NAME

       Num - Operation on arbitrary-precision numbers.

Module

       Module   Num

Documentation

       Module Num
        : sig end

       Operation on arbitrary-precision numbers.

       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.big_int
        | Ratio of Ratio.ratio

       The type of numbers.

       === Arithmetic operations ===

       val (+/) : num -> num -> num

       Same as Num.add_num .

       val add_num : num -> num -> num

       Addition

       val minus_num : num -> num

       Unary negation.

       val (-/) : num -> num -> num

       Same as Num.sub_num .

       val sub_num : num -> num -> num

       Subtraction

       val ( */ ) : num -> num -> num

       Same as Num.mult_num .

       val mult_num : num -> num -> num

       Multiplication

       val square_num : num -> num

       Squaring

       val (//) : num -> num -> num

       Same as Num.div_num .

       val div_num : num -> num -> num

       Division

       val quo_num : num -> num -> num

       Euclidean division: quotient.

       val mod_num : num -> num -> num

       Euclidean division: remainder.

       val ( **/ ) : num -> num -> num

       Same as Num.power_num .

       val power_num : num -> num -> num

       Exponentiation

       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 Pervasives.ref -> unit

       incr r is r:=!r+1 , where r is a reference to a number.

       val decr_num : num Pervasives.ref -> unit

       decr r is r:=!r-1 , where r is a reference to a number.

       val is_integer_num : num -> bool

       Test if a number is an integer

       === The four following functions approximate a number by an integer : ===

       val integer_num : num -> num

       integer_num n returns the integer closest to n . In case of ties, rounds towards zero.

       val floor_num : num -> num

       floor_num n returns the largest integer smaller or equal to n .

       val round_num : num -> num

       round_num n returns the integer closest to n . In case of ties, rounds off zero.

       val ceiling_num : num -> num

       ceiling_num n returns the smallest integer bigger or equal to n .

       val sign_num : num -> int

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

       === 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

       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

       Return the greater of the two arguments.

       val min_num : num -> num -> num

       Return the smaller of the two arguments.

       === 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

       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 num_of_string : string -> num

       Convert  a  string  to a number.  Raise Failure num_of_string if the given string is not a
       valid representation of an integer

       === Coercions between numerical types ===

       val int_of_num : num -> int

       val num_of_int : int -> num

       val nat_of_num : num -> Nat.nat

       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