Rounding modes

When a result value has more significant digits than digits, the digits in excess are discarded with respect to the rounding mode.

round-down
Truncate : just drop the digits in excess.
round-half-up
If the discarded digits represent greater than or equal to half (0.5) of the value of a one in the next left position then the result should be incremented by 1 (rounded up).
round-half-even
If the discarded digits represent greater than half (0.5) the value of a one in the next left position then the result should be incremented by 1 (rounded up). If they represent less than half, then the result is not adjusted (that is, the discarded digits are ignored). Otherwise (they represent exactly half) the result is unaltered if its rightmost digit is even, or incremented by 1 (rounded up) if its rightmost digit is odd (to make an even digit).
round-ceiling
Round toward +Infinity. If all of the discarded digits are zero or if the sign is negative the result is unchanged. Otherwise, the result should be incremented by 1 (rounded up). If this would cause overflow then the result will be +Infinity.
round-floor
Round toward -Infinity. If all of the discarded digits are zero or if the sign is positive the result is unchanged. Otherwise, the sign is 1 and the coefficient should be incremented by 1. If this would cause overflow then the result will be -Infinity.
round-half-down
Round to nearest, where a 0.5 case is rounded down.
round-up
Round away from zero.