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37 int64

%--------------------------------------------------%
% vim: ts=4 sw=4 et ft=mercury
%--------------------------------------------------%
% Copyright (C) 2018 The Mercury team.
% This file is distributed under the terms specified in COPYING.LIB.
%--------------------------------------------------%
%
% File: int64.m
% Main author: juliensf
% Stability: low.
%
% Predicates and functions for dealing with signed 64-bit integer numbers.
%
%--------------------------------------------------%

:- module int64.
:- interface.

:- import_module pretty_printer.

%--------------------------------------------------%
%
% Conversion from int.
%

    % from_int(I) = I64:
    %
    % Convert an int to an int64.
    %
    % Since an int can be only 32 or 64 bits, this is guaranteed to yield
    % a result that is mathematically equal to the original.
    %
:- func from_int(int) = int64.

    % cast_from_int(I) = I64:
    %
    % Convert an int to an int64.
    %
    % While a cast from int to intN for N =< 32 may yield a result
    % that is not mathematically equal to the original (because
    % the original integer may be too big to be representable),
    % casting an int to int64 *will* yield a result that is mathematically
    % equal to the original. It is therefore a synonym for the from_int
    % function. It is provided only for uniformity, to allow an int
    % to be cast to intN for *all* of int8, int16, int32 and int64.
    %
:- func cast_from_int(int) = int64.

%--------------------------------------------------%
%
% Conversion to int.
%

    % cast_to_int(I64) = I:
    %
    % Convert an int64 to an int.
    % Always succeeds. If ints are 64 bits, I will always be
    % mathematically equal to I64. However, if ints are 32 bits,
    % then I will be mathematically equal to I64 only if
    % I64 is in [-(2^31), 2^31 - 1].
    %
:- func cast_to_int(int64) = int.

%--------------------------------------------------%
%
% Change of signedness.
%

    % cast_from_uint64(U64) = I64:
    %
    % Convert a uint64 to an int64. This will yield a result that is
    % mathematically equal to U64 only if U64 is in [0, 2^63 - 1].
    %
:- func cast_from_uint64(uint64) = int64.

%--------------------------------------------------%
%
% Conversion from byte sequence.
%

    % from_bytes_le(Byte0, Byte1, ..., Byte7) = I64:
    %
    % I64 is the int64 whose bytes are given in little-endian order by the
    % arguments from left-to-right (i.e. Byte0 is the least significant byte
    % and Byte7 is the most significant byte).
    %
:- func from_bytes_le(uint8, uint8, uint8, uint8, uint8, uint8, uint8, uint8)
    = int64.

    % from_bytes_be(Byte0, Byte1, ..., Byte7) = I64:
    %
    % I64 is the int64 whose bytes are given in big-endian order by the
    % arguments in left-to-right order (i.e. Byte0 is the most significant
    % byte and Byte7 is the least significant byte).
    %
:- func from_bytes_be(uint8, uint8, uint8, uint8, uint8, uint8, uint8, uint8)
    = int64.

%--------------------------------------------------%
%
% Comparisons and related operations.
%

    % Less than.
    %
:- pred (int64::in) < (int64::in) is semidet.

    % Greater than.
    %
:- pred (int64::in) > (int64::in) is semidet.

    % Less than or equal.
    %
:- pred (int64::in) =< (int64::in) is semidet.

    % Greater than or equal.
    %
:- pred (int64::in) >= (int64::in) is semidet.

    % Maximum.
    %
:- func max(int64, int64) = int64.

    % Minimum.
    %
:- func min(int64, int64) = int64.

%--------------------------------------------------%
%
% Absolute values.
%

    % abs(X) returns the absolute value of X.
    % Throws an exception if X = int64.min_int64.
    %
:- func abs(int64) = int64.

    % unchecked_abs(X) returns the absolute value of X, except that the result
    % is undefined if X = int64.min_int64.
    %
:- func unchecked_abs(int64) = int64.

    % nabs(X) returns the negative of the absolute value of X.
    % Unlike abs/1 this function is defined for X = int64.min_int64.
    %
:- func nabs(int64) = int64.

%--------------------------------------------------%
%
% Arithmetic operations.
%

    % Unary plus.
    %
:- func + (int64::in) = (int64::uo) is det.

    % Unary minus.
    %
:- func - (int64::in) = (int64::uo) is det.

    % Addition.
    %
:- func int64 + int64 = int64.
:- mode in + in = uo is det.
:- mode uo + in = in is det.
:- mode in + uo = in is det.

:- func plus(int64, int64) = int64.

    % Subtraction.
    %
:- func int64 - int64 = int64.
:- mode in - in = uo is det.
:- mode uo - in = in is det.
:- mode in - uo = in is det.

:- func minus(int64, int64) = int64.

    % Multiplication.
    %
:- func (int64::in) * (int64::in) = (int64::uo) is det.
:- func times(int64, int64) = int64.

    % Flooring integer division.
    % Truncates towards minus infinity, e.g. -10_i64 div 3_i64 = -4_i64.
    %
    % Throws a `math.domain_error' exception if the right operand is zero.
    %
:- func (int64::in) div (int64::in) = (int64::uo) is det.

