%--------------------------------------------------%
% vim: ts=4 sw=4 et ft=mercury
%--------------------------------------------------%
% Copyright (C) 2018-2021 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.
%
% to_int(I64, I):
%
% Convert an int64 into an int.
% Fails if I64 is not in [int.min_int, int.max_int].
%
:- pred to_int(int64::in, int::out) is semidet.
% det_to_int(I64) = I:
%
% Convert an int64 into an int.
% Throws an exception if I64 is not in [int.min_int, int.max_int].
%
:- func det_to_int(int64) = 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 `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 `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 `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 `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.
:- func (int64::in) <<u (uint::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.
:- func unchecked_left_ushift(int64::in, uint::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.
:- func (int64::in) >>u (uint::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.
:- func unchecked_right_ushift(int64::in, uint::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.
:- pragma obsolete(func(int64_to_doc/1), [pretty_printer.int64_to_doc/1]).
%--------------------------------------------------%
%--------------------------------------------------%