module BatBig_int:sig
..end
Big integers (type BatBig_int.big_int
or equivalently Big_int.t
) are
signed integers of arbitrary size. This module lets you compute
with huge numbers, whose size is limited only by the amount of
memory given to OCaml. The downside is speed, as big integers
are much slower than any other type of integer known to OCaml.
This module replaces Stdlib's
Big_int
module.
Author(s): Valerie Menissier-Morain (base module), Gabriel Scherer, David Teller
typebig_int =
Big_int.big_int
val zero : big_int
val zero_big_int : big_int
0
.val one : big_int
val unit_big_int : big_int
1
.val neg : big_int -> big_int
val succ : big_int -> big_int
val pred : big_int -> big_int
val abs : big_int -> big_int
val add : big_int -> big_int -> big_int
val sub : big_int -> big_int -> big_int
val mul : big_int -> big_int -> big_int
val div : big_int -> big_int -> big_int
val modulo : big_int -> big_int -> big_int
val pow : big_int -> big_int -> big_int
typet =
big_int
val (+) : t -> t -> t
val (-) : t -> t -> t
val ( * ) : t -> t -> t
val (/) : t -> t -> t
val ( ** ) : t -> t -> t
val minus_big_int : big_int -> big_int
val abs_big_int : big_int -> big_int
val add_big_int : big_int -> big_int -> big_int
val succ_big_int : big_int -> big_int
val add_int_big_int : int -> big_int -> big_int
val sub_big_int : big_int -> big_int -> big_int
val pred_big_int : big_int -> big_int
val mult_big_int : big_int -> big_int -> big_int
val mult_int_big_int : int -> big_int -> big_int
val square_big_int : big_int -> big_int
val sqrt_big_int : big_int -> big_int
sqrt_big_int a
returns the integer square root of a
,
that is, the largest big integer r
such that r * r <= a
.Invalid_argument
if a
is negative.val quomod_big_int : big_int ->
big_int -> big_int * big_int
(q,r) = quomod_big_int a b
, we have
a = q * b + r
and 0 <= r < |b|
.Division_by_zero
if the divisor is zero.val div_big_int : big_int -> big_int -> big_int
q
of quomod_big_int
(see above).val mod_big_int : big_int -> big_int -> big_int
r
of quomod_big_int
(see above).val gcd_big_int : big_int -> big_int -> big_int
val power_int_positive_int : int -> int -> big_int
val power_big_int_positive_int : big_int -> int -> big_int
val power_int_positive_big_int : int -> big_int -> big_int
val power_big_int_positive_big_int : big_int -> big_int -> big_int
a
raised to the power b
(the second argument). Depending
on the function, a
and b
can be either small integers
or big integers.Invalid_argument
if b
is negative.val operations : t BatNumber.numeric
val (--) : big_int -> big_int -> big_int BatEnum.t
val (---) : big_int -> big_int -> big_int BatEnum.t
val compare : big_int -> big_int -> int
val ord : big_int -> big_int -> BatOrd.order
val equal : big_int -> big_int -> bool
val sign_big_int : big_int -> int
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
val max_big_int : big_int -> big_int -> big_int
val min_big_int : big_int -> big_int -> big_int
val num_digits_big_int : big_int -> int
val to_string : big_int -> string
val string_of_big_int : big_int -> string
val of_string : string -> big_int
val big_int_of_string : string -> big_int
-
or +
sign,
followed by one or several decimal digits.val to_string_in_binary : big_int -> string
string_of_big_int
, but in base 2val to_string_in_octal : big_int -> string
string_of_big_int
, but in base 8val to_string_in_hexa : big_int -> string
string_of_big_int
, but in base 16val to_string_in_base : int -> big_int -> string
to_string_in_base b n
returns the string representation in base b
of
the given big integer n
. Should you have advanced needs (arbitrarily large
bases, or custom digits instead of the usual 0,1,...9,a,b,...,z
), use
to_string_in_custom_base
instead.Invalid_argument
if b is not in
2 .. 36
.val to_string_in_custom_base : string -> int -> big_int -> string
symbols
, is the vector of the symbols used to
represent the digits in base b
. to_string_in_base
is almost equivalent to
to_string_in_custom_base big_int_base_default_symbols
, the difference being
that to_string_in_custom_base
allows the base to be arbitrarily large,
provided that symbols
can accommodate it. Concretely, the base b
must be at
least 2
, and symbols
must be of size at least b
. The default value of
big_int_base_default_symbols
contains 62 symbols, as it uses lowercase and
uppercase letters both. See below for more information.Invalid_argument
if b
is incorrect.val big_int_base_default_symbols : string
to_string_in_base
and its fixed-base
derivatives to_string_in_binary
, to_string_in_octal
and to_string_in_hexa
to represent digits. The symbol at position p
encodes the value p
. The
original value of this vector is, schematically, ['0'..'9' 'a' 'b'..'z' 'A'
'B'..'Z']
, which is sufficient for bases up to and including 62. The basic
to_string_in_base
function is capped to base 36 to avoid unexpected
behaviours do to the case-sensitivity of the output in bases 37 to 62. You
technically can mutate the vector, for instance if you prefer to exchange
lower- and upper-case symbols program-wide. As usual where mutability is
concerned, discretion is advised. Most of the time, it is better to build
custom functions using to_string_in_custom_base
.val of_int : int -> big_int
val big_int_of_int : int -> big_int
val is_int_big_int : big_int -> bool
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 to_int : big_int -> int
val int_of_big_int : big_int -> int
int
).Failure
if the big integer
is not representable as a small integer.val big_int_of_int32 : int32 -> big_int
val big_int_of_nativeint : nativeint -> big_int
val big_int_of_int64 : int64 -> big_int
val int32_of_big_int : big_int -> int32
Failure
if the big integer is outside the
range [-2{^31}, 2{^31}-1]
.val nativeint_of_big_int : big_int -> nativeint
Failure
if the big integer is outside the
range [Nativeint.min_int, Nativeint.max_int]
.val int64_of_big_int : big_int -> int64
Failure
if the big integer is outside the
range [-2{^63}, 2{^63}-1]
.val float_of_big_int : big_int -> float
val of_float : float -> big_int
Invalid_argument
when given NaN or +/-infinityval to_float : big_int -> float
val and_big_int : big_int -> big_int -> big_int
val or_big_int : big_int -> big_int -> big_int
val xor_big_int : big_int -> big_int -> big_int
val shift_left_big_int : big_int -> int -> big_int
shift_left_big_int b n
returns b
shifted left by n
bits.
Equivalent to multiplication by 2^n
.val shift_right_big_int : big_int -> int -> big_int
shift_right_big_int b n
returns b
shifted right by n
bits.
Equivalent to division by 2^n
with the result being
rounded towards minus infinity.val shift_right_towards_zero_big_int : big_int -> int -> big_int
shift_right_towards_zero_big_int b n
returns b
shifted
right by n
bits. The shift is performed on the absolute
value of b
, and the result has the same sign as b
.
Equivalent to division by 2^n
with the result being
rounded towards zero.val extract_big_int : big_int -> int -> int -> big_int
extract_big_int bi ofs n
returns a nonnegative number
corresponding to bits ofs
to ofs + n - 1
of the
binary representation of bi
. If bi
is negative,
a two's complement representation is used.module Infix:BatNumber.Infix
with type bat__infix_t = t
module Compare:BatNumber.Compare
with type bat__compare_t = t
val print : 'a BatIO.output -> t -> unit