package num

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package num
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Module Num

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 =
  1. | Int of int
  2. | Big_int of Big_int.big_int
  3. | 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 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.

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

val num_of_string_opt : string -> num option

Convert a string to a number. Return None if the given string is not a valid representation of an integer.

  • since 4.05
Coercions between numerical types
val int_of_num : num -> int
val int_of_num_opt : num -> int option
val num_of_int : int -> num
val nat_of_num : num -> Nat.nat
val nat_of_num_opt : num -> Nat.nat option
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 big_int_of_num_opt : num -> Big_int.big_int option
val ratio_of_num : num -> Ratio.ratio
val num_of_ratio : Ratio.ratio -> num
val float_of_num : num -> float