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

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.

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