Module Num

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

let (+/): (num, num) => num;

Same as Num.add_num.

let add_num: (num, num) => num;

Addition

let minus_num: num => num;

Unary negation.

let (-/): (num, num) => num;

Same as Num.sub_num.

let sub_num: (num, num) => num;

Subtraction

let ( *\/ ): (num, num) => num;

Same as Num.mult_num.

let mult_num: (num, num) => num;

Multiplication

let square_num: num => num;

Squaring

let (/\/): (num, num) => num;

Same as Num.div_num.

let div_num: (num, num) => num;

Division

let quo_num: (num, num) => num;

Euclidean division: quotient.

let mod_num: (num, num) => num;

Euclidean division: remainder.

let ( **\/ ): (num, num) => num;

Same as Num.power_num.

let power_num: (num, num) => num;

Exponentiation

let abs_num: num => num;

Absolute value.

let succ_num: num => num;

succ n is n+1

let pred_num: num => num;

pred n is n-1

let incr_num: Pervasives.ref(num) => unit;

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

let decr_num: Pervasives.ref(num) => unit;

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

let is_integer_num: num => bool;

Test if a number is an integer

The four following functions approximate a number by an integer :

let integer_num: num => num;

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

let floor_num: num => num;

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

let round_num: num => num;

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

let ceiling_num: num => num;

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

let sign_num: num => int;

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

Comparisons between numbers

let (=/): (num, num) => bool;

let (</): (num, num) => bool;

let (>/): (num, num) => bool;

let (<=/): (num, num) => bool;

let (>=/): (num, num) => bool;

let (<>/): (num, num) => bool;

let eq_num: (num, num) => bool;

let lt_num: (num, num) => bool;

let le_num: (num, num) => bool;

let gt_num: (num, num) => bool;

let ge_num: (num, num) => bool;

let 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.

let max_num: (num, num) => num;

Return the greater of the two arguments.

let min_num: (num, num) => num;

Return the smaller of the two arguments.

Coercions with strings

let string_of_num: num => string;

Convert a number to a string, using fractional notation.

let approx_num_fix: (int, num) => string;

See Num.approx_num_exp.

let 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.

let 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

let int_of_num: num => int;

let num_of_int: int => num;

let nat_of_num: num => Nat.nat;

let num_of_nat: Nat.nat => num;

let num_of_big_int: Big_int.big_int => num;

let big_int_of_num: num => Big_int.big_int;

let ratio_of_num: num => Ratio.ratio;

let num_of_ratio: Ratio.ratio => num;

let float_of_num: num => float;