package batteries

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package batteries
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Operation on arbitrary-precision numbers.

Numbers (type num) are arbitrary-precision rational numbers, plus the special elements 1/0 (infinity) and 0/0 (undefined).

  • author Valerie Menissier-Morain (base module)
  • author Gabriel Scherer
  • author David Teller

@documents Num

type num = Num.num =
  1. | Int of int
  2. | Big_int of Big_int.big_int
  3. | Ratio of Ratio.ratio

The type of numbers.

type t = num
val zero : num

Usual operations

val one : num
val neg : num -> num
val abs : num -> num
val add : num -> num -> num
val sub : num -> num -> num
val mul : num -> num -> num
val div : num -> num -> num
val modulo : num -> num -> num
val pow : num -> num -> num
val compare : num -> num -> int
val ord : num -> num -> BatOrd.order
val equal : num -> num -> bool
val of_int : int -> num
val to_int : num -> int
val of_float : float -> num
val to_float : num -> float
val of_string : string -> num
val to_string : num -> string

Convert a number to a string, using fractional notation. Two formats are recognized: simple integer literals and a pair of integer literals separated by a '/', to indicate a rational number.

val of_float_string : string -> num

Convert a simple floating point literal to a num. Plain integer literals are also accepted; numbers written with a trailing exponent are not currently accepted.

val (+) : num -> num -> num
val (-) : num -> num -> num
val (*) : num -> num -> num
val (/) : num -> num -> num
val (**) : num -> num -> num
val max_num : num -> num -> num
val min_num : num -> num -> num
val quo : num -> num -> num

Additional operations

Euclidian divisiom

val square : num -> num
val succ : num -> num
val pred : num -> num
val is_integer : num -> bool

is_integer x returns true if x represents an integer value, false otherwise

val round : num -> num
val floor : num -> num
val ceil : num -> num
val approx : num -> num

approx n return the integer closest to n

val sign : num -> int

Return -1, 0 or 1 according to the sign of the argument.

val operations : num BatNumber.numeric
Comparisons between numbers
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
Coercions with strings
val approx_num_fix : int -> num -> string

See Num.approx_num_exp.

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. Num.approx_num_fix uses decimal notation; the first argument is the number of digits after the decimal point. approx_num_exp uses scientific (exponential) notation; the first argument is the number of digits in the mantissa.

val nat_of_num : num -> Nat.nat

Coercions between numerical types

val num_of_nat : Nat.nat -> num
val num_of_big_int : Big_int.big_int -> num
val big_int_of_num : num -> Big_int.big_int
val ratio_of_num : num -> Ratio.ratio
val num_of_ratio : Ratio.ratio -> num
val float_of_num : num -> float
Boilerplate code
val print : 'a BatInnerIO.output -> t -> unit

Printing

Submodules grouping all infix operators
module TaggedInfix : sig ... end
module Infix : sig ... end
Deprecated
val (+/) : num -> num -> num
val add_num : num -> num -> num
val minus_num : num -> num
val (-/) : num -> num -> num
val sub_num : num -> num -> num
val (*/) : num -> num -> num
val mult_num : num -> num -> num
val square_num : num -> num
val (//) : num -> num -> num
val div_num : num -> num -> num
val quo_num : num -> num -> num
val mod_num : num -> num -> num
val (**/) : num -> num -> num
val power_num : num -> num -> num
val abs_num : num -> num
val succ_num : num -> num
val pred_num : num -> num
val incr_num : num ref -> unit
val decr_num : num ref -> unit
val is_integer_num : num -> bool
val integer_num : num -> num
val floor_num : num -> num
val round_num : num -> num
val ceiling_num : num -> num
val sign_num : num -> int
val string_of_num : num -> string
val num_of_string : string -> num
val int_of_num : num -> int
val num_of_int : int -> num
val compare_num : num -> num -> int