num

The legacy Num library for arbitrary-precision integer and rational arithmetic
Library nums
Module Big_int
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.

  • since 4.03.0
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.

val big_int_of_string_opt : string -> big_int option

Convert a string to a big integer, in decimal. The string consists of an optional - or + sign, followed by one or several decimal digits. Other the function returns None.

  • since 4.05
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 int_of_big_int_opt : big_int -> int option

Convert a big integer to a small integer (type int). Return None if the big integer is not representable as a small integer.

  • since 4.05
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 int32_of_big_int_opt : big_int -> int32 option

Convert a big integer to a 32-bit integer. Return None if the big integer is outside the range [-231, 231-1].

  • since 4.05
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 nativeint_of_big_int_opt : big_int -> nativeint option

Convert a big integer to a native integer. Return None if the big integer is outside the range [Nativeint.min_int, Nativeint.max_int];

  • since 4.05
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 int64_of_big_int_opt : big_int -> int64 option

Convert a big integer to a 64-bit integer. Return None if the big integer is outside the range [-263, 263-1].

  • since 4.05
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.