    % Truncating integer division.
    % Truncates towards zero, e.g. -10_i64 // 3_i64 = -3_i64.
    % `div' has nicer mathematical properties for negative operands,
    % but `//' is typically more efficient.
    %
    % Throws a `math.domain_error' exception if the right operand is zero.
    %
:- func (int64::in) // (int64::in) = (int64::uo) is det.

    % (/)/2 is a synonym for (//)/2.
    %
:- func (int64::in) / (int64::in) = (int64::uo) is det.

    % unchecked_quotient(X, Y) is the same as X // Y, but the behaviour
    % is undefined if the right operand is zero.
    %
:- func unchecked_quotient(int64::in, int64::in) = (int64::uo) is det.

    % Modulus.
    % X mod Y = X - (X div Y) * Y
    %
    % Throws a `math.domain_error' exception if the right operand is zero.
    %
:- func (int64::in) mod (int64::in) = (int64::uo) is det.

    % Remainder.
    % X rem Y = X - (X // Y) * Y.
    %
    % Throws a `math.domain_error/` exception if the right operand is zero.
    %
:- func (int64::in) rem (int64::in) = (int64::uo) is det.

    % unchecked_rem(X, Y) is the same as X rem Y, but the behaviour is
    % undefined if the right operand is zero.
    %
:- func unchecked_rem(int64::in, int64::in) = (int64::uo) is det.

    % even(X) is equivalent to (X mod 2 = 0).
    %
:- pred even(int64::in) is semidet.

    % odd(X) is equivalent to (not even(X)), i.e. (X mod 2 = 1).
    %
:- pred odd(int64::in) is semidet.

%--------------------------------------------------%
%
% Shift operations.
%

    % Left shift.
    % X << Y returns X "left shifted" by Y bits.
    % The bit positions vacated by the shift are filled by zeros.
    % Throws an exception if Y is not in [0, 64).
    %
:- func (int64::in) << (int::in) = (int64::uo) is det.

    % unchecked_left_shift(X, Y) is the same as X << Y except that
    % the behaviour is undefined if Y is not in [0, 64).
    % It will typically be implemented more efficiently than X << Y.
    %
:- func unchecked_left_shift(int64::in, int::in) = (int64::uo) is det.

    % Right shift.
    % X >> Y returns X "right shifted" by Y bits.
    % The bit positions vacated by the shift are filled by the sign bit.
    % Throws an exception if Y is not in [0, 64).
    %
:- func (int64::in) >> (int::in) = (int64::uo) is det.

    % unchecked_right_shift(X, Y) is the same as X >> Y except that
    % the behaviour is undefined if Y is not in [0, 64).
    % It will typically be implemented more efficiently than X >> Y.
    %
:- func unchecked_right_shift(int64::in, int::in) = (int64::uo) is det.

%--------------------------------------------------%
%
% Logical operations.
%

    % Bitwise and.
    %
:- func (int64::in) /\ (int64::in) = (int64::uo) is det.

    % Bitwise or.
    %
:- func (int64::in) \/ (int64::in) = (int64::uo) is det.

    % Bitwise exclusive or (xor).
    %
:- func xor(int64, int64) = int64.
:- mode xor(in, in) = uo is det.
:- mode xor(in, uo) = in is det.
:- mode xor(uo, in) = in is det.

    % Bitwise complement.
    %
:- func \ (int64::in) = (int64::uo) is det.

%--------------------------------------------------%
%
% Operations on bits and bytes.
%

    % num_zeros(I) = N:
    %
    % N is the number of zeros in the binary representation of I.
    %
:- func num_zeros(int64) = int.

    % num_ones(I) = N:
    %
    % N is the number of ones in the binary representation of I.
    %
:- func num_ones(int64) = int.

    % num_leading_zeros(I) = N:
    %
    % N is the number of leading zeros in the binary representation of I,
    % starting at the most significant bit position.
    % Note that num_leading_zeros(0i64) = 64.
    %
:- func num_leading_zeros(int64) = int.

    % num_trailing_zeros(I) = N:
    %
    % N is the number of trailing zeros in the binary representation of I,
    % starting at the least significant bit position.
    % Note that num_trailing_zeros(0i64) = 64.
    %
:- func num_trailing_zeros(int64) = int.

    % reverse_bytes(A) = B:
    %
    % B is the value that results from reversing the bytes
    % in the binary representation of A.
    %
:- func reverse_bytes(int64) = int64.

    % reverse_bits(A) = B:
    %
    % B is the is value that results from reversing the bits
    % in the binary representation of A.
    %
:- func reverse_bits(int64) = int64.

%--------------------------------------------------%
%
% Limits.
%

:- func min_int64 = int64.

:- func max_int64 = int64.

%--------------------------------------------------%
%
% Prettyprinting.
%

    % Convert an int64 to a pretty_printer.doc for formatting.
    %
:- func int64_to_doc(int64) = pretty_printer.doc.

%--------------------------------------------------%
%--------------------------------------------------%


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