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35 int16

%--------------------------------------------------%
% vim: ts=4 sw=4 et ft=mercury
%--------------------------------------------------%
% Copyright (C) 2017-2018 The Mercury team.
% This file is distributed under the terms specified in COPYING.LIB.
%--------------------------------------------------%
%
% File: int16.m
% Main author: juliensf
% Stability: low.
%
% Predicates and functions for dealing with signed 16-bit integer numbers.
%
%--------------------------------------------------%

:- module int16.
:- interface.

:- import_module pretty_printer.

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

    % from_int(I, I16):
    %
    % Convert an int to an int16.
    % Fails if I is not in [-(2^15), 2^15 - 1].
    %
:- pred from_int(int::in, int16::out) is semidet.

    % det_from_int(I) = I16:
    %
    % Convert an int to an int16.
    % Throws an exception if I is not in [-(2^15), 2^15 - 1].
    %
:- func det_from_int(int) = int16.

    % cast_from_int(I) = I16:
    %
    % Convert an int to an int16.
    % Always succeeds, but will yield a result that is mathematically equal
    % to I only if I is in [-(2^15), 2^15 - 1].
    %
:- func cast_from_int(int) = int16.

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

    % to_int(I16) = I:
    %
    % Convert an int16 to an int. 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 to_int(int16) = int.

    % cast_to_int(I16) = I:
    %
    % Convert an int16 to an int. 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 cast_to_int(int16) = int.

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

    % cast_from_uint16(U16) = I16:
    %
    % Convert a uint16 to an int16. This will yield a result that is
    % mathematically equal to U16 only if U16 is in [0, 2^15 - 1].
    %
:- func cast_from_uint16(uint16) = int16.

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

    % from_bytes_le(LSB, MSB) = I16:
    %
    % I16 is the int16 whose least and most significant bytes are given by the
    % uint8s LSB and MSB respectively.
    %
:- func from_bytes_le(uint8, uint8) = int16.

    % from_bytes_be(MSB, LSB) = I16:
    %
    % I16 is the int16 whose least and most significant bytes are given by the
    % uint8s LSB and MSB respectively.
    %
:- func from_bytes_be(uint8, uint8) = int16.

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

    % Less than.
    %
:- pred (int16::in) < (int16::in) is semidet.

    % Greater than.
    %
:- pred (int16::in) > (int16::in) is semidet.

    % Less than or equal.
    %
:- pred (int16::in) =< (int16::in) is semidet.

    % Greater than or equal.
    %
:- pred (int16::in) >= (int16::in) is semidet.

    % Maximum.
    %
:- func max(int16, int16) = int16.

    % Minimum.
    %
:- func min(int16, int16) = int16.

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

    % abs(X) returns the absolute value of X.
    % Throws an exception if X = int16.min_int16.
    %
:- func abs(int16) = int16.

    % unchecked_abs(X) returns the absolute value of X, except that the result
    % is undefined if X = int16.min_int16.
    %
:- func unchecked_abs(int16) = int16.

    % nabs(X) returns the negative of the absolute value of X.
    % Unlike abs/1 this function is defined for X = int16.min_int16.
    %
:- func nabs(int16) = int16.

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

    % Unary plus.
    %
:- func + (int16::in) = (int16::uo) is det.

    % Unary minus.
    %
:- func - (int16::in) = (int16::uo) is det.

    % Addition.
    %
:- func int16 + int16 = int16.
:- mode in + in = uo is det.
:- mode uo + in = in is det.
:- mode in + uo = in is det.

:- func plus(int16, int16) = int16.

    % Subtraction.
    %
:- func int16 - int16 = int16.
:- mode in - in = uo is det.
:- mode uo - in = in is det.
:- mode in - uo = in is det.

:- func minus(int16, int16) = int16.

    % Multiplication.
    %
:- func (int16::in) * (int16::in) = (int16::uo) is det.
:- func times(int16, int16) = int16.

    % Flooring integer division.
    % Truncates towards minus infinity, e.g. (-10_i16) div 3_i16 = (-4_i16).
    %
    % Throws a `math.domain_error' exception if the right operand is zero.
    %
:- func (int16::in) div (int16::in) = (int16::uo) is det.

    % Truncating integer division.
    % Truncates towards zero, e.g. (-10_i16) // 3_i16 = (-3_i16).
    % `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 (int16::in) // (int16::in) = (int16::uo) is det.

    % (/)/2 is a synonym for (//)/2.
    %
:- func (int16::in) / (int16::in) = (int16::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(int16::in, int16::in) = (int16::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 (int16::in) mod (int16::in) = (int16::uo) is det.

    % Remainder.
    % X rem Y = X - (X // Y) * Y.
    %
    % Throws a `math.domain_error/` exception if the right operand is zero.
    %
:- func (int16::in) rem (int16::in) = (int16::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(int16::in, int16::in) = (int16::uo) is det.

    % even(X) is equivalent to (X mod 2i16 = 0i16).
    %
:- pred even(int16::in) is semidet.

    % odd(X) is equivalent to (not even(X)), i.e. (X mod 2i16 = 1i16).
    %
:- pred odd(int16::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, 16).
    %
:- func (int16::in) << (int::in) = (int16::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, 16).
    % It will typically be implemented more efficiently than X << Y.
    %
:- func unchecked_left_shift(int16::in, int::in) = (int16::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, 16).
    %
:- func (int16::in) >> (int::in) = (int16::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, 16).
    % It will typically be implemented more efficiently than X >> Y.
    %
:- func unchecked_right_shift(int16::in, int::in) = (int16::uo) is det.

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

    % Bitwise and.
    %
:- func (int16::in) /\ (int16::in) = (int16::uo) is det.

    % Bitwise or.
    %
:- func (int16::in) \/ (int16::in) = (int16::uo) is det.

    % Bitwise exclusive or (xor).
    %
:- func xor(int16, int16) = int16.
:- mode xor(in, in) = uo is det.
:- mode xor(in, uo) = in is det.
:- mode xor(uo, in) = in is det.

    % Bitwise complement.
    %
:- func \ (int16::in) = (int16::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(int16) = int.

    % num_ones(I) = N:
    %
    % N is the number of ones in the binary representation of I.
    %
:- func num_ones(int16) = 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(0i16) = 16.
    %
:- func num_leading_zeros(int16) = 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(0i16) = 16.
    %
:- func num_trailing_zeros(int16) = int.

    % reverse_bytes(A) = B:
    %
    % B is the value that results from reversing the bytes in the binary
    % representation of A.
    %
:- func reverse_bytes(int16) = int16.

    % reverse_bits(A) = B:
    %
    % B is the is value that results from reversing the bits in the binary
    % representation of A.
    %
:- func reverse_bits(int16) = int16.

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

:- func min_int16 = int16.

:- func max_int16 = int16.

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

    % Convert an int16 to a pretty_printer.doc for formatting.
    %
:- func int16_to_doc(int16) = pretty_printer.doc.

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


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