121 lines
4.5 KiB
OCaml
121 lines
4.5 KiB
OCaml
(***********************************************************************)
|
|
(* *)
|
|
(* Objective Caml *)
|
|
(* *)
|
|
(* Valerie Menissier-Morain, projet Cristal, INRIA Rocquencourt *)
|
|
(* *)
|
|
(* Copyright 1996 Institut National de Recherche en Informatique et *)
|
|
(* Automatique. Distributed only by permission. *)
|
|
(* *)
|
|
(***********************************************************************)
|
|
|
|
(* $Id$ *)
|
|
|
|
(* Module [Num]: operation on arbitrary-precision numbers *)
|
|
|
|
open Nat
|
|
open Big_int
|
|
open Ratio
|
|
|
|
(* Numbers (type [num]) are arbitrary-precision rational numbers,
|
|
plus the special elements [1/0] (infinity) and [0/0] (undefined). *)
|
|
|
|
type num = Int of int | Big_int of big_int | Ratio of ratio
|
|
(* The type of numbers. *)
|
|
|
|
(* Arithmetic operations *)
|
|
|
|
val (+/) : num -> num -> num
|
|
val add_num : num -> num -> num
|
|
(* Addition *)
|
|
val minus_num : num -> num
|
|
(* Unary negation. *)
|
|
val (-/) : num -> num -> num
|
|
val sub_num : num -> num -> num
|
|
(* Subtraction *)
|
|
val ( */ ) : num -> num -> num
|
|
val mult_num : num -> num -> num
|
|
(* Multiplication *)
|
|
val square_num : num -> num
|
|
(* Squaring *)
|
|
val (//) : num -> num -> num
|
|
val div_num : num -> num -> num
|
|
(* Division *)
|
|
val quo_num : num -> num -> num
|
|
val mod_num : num -> num -> num
|
|
(* Euclidean division: quotient and remainder *)
|
|
val ( **/ ) : num -> num -> num
|
|
val power_num : num -> num -> num
|
|
(* Exponentiation *)
|
|
val is_integer_num : num -> bool
|
|
(* Test if a number is an integer *)
|
|
val integer_num : num -> num
|
|
val floor_num : num -> num
|
|
val round_num : num -> num
|
|
val ceiling_num : num -> num
|
|
(* Approximate a number by an integer.
|
|
[floor_num n] returns the largest integer smaller or equal to [n].
|
|
[ceiling_num n] returns the smallest integer bigger or equal to [n].
|
|
[integer_num n] returns the integer closest to [n]. In case of ties,
|
|
rounds towards zero.
|
|
[round_num n] returns the integer closest to [n]. In case of ties,
|
|
rounds off zero. *)
|
|
val sign_num : num -> int
|
|
(* Return [-1], [0] or [1] according to the sign of the argument. *)
|
|
val (=/) : num -> num -> bool
|
|
val (</) : num -> num -> bool
|
|
val (>/) : num -> num -> bool
|
|
val (<=/) : num -> num -> bool
|
|
val (>=/) : num -> num -> bool
|
|
val (<>/) : num -> num -> bool
|
|
val eq_num : num -> num -> bool
|
|
val lt_num : num -> num -> bool
|
|
val le_num : num -> num -> bool
|
|
val gt_num : num -> num -> bool
|
|
val ge_num : num -> num -> bool
|
|
(* Usual comparisons between numbers *)
|
|
val compare_num : num -> num -> int
|
|
(* Return [-1], [0] or [1] if the first argument is less than,
|
|
equal to, or greater than the second argument. *)
|
|
val max_num : num -> num -> num
|
|
val min_num : num -> num -> num
|
|
(* Return the greater (resp. the smaller) of the two arguments. *)
|
|
val abs_num : num -> num
|
|
(* Absolute value. *)
|
|
val succ_num: num -> num
|
|
(* [succ n] is [n+1] *)
|
|
val pred_num: num -> num
|
|
(* [pred n] is [n-1] *)
|
|
val incr_num: num ref -> unit
|
|
(* [incr r] is [r:=!r+1], where [r] is a reference to a number. *)
|
|
val decr_num: num ref -> unit
|
|
(* [decr r] is [r:=!r-1], where [r] is a reference to a number. *)
|
|
|
|
(* Coercions with strings *)
|
|
|
|
val string_of_num : num -> string
|
|
(* Convert a number to a string, using fractional notation. *)
|
|
val approx_num_fix : int -> num -> string
|
|
val approx_num_exp : int -> num -> string
|
|
(* Approximate a number by a decimal. The first argument is the
|
|
required precision. The second argument is the number to
|
|
approximate. [approx_fix] uses decimal notation; the first
|
|
argument is the number of digits after the decimal point.
|
|
[approx_exp] uses scientific (exponential) notation; the
|
|
first argument is the number of digits in the mantissa. *)
|
|
val num_of_string : string -> num
|
|
(* Convert a string to a number. *)
|
|
|
|
(* Coercions between numerical types *)
|
|
|
|
val int_of_num : num -> int
|
|
val num_of_int : int -> num
|
|
val nat_of_num : num -> nat
|
|
val num_of_nat : nat -> num
|
|
val num_of_big_int : big_int -> num
|
|
val big_int_of_num : num -> big_int
|
|
val ratio_of_num : num -> ratio
|
|
val num_of_ratio : ratio -> num
|
|
val float_of_num : num -> float
|
|
|