MOD

MOD returns the modular equivalent of the remainder of one value divided by another.

MOD returns the smallest nonnegative value, R, such that (x - R)/y = n.

In this example, the value for n is an integer value. That is, R is the smallest nonnegative value that must be subtracted from x to make it divisible by y.

x: Real expression.
y: Real expression. If y = 0, the ZERODIVIDE condition is raised.

The result, R, is real with the common base and scale of the arguments. If the result is floating-point, the precision is the greater of those of x and y. If the result is fixed-point, the precision is given by the following:

  (min(n,p2-q2+max(q1,q2)),max(q1,q2))

In this example, (p1,q1) and (p2,q2) are the precisions of x and y, respectively, and n is N for FIXED DECIMAL or M for FIXED BINARY.

If x and y are fixed-point with different scaling factors, the argument with the smaller scaling factor is converted to the larger scaling factor before R is calculated. If the conversion fails, the result is unpredictable.

If the result has the attributes FIXED BIN and one or more of the operands has the attributes UNSIGNED FIXED BIN, the result has the SIGNED attribute unless both of the following conditions are true:

All of the operands are UNSIGNED FIXED BIN.
The RULES(ANS) compiler option is in effect.

If any of the conditions above is not true, each UNSIGNED operand is converted to SIGNED. If the operand is too large, the conversion would:

Raise the SIZE condition if SIZE is enabled.
Produce a negative value if SIZE is not enabled.

Example

The following example contrasts the MOD and REM built-in functions.

  rem( +10, +8 ) = 2
  mod( +10, +8 ) = 2

  rem( +10, -8 ) = 2
  mod( +10, -8 ) = 2

  rem( -10, +8 ) = -2
  mod( -10, +8 ) = 6

  rem( -10, -8 ) = -2
  mod( -10, -8 ) = 6