How python calculate this modulo? -

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how python calculate mathematically modulo?

>>>-1%10   9

the wikipedia article on modulo operation provides following constraint a % q:

a = nq + r

substituting a = -1, q = 10 , r = 9, see n must equal -1.

plugging in -1 n:

-1 % 10  # python evaluates 9 -1 = n * 10 + r -1 = -1 * 10 + r 9 = r

testing example (again plugging in -1 n):

-7 % 17  # python evaluates 10 -7 = n * 17 + r -7 = -17 + r 10 = r

a third example positive numerator , negative denominator:

7 % -17  # python evaluates -10 7 = n * (-17) + r 7 = -1 * (-17) + r 7 = 17 + r -10 = r

it appears when a , q have different signs, start n = -1 , decrement n 1 until we've found n closest 0 such n*q < a. can test trying out a , q such |a| > |q|:

-100 % 11  # python evaluates 10 -100 = n * 11 + r  ...   -1  # -11 > -100  ...   -2  # -22 > -100  ...   -3  ...  ...   -4  ...  ...   -5  ...  ...   -6  ...  ...   -7  ...  ...   -8  ...  ...   -9  # -99 > -100  -100 = -10 * 11 + r  # -110 < -100  -100 = -110 + r  10 = r

so while might not algorithm python uses calculate modulo, @ least have useful mental model reasoning how given result arrived at.


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