Module Integers

module Integers: sig .. end
Operations on arbitrary-precision integers, subset of Big_int module.

type big_int 
The type of big integers.
val zero_big_int : big_int
The big integer 0.
val unit_big_int : big_int
The big integer 1.

Arithmetic operations

val minus_big_int : big_int -> big_int
Unary negation.
val abs_big_int : big_int -> big_int
Absolute value.
val add_big_int : big_int -> big_int -> big_int
val add_int_big_int : int -> big_int -> big_int
Addition of a small integer to a big integer.
val sub_big_int : big_int -> big_int -> big_int
val mult_big_int : big_int -> big_int -> big_int
Multiplication of two big integers.
val mult_int_big_int : int -> big_int -> big_int
Multiplication of a big integer by a small integer
val quomod_big_int : big_int -> big_int -> big_int * big_int
Euclidean division of two big integers. The first part of the result is the quotient, the second part is the remainder. Writing (q,r) = quomod_big_int a b, we have a = q * b + r and 0 <= r < |b|. Raise Division_by_zero if the divisor is zero.
val div_big_int : big_int -> big_int -> big_int
Euclidean quotient of two big integers. This is the first result q of quomod_big_int (see above).
val mod_big_int : big_int -> big_int -> big_int
Euclidean modulus of two big integers. This is the second result r of quomod_big_int (see above).
val gcd_big_int : big_int -> big_int -> big_int
Greatest common divisor of two big integers.

Comparisons and tests

val sign_big_int : big_int -> int
Return 0 if the given big integer is zero, 1 if it is positive, and -1 if it is negative.
val compare_big_int : big_int -> big_int -> int
compare_big_int a b returns 0 if a and b are equal, 1 if a is greater than b, and -1 if a is smaller than b.
val eq_big_int : big_int -> big_int -> bool
val le_big_int : big_int -> big_int -> bool
val ge_big_int : big_int -> big_int -> bool
val lt_big_int : big_int -> big_int -> bool
val gt_big_int : big_int -> big_int -> bool
Usual boolean comparisons between two big integers.
val max_big_int : big_int -> big_int -> big_int
Return the greater of its two arguments.
val min_big_int : big_int -> big_int -> big_int
Return the smaller of its two arguments.
val num_digits_big_int : big_int -> int
Return the number of machine words used to store the given big integer.

Conversions to and from strings

val string_of_big_int : big_int -> string
Return the string representation of the given big integer, in decimal (base 10).
val big_int_of_string : string -> big_int
Convert a string to a big integer, in decimal. The string consists of an optional - or + sign, followed by one or several decimal digits.

Conversions to and from other numerical types

val big_int_of_int : int -> big_int
Convert a small integer to a big integer.
val big_int_of_nat : Naturals.nat -> big_int
Convert a natural to a big integer.
val is_int_big_int : big_int -> bool
Test whether the given big integer is small enough to be representable as a small integer (type int) without loss of precision. On a 32-bit platform, is_int_big_int a returns true if and only if a is between 230 and 230-1. On a 64-bit platform, is_int_big_int a returns true if and only if a is between -262 and 262-1.
val int_of_big_int : big_int -> int
Convert a big integer to a small integer (type int). Raises Failure "int_of_big_int" if the big integer is not representable as a small integer.
val float_of_big_int : big_int -> float
Returns a floating-point number approximating the given big integer.

For internal use

val nat_of_big_int : big_int -> Naturals.nat
val approx_big_int : int -> big_int -> string
val base_power_big_int : int -> int -> big_int -> big_int
val round_futur_last_digit : string -> int -> int -> bool
val sys_big_int_of_string : string -> int -> int -> big_int