%--------------------------------------------------%
% 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 `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 `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 `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 `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.
%--------------------------------------------------%
%--------------------------------------------------%