The type of big integers.

The big integer 0.

The big integer 1.

The big integer 2.

Unary negation.

Absolute value.

Addition.

Successor (add 1).

Addition of a small integer to a big integer.

Subtraction.

Predecessor (subtract 1).

Multiplication of two big integers.

Multiplication of a big integer by a small integer

Return the square of the given big integer

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.

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.

Euclidean quotient of two big integers. This is the first result q of quomod_big_int (see above).

Euclidean modulus of two big integers. This is the second result r of quomod_big_int (see above).

Greatest common divisor of two big integers.

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.

Return 0 if the given big integer is zero, 1 if it is positive, and -1 if it is negative.

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.

Usual boolean comparisons between two big integers.

Return the greater of its two arguments.

Return the smaller of its two arguments.

Return the string representation of the given big integer, in decimal (base 10).

Convert a string to a big integer, in decimal. The string consists of an optional - or + sign, followed by one or several decimal digits.

Convert a small integer to a big integer.

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.

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.