diff options
| -rw-r--r-- | otherlibs/num/big_int.mli | 124 |
1 files changed, 100 insertions, 24 deletions
diff --git a/otherlibs/num/big_int.mli b/otherlibs/num/big_int.mli index 598bddd0f..c2dc034d4 100644 --- a/otherlibs/num/big_int.mli +++ b/otherlibs/num/big_int.mli @@ -12,54 +12,130 @@ (* $Id$ *) -(* Module [Big_int]: operations on big integers *) +(* Module [Big_int]: operations on arbitrary-precision integers *) (* Big integers (type [big_int]) are signed integers of arbitrary size. *) open Nat type big_int + (* The type of big integers. *) -val sign_big_int : big_int -> int val zero_big_int : big_int + (* The big integer [0]. *) val unit_big_int : big_int -val num_digits_big_int : big_int -> 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 -val pred_big_int : big_int -> big_int -val succ_big_int : big_int -> big_int -val add_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. *) + +(*** 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 -val add_int_big_int : int -> big_int -> big_int -val sub_big_int : big_int -> big_int -> big_int -val mult_int_big_int : int -> big_int -> big_int -val mult_big_int : big_int -> big_int -> big_int -val quomod_big_int : big_int -> big_int -> big_int * big_int -val div_big_int : big_int -> big_int -> big_int -val mod_big_int : big_int -> big_int -> big_int -val gcd_big_int : big_int -> big_int -> big_int -val int_of_big_int : big_int -> 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 $-2^{30}$ and $2^{30}-1$. On a 64-bit platform, + [is_int_big_int a] returns [true] if and only if + [a] is between $-2^{62}$ and $2^{62}-1$. *) +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. *) + +(*--*) + +(*** For internal use *) val nat_of_big_int : big_int -> nat val big_int_of_nat : nat -> big_int -val string_of_big_int : big_int -> string -val big_int_of_string : string -> big_int -val float_of_big_int : big_int -> float -val square_big_int: big_int -> big_int -val sqrt_big_int: big_int -> big_int val base_power_big_int: int -> int -> big_int -> big_int val sys_big_int_of_string: string -> int -> 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 val round_futur_last_digit : string -> int -> int -> bool val approx_big_int: int -> big_int -> string |