Module Big_int

module Big_int: sig .. 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.

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
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.

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.
val num_bits_big_int : big_int -> int
Return the number of significant bits in the absolute value of the given big integer. num_bits_big_int a returns 0 if a is 0; otherwise it returns a positive integer n such that 2^(n-1) <= |a| < 2^n.

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 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 big_int_of_int32 : int32 -> big_int
Convert a 32-bit integer to a big integer.
val big_int_of_nativeint : nativeint -> big_int
Convert a native integer to a big integer.
val big_int_of_int64 : int64 -> big_int
Convert a 64-bit integer to a big integer.
val int32_of_big_int : big_int -> int32
Convert a big integer to a 32-bit integer. Raises Failure if the big integer is outside the range [-231, 231-1].
val nativeint_of_big_int : big_int -> nativeint
Convert a big integer to a native integer. Raises Failure if the big integer is outside the range [Nativeint.min_int, Nativeint.max_int].
val int64_of_big_int : big_int -> int64
Convert a big integer to a 64-bit integer. Raises Failure if the big integer is outside the range [-263, 263-1].
val float_of_big_int : big_int -> float
Returns a floating-point number approximating the given big integer.

Bit-oriented operations

val and_big_int : big_int -> big_int -> big_int
Bitwise logical 'and'. The arguments must be positive or zero.
val or_big_int : big_int -> big_int -> big_int
Bitwise logical 'or'. The arguments must be positive or zero.
val xor_big_int : big_int -> big_int -> big_int
Bitwise logical 'exclusive or'. The arguments must be positive or zero.
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.
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