Module dashu::float::round::mode

Built-in rounding modes of the floating numbers.

Rounding Error

For different rounding modes, the Rounding error in the output of operations tells the error range, as described in the table below.

Mode	Rounding	Error (truth - estimation) Range
Zero	NoOp	(-1 ulp 0) or (0, 1 ulp)*
Away	AddOne	(-1 ulp, 0)
Away	SubOne	(0, 1 ulp)
Down	SubOne	(0, 1 ulp)
Up	AddOne	(-1 ulp, 0)
HalfAway	AddOne	[-1/2 ulp, 0)
HalfAway	NoOp	(-1/2 ulp, 1/2 ulp)
HalfAway	SubOne	(0, 1/2 ulp]
HalfEven	AddOne	[-1/2 ulp, 0)
HalfEven	NoOp	[-1/2 ulp, 1/2 ulp]
HalfEven	SubOne	(0, 1/2 ulp]

*: Dependends on the sign of the result

Structs

• Away
  Round away from 0
• Down
  Round toward -∞
• HalfAway
  Round to the nearest value, ties away from zero
• HalfEven
  Round to the nearest value, ties are rounded to an even value. (default mode for decimal float)
• Up
  Round toward +∞
• Zero
  Round toward 0 (default mode for binary float)