module Big_int = struct ... end
Operations on arbitrary-precision integers.
Big integers (type big_int) are signed integers of arbitrary size.
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.
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
Addition.
val succ_big_int : big_int -> big_int
Successor (add 1).
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
Subtraction.
val pred_big_int : big_int -> big_int
Predecessor (subtract 1).
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 square_big_int : big_int -> big_int
Return the square of the given big integer
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.
Raise Invalid_argument if a is negative.
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.
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
Exponentiation functions. Return the big integer
representing the first argument a raised to the power b
(the second argument). Depending
on the function, a and b can be either small integers
or big integers. Raise Invalid_argument if b is negative.
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.
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Conversions to and from strings
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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.
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Conversions to and from other numerical types
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val big_int_of_int : int -> big_int
Convert a small integer 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.