14.7.3 Remainder operator

For an operation of the form x % y, binary operator overload resolution (?4.
2.4) is applied to select a
specific operator implementation. The operands are converted to the
parameter types of the selected
operator, and the type of the result is the return type of the operator.
The predefined remainder operators are listed below. The operators all
compute the remainder of the
division between x and y.
?Integer remainder:
int operator %(int x, int y);
uint operator %(uint x, uint y);
long operator %(long x, long y);
ulong operator %(ulong x, ulong y);
The result of x % y is the value produced by x ? (x / y) * y. If y is zero,
a
System.DivideByZeroException is thrown. The remainder operator never causes
an overflow.
?Floating-point remainder:
float operator %(float x, float y);
double operator %(double x, double y);
The following table lists the results of all possible combinations of
nonzero finite values, zeros,
infinities, and NaN?s. In the table, x and y are positive finite values. z
is the result of x % y and is
computed as x ? n * y, where n is the largest possible integer that is less
than or equal to x / y. This
method of computing the remainder is analogous to that used for integer
operands, but differs from the
IEC 60559 definition (in which n is the integer closest to x / y).

    +y  -y  +0  -0  +8  -8  NaN
+x  +z  +z  NaN NaN x   x   NaN
-x  -z  -z  NaN NaN -x  -x  NaN
+0  +0  +0  NaN NaN +0  +0  NaN
-0  -0  -0  NaN NaN -0  -0  NaN
+8  NaN NaN NaN NaN NaN NaN NaN
-8  NaN NaN NaN NaN NaN NaN NaN
NaN NaN NaN NaN NaN NaN NaN NaN

?Decimal remainder:
decimal operator %(decimal x, decimal y);
If the value of the right operand is zero, a System.DivideByZeroException
is thrown. If the resulting
value is too large to represent in the decimal format, a
System.OverflowException is thrown. If the
result value is too small to represent in the decimal format, the result is
zero. The scale of the result, before
any rounding, is the larger of the scales of the two operands, and the sign
of the result, if non-zero, is the
same as that of x.
Decimal remainder is equivalent to using the remainder operator of type
System.Decimal.