What s the difference between mod and remainder

Question

My friend said that there are differences between  mod  and  remainder    If so  what are those differences in C and C    Does     mean either  mod  or  rem  in C

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Modulus  in modular arithmetic as you re referring  is the value left over or remaining value after arithmetic division   This is commonly known as remainder     is formally the remainder operator in C   C    Example   7   3   1     dividend   divisor   remainder   What s left for discussion is how to treat negative inputs to this   operation   Modern C and C   produce a signed remainder value for this operation where the sign of the result always matches the dividend input without regard to the sign of the divisor input

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sign of remainder will be same as the divisible and the sign of modulus will be same as divisor  Remainder is simply the remaining part after the arithmetic division between two integer number whereas Modulus is the sum of remainder and divisor when they are oppositely signed and remaining part after the arithmetic division when remainder and divisor both are of same sign  Example of Remainder  10   3   1  here divisible is 10 which is positively signed so the result will also be positively signed  -10   3   -1  here divisible is -10 which is negatively signed so the result will also be negatively signed  10   -3   1  here divisible is 10 which is positively signed so the result will also be positively signed  -10   -3   -1  here divisible is -10 which is negatively signed so the result will also be negatively signed  Example of Modulus  5   3   2  here divisible is 5 which is positively signed so the remainder will also be positively signed and the divisor is also positively signed  As both remainder and divisor are of same sign the result will be same as remainder  -5   3   1  here divisible is -5 which is negatively signed so the remainder will also be negatively signed and the divisor is positively signed  As both remainder and divisor are of opposite sign the result will be sum of remainder and divisor -2   3   1  5   -3   -1  here divisible is 5 which is positively signed so the remainder will also be positively signed and the divisor is negatively signed  As both remainder and divisor are of opposite sign the result will be sum of remainder and divisor 2   -3   -1  -5   -3   -2  here divisible is -5 which is negatively signed so the remainder will also be negatively signed and the divisor is also negatively signed  As both remainder and divisor are of same sign the result will be same as remainder  I hope this will clearly distinguish between remainder and modulus

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Does     mean either  quot mod quot  or  quot rem quot  in C   In C    is the remainder1        the result of the   operator is the algebraic quotient with any fractional part discarded      This is often called  quot truncation toward zero quot    C11dr   6 5 5 6 The operands of the   operator shall have integer type   C11dr   6 5 5 2 The result of the   operator is the quotient from the division of the first operand by the second  the result of the   operator is the remainder      C11dr   6 5 5 5    What s the difference between    mod    and    remainder      C does not define  quot mod quot   such as the integer modulus function used in Euclidean division or other modulo   quot Euclidean mod quot  differs from C s a b operation when a is negative      a   b  7    3 -- gt   1    7   -3 -- gt   1   -7    3 -- gt  -1   -7   -3 -- gt  -1     Modulo as Euclidean division  7 modulo  3 -- gt   1    7 modulo -3 -- gt   1   -7 modulo  3 -- gt   2   -7 modulo -3 -- gt   2      Candidate modulo code  int modulo Euclidean int a  int b      int m   a   b    if  m  lt  0           m     b  lt  0    -b   b     avoid this form  it is UB when b    INT MIN     m    b  lt  0    m - b   m   b        return m      Note about floating point  double fmod double x  double y   even though called  quot fmod quot   it is not the same as Euclidean division  quot mod quot   but similar to C integer remainder   The fmod functions compute the floating-point remainder of x y   C11dr   7 12 10 1 2  fmod  7   3  -- gt   1 0   fmod  7  -3  -- gt   1 0   fmod -7   3  -- gt  -1 0   fmod -7  -3  -- gt  -1 0      Disambiguation  C also has a similar named function double modf double value  double  iptr  which breaks the argument value into integral and fractional parts  each of which has the same type and sign as the argument  This has little to do with the  quot mod quot  discussion here except name similarity    Edit Dec 2020  For those who want proper functionality in all cases  an improved modulo Euclidean   that 1  detects mod x 0  and 2  a good and no UB result with modulo Euclidean2 INT MIN  -1    Inspired by 4 different implementations of modulo with fully defined behavior  int modulo Euclidean2 int a  int b      if  b    0  TBD Code       perhaps return -1 to indicate failure    if  b    -1  return 0     This test needed to prevent UB of  INT MIN   -1     int m   a   b    if  m  lt  0           m     b  lt  0    -b   b     avoid this form  it is UB when b    INT MIN     m    b  lt  0    m - b   m   b        return m      1 Prior to C99  C s definition of   was still the remainder from division  yet then   allowed negative quotients to round down rather than  quot truncation toward zero quot    See Why do you get different values for integer division in C89   Thus with some pre-C99 compilation    code can act just like the Euclidean division  quot mod quot    The above modulo Euclidean   will work with this alternate old-school remainder too

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In C and C   and many languages    is the remainder NOT the modulus operator  For example in the operation -21   4 the integer part is -5 and the decimal part is - 25  The remainder is the fractional part times the divisor  so our remainder is -1  JavaScript uses the remainder operator and confirms this  x000D   x000D  console log -21   4    -1   x000D   x000D   x000D   The modulus operator is like you had a  quot clock quot   Imagine a circle with the values 0  1  2  and 3 at the 12 o clock  3 o clock  6 o clock  and 9 o clock positions respectively  Stepping quotient times around the clock clock-wise lands us on the result of our modulus operation  or  in our example with a negative quotient  counter-clockwise  yielding 3  Note  Modulus is always the same sign as the divisor and remainder the same sign as the quotient  Adding the divisor and the remainder when at least one is negative yields the modulus

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In mathematics the result of the modulo operation is the remainder of the Euclidean division  However  other conventions are possible  Computers and calculators have various ways of storing and representing numbers  thus their definition of the modulo operation depends on the programming language and or the underlying hardware    7 modulo  3 -- gt   1    7 modulo -3 -- gt  -2  -7 modulo  3 -- gt   2   -7 modulo -3 -- gt  -1

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There is a difference between modulus and remainder  For example   -21 mod 4 is 3 because -21   4 x 6 is 3   But -21 divided by 4 gives -5 with a remainder of -1   For positive values  there is no difference

[c] What's the difference between “mod” and “remainder”?

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