  gt  gt  x   abc value     Again  off topic  but it seems to be a little documented feature which took me awhile to track down  and I thought it was related to Pythons modulo calculation for which this SO page ranks highly

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is modulo  3   2   1  4   2   0    is  an integer in this case  division  so   3   2   1 - 5   4   2 - 1   4   6 1   4 2 - 1 4   6 1   0 - 0   6 7

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The    modulo  operator yields the remainder from the division of the first argument by the second  The numeric arguments are first converted to a common type      3   2   1 - 5   4   2 - 1   4   6   7   This is based on operator precedence

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Modulo operator can be also used for printing strings  Just like in C  as defined on Google https   developers google com edu python strings              operator   text     d little pigs come out or I ll  s and  s and  s     3   huff    puff    blow down     This seems to bit off topic but It will certainly help someone

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Python - Basic Operators http   www tutorialspoint com python python basic operators htm       Modulus - Divides left hand operand by right hand operand and returns remainder   a   10 and b   20    b   a   0

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It s a modulo operation  except when it s an old-fashioned C-style string formatting operator  not a modulo operation  See here for details  You ll see a lot of this in existing code

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Also  there is a useful built-in function called divmod      divmod a  b       Take two  non complex  numbers as arguments and return a pair of numbers   consisting of their quotient and   remainder when using long division

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