package interval_base

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Module `Interval_base.RoundDown`Source

Functions rounding down their results.

include DIRECTED with type t = float

Sourcetype t = float

Type of numbers.

Sourceval zero : t

The neutral element for addition.

Sourceval one : t

The neutral element for multiplication.

Sourceval pi : t

Upper/lower bound on π.

Sourceval two_pi : t

Upper/lower bound on 2π.

Sourceval half_pi : t

Upper/lower bound on π/2.

Sourceval euler : t

Upper/lower bound on Euler's constant.

Sourceval float : int -> t

When t = float, the float function is exact on 32 bits machine but not on 64 bits machine with ints larger than 53 bits.

Sourceval dist : t -> t -> t

dist x y return the distance between x and y (i.e., |x-y|) rounded up or down according to the module.

Sourceval (+.) : t -> t -> t

Sourceval (-.) : t -> t -> t

Sourceval (*.) : t -> t -> t

Sourceval (/.) : t -> t -> t

Sourceval sqr : t -> t

sqr x returns an upper/lower bound on x².

Sourceval cbr : t -> t

cbr x returns an upper/lower bound on x³.

Sourceval pow_i : t -> int -> t

pow_i x n return a upper/lower bound on xⁿ.

Sourceval sqrt : t -> t

sqrt x return the square root of x rounded up/down.

Sourceval hypot : t -> t -> t

hypot x y returns sqrt(x *. x + y *. y) rounded up/down. Returns NaN if any of the arguments is NaN.

Sourcemodule U = I.U

Locally open to restore standard integer and floating point operators.