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Dual numbers. This module provides arithmetic operations on dual numbers represented as double-precision floating-point numbers (type float).
float
type t = {
re : float;
dre : float;
}
The type of dual numbers. re is the value and dre the derivative.
re
dre
val dual : ?y:float -> float -> t
Create a dual number. By default dre is set to 1.
val print_dual : t -> unit
Pretty print dual number.
val equal : t -> t -> bool
Check equality between two dual numbers.
val add : t -> t -> t
Addition.
val sub : t -> t -> t
Subtraction.
val neg : t -> t
Unary negation.
val mul : t -> t -> t
Multiplication.
val div : t -> t -> t
Division
val pow : t -> float -> t
Power function. pow d1 d2 returns d1 to the d2 power.
pow d1 d2
d1
d2
val sqrt : t -> t
Square root.
val exp : t -> t
Exponentiation. exp d returns e to the d power.
exp d
e
d
val log : t -> t
Natural logarithm (in base e).
val sin : t -> t
Sine function.
val cos : t -> t
Cosine function.
val tan : t -> t
Tangent function.
val asin : t -> t
Inverse sine function.
val acos : t -> t
Inverse cosine function.
val atan : t -> t
Inverse tangent function.
val sinh : t -> t
Hyperbolic sine function.
val cosh : t -> t
Hyperbolic cosine function.
val tanh : t -> t
Hyperbolic tangent function.
val root : (t -> t) -> t -> t
root f x0 returns the root of f with starting value x0 via Newton's method.
root f x0
f
x0