# Floating Point Rounding

The IEEE floating-point format defines four different rounding modes.

## # Round-to-even (round-to-nearest)

**It’s the default mode**

It**first**attempts to find a closest match. Thus, it rounds 1.40 to 1 and 1.60 to 2,

If it falls halfway, it rounds the number either upward or downward such that the**least significant digit**of the result is**even**(Which in most case means even).- Why?
- It will round upward about 50% of the time and round downward about 50% of the time.

## # Round-toward-zero

Round-toward-zero mode rounds positive numbers **downward** and negative numbers **upward**

giving $|\hat{x}| \leq |x|$

## # Round-down

Round-down mode rounds both positive and negative numbers **downward**

giving $x^- \leq x$

## # Round-up

Round-up mode rounds both positive and negative numbers **upward**

giving $x^+ \geq x$