## File: creal.mli

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mlgmp 20021123-20
 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123 (* * Exact real arithmetic (Constructive reals). * Copyright (C) 2000 Jean-Christophe FILLIATRE * * This software is free software; you can redistribute it and/or * modify it under the terms of the GNU Library General Public * License version 2, as published by the Free Software Foundation. * * This software is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * * See the GNU Library General Public License version 2 for more details * (enclosed in the file LGPL). *) (*i $Id: creal.mli,v 1.1 2001/12/17 08:20:29 monniaux Exp$ i*) (*s {\bf Constructive reals} are implemented by the following abstract datatype [t]. If [x] is a constructive real, then the function call [approx x n] returns an approximation of [x] up to $4^{-n}$, as an arbitrary precision integer $x_n$ such that $|4^n\cdot x - x_n| < 1$. *) open Gmp type t val approx : t -> int -> Z.t (*s Basic operations. *) val add : t -> t -> t val neg : t -> t val sub : t -> t -> t val abs : t -> t val mul : t -> t -> t val inv : t -> t val div : t -> t -> t val pow_int : t -> int -> t val sqrt : t -> t (*s Transcendental functions. [log x y] is $\log_x(y)$. *) val ln : t -> t val log : t -> t -> t val exp : t -> t val pow : t -> t -> t (*s Trigonometric functions. *) val sin : t -> t val cos : t -> t val tan : t -> t val arcsin : t -> t val arccos : t -> t val arctan : t -> t (*s [arctan_reciproqual n] is $\arctan(1/n)$, but is more efficient than using [arctan]. *) val arctan_reciproqual : int -> t (*s Hyperbolic functions. *) val sinh : t -> t val cosh : t -> t val tanh : t -> t val arcsinh : t -> t val arccosh : t -> t val arctanh : t -> t (*s Some constants. *) val zero : t val one : t val two : t val pi : t val pi_over_2 : t val e : t (*s Comparisons. [cmp] is absolute comparison: it may not terminate and only returns [-1] or [+1]. [rel_cmp] is relative comparison, up to $4^{-k}$, and it returns [-1],  or [+1]. *) val cmp : t -> t -> int val rel_cmp : int -> t -> t -> int (*s Coercions. [to_q] and [to_float] expect a precision. [to_float x n] returns the best floating point representation of the rational $\ap{x}{n} / 4^n$. [of_string] expects a base as second argument. *) val of_int : int -> t val of_z : Z.t -> t val of_q : Q.t -> t val of_float : float -> t val of_string : string -> int -> t val to_float : t -> int -> float val to_q : t -> int -> Q.t (*s Coercion to type [string]. Given a decimal precision [p], [to_string x p] returns a decimal approximation [d] of [x] with [p] digits such that $|d - x| < 10^{-p}$. [to_beautiful_string] returns the same decimal number but with digits packed 5 by 5. *) val to_string : t -> int -> string val to_beautiful_string : t -> int -> string (*s Infix notations. *) val ( +! ) : t -> t -> t val ( -! ) : t -> t -> t val ( *! ) : t -> t -> t val ( /! ) : t -> t -> t