package interval_intel

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Module Fpu.RoundUpSource

Functions rounding up their results.

include module type of Interval_base.RoundUp
include Interval_base.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.

  • since 1.6
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.

Locally open to restore standard integer and floating point operators.

Sourceval (**) : float -> float -> float

x**y computes x at power y, rounded up, expanded to its mathematical limit when it exists.

Sourceval pow : float -> float -> float

pow x y computes x at power y, rounded up, for 0 < x < ∞ and -∞ < y < infty.

Sourceval exp : float -> float

Floating point exponential, rounded up.

Sourceval log : float -> float

Floating point log, rounded up.

Sourceval sin : float -> float

Computes sin(x) for x ∈ ]-2⁶³, 2⁶³[.

Sourceval cos : float -> float

Computes cos(x) for x in ]-2⁶³, 2⁶³[.

Sourceval tan : float -> float

Computes tan(x) for x in ]-2⁶³, 2⁶³[.

Sourceval asin : float -> float

Arc-sine function.

Sourceval acos : float -> float

Arc-cosine function.

Sourceval atan : float -> float

Arc-tangent function.

Sourceval atan2 : float -> float -> float

atan2 y x returns the arc tangent of y /. x. The signs of x and y are used to determine the quadrant of the result. Result is in radians and is between -π and π.

Sourceval sinh : float -> float

Computes the hyperbolic sine, sinh(x).

Sourceval cosh : float -> float

Computes the hyperbolic cosine, cosh(x).

Sourceval tanh : float -> float

Computes the hyperbolic tangent, tanh(x).