%--------------------------------------------------%
% vim: ft=mercury ts=4 sw=4 et
%--------------------------------------------------%
% Copyright (C) 1994-2012 The University of Melbourne.
% Copyright (C) 2013-2018, 2020 The Mercury team.
% This file is distributed under the terms specified in COPYING.LIB.
%--------------------------------------------------%
%
% File: int.m.
% Main authors: conway, fjh.
% Stability: medium.
%
% Predicates and functions for dealing with machine-size integer numbers.
%
% The behaviour of a computation for which overflow occurs is undefined.
% (In the current implementation, the predicates and functions in this
% module do not check for overflow, and the results you get are those
% delivered by the C compiler. However, future implementations
% might check for overflow.)
%
%--------------------------------------------------%
%--------------------------------------------------%
:- module int.
:- interface.
:- import_module array.
:- import_module enum.
:- import_module pretty_printer.
%--------------------------------------------------%
:- instance enum(int).
%--------------------------------------------------%
% Less than.
%
:- pred (int::in) < (int::in) is semidet.
% Greater than.
%
:- pred (int::in) > (int::in) is semidet.
% Less than or equal.
%
:- pred (int::in) =< (int::in) is semidet.
% Greater than or equal.
%
:- pred (int::in) >= (int::in) is semidet.
%--------------------------------------------------%
% abs(X) returns the absolute value of X.
% Throws an exception if X = int.min_int.
%
:- func abs(int) = int.
:- pred abs(int::in, int::out) is det.
% unchecked_abs(X) returns the absolute value of X, except that the result
% is undefined if X = int.min_int.
%
:- func unchecked_abs(int) = int.
% nabs(X) returns the negative absolute value of X.
% Unlike abs/1 this function is defined for X = int.min_int.
%
:- func nabs(int) = int.
%--------------------------------------------------%
% Maximum.
%
:- func max(int, int) = int.
:- pred max(int::in, int::in, int::out) is det.
% Minimum.
%
:- func min(int, int) = int.
:- pred min(int::in, int::in, int::out) is det.
%--------------------------------------------------%
% Unary plus.
%
:- func + (int::in) = (int::uo) is det.
% Unary minus.
%
:- func - (int::in) = (int::uo) is det.
% Addition.
%
:- func int + int = int.
:- mode in + in = uo is det.
:- mode uo + in = in is det.
:- mode in + uo = in is det.
:- func plus(int, int) = int.
% Subtraction.
%
:- func int - int = int.
:- mode in - in = uo is det.
:- mode uo - in = in is det.
:- mode in - uo = in is det.
:- func minus(int, int) = int.
% Multiplication.
%
:- func (int::in) * (int::in) = (int::uo) is det.
:- func times(int, int) = int.
% Flooring integer division.
% Truncates towards minus infinity, e.g. (-10) div 3 = (-4).
%
% Throws a `domain_error' exception if the right operand is zero.
% See the comments at the top of math.m to find out how to disable
% domain checks.
%
:- func div(int::in, int::in) = (int::uo) is det.
% Truncating integer division.
% Truncates towards zero, e.g. (-10) // 3 = (-3).
% `div' has nicer mathematical properties for negative operands,
% but `//' is typically more efficient.
%
% Throws a `domain_error' exception if the right operand is zero.
% See the comments at the top of math.m to find out how to disable
% domain checks.
%
:- func (int::in) // (int::in) = (int::uo) is det.
% (/)/2 is a synonym for (//)/2 to bring Mercury into line with
% the common convention for naming integer division.
%
:- func (int::in) / (int::in) = (int::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(int::in, int::in) = (int::uo) is det.
% Modulus.
% X mod Y = X - (X div Y) * Y
%
:- func (int::in) mod (int::in) = (int::uo) is det.
% Remainder.
% X rem Y = X - (X // Y) * Y
% `mod' has nicer mathematical properties for negative X,
% but `rem' is typically more efficient.
%
% Throws a `domain_error' exception if the right operand is zero.
% See the comments at the top of math.m to find out how to disable
% domain checks.
%
:- func (int::in) rem (int::in) = (int::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(int::in, int::in) = (int::uo) is det.
% even(X) is equivalent to (X mod 2 = 0).
%
:- pred even(int::in) is semidet.
% odd(X) is equivalent to (not even(X)), i.e. (X mod 2 = 1).
%
:- pred odd(int::in) is semidet.
% Exponentiation.
% pow(X, Y, Z): Z is X raised to the Yth power.
% Throws a `domain_error' exception if Y is negative.
%
:- func pow(int, int) = int.
:- pred pow(int::in, int::in, int::out) is det.
% Base 2 logarithm.
% log2(X) = N is the least integer such that 2 to the power N
% is greater than or equal to X.
% Throws a `domain_error' exception if X is not positive.
%
:- func log2(int) = int.
:- pred log2(int::in, int::out) is det.
%--------------------------------------------------%
% 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, bits_per_int).
%
:- func (int::in) << (int::in) = (int::uo) is det.
% unchecked_left_shift(X, Y) is the same as X << Y
% except that the behaviour is undefined if Y is negative,
% or greater than or equal to the result of `bits_per_int/1'.
% It will typically be implemented more efficiently than X << Y.
%
:- func unchecked_left_shift(int::in, int::in) = (int::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, bits_per_int).
%
:- func (int::in) >> (int::in) = (int::uo) is det.
% unchecked_right_shift(X, Y) is the same as X >> Y
% except that the behaviour is undefined if Y is negative,
% or greater than or equal to the result of `bits_per_int/1'.
% It will typically be implemented more efficiently than X >> Y.
%
:- func unchecked_right_shift(int::in, int::in) = (int::uo) is det.
%--------------------------------------------------%
% Bitwise complement.
%
:- func \ (int::in) = (int::uo) is det.
% Bitwise and.
%
:- func (int::in) /\ (int::in) = (int::uo) is det.
% Bitwise or.
%
:- func (int::in) \/ (int::in) = (int::uo) is det.
% Bitwise exclusive or (xor).
%
:- func xor(int, int) = int.
:- mode xor(in, in) = uo is det.
:- mode xor(in, uo) = in is det.
:- mode xor(uo, in) = in is det.
%--------------------------------------------------%
% max_int is the maximum value of an int on this machine.
%
:- func max_int = int.
:- pred max_int(int::out) is det.
% min_int is the minimum value of an int on this machine.
%
:- func min_int = int.
:- pred min_int(int::out) is det.
% bits_per_int is the number of bits in an int on this machine.
%
:- func bits_per_int = int.
:- pred bits_per_int(int::out) is det.
%--------------------------------------------------%
% fold_up(F, Low, High, Acc) <=> list.foldl(F, Low .. High, Acc)
%
% NOTE: fold_up/4 is undefined if High = max_int.
%
:- func fold_up(func(int, T) = T, int, int, T) = T.
% fold_up(F, Low, High, !Acc) <=> list.foldl(F, Low .. High, !Acc)
%
% NOTE: fold_up/5 is undefined if High = max_int.
%
:- pred fold_up(pred(int, T, T), int, int, T, T).
:- mode fold_up(pred(in, in, out) is det, in, in, in, out) is det.
:- mode fold_up(pred(in, mdi, muo) is det, in, in, mdi, muo) is det.
:- mode fold_up(pred(in, di, uo) is det, in, in, di, uo) is det.
:- mode fold_up(pred(in, array_di, array_uo) is det, in, in,
array_di, array_uo) is det.
:- mode fold_up(pred(in, in, out) is semidet, in, in, in, out)
is semidet.
:- mode fold_up(pred(in, mdi, muo) is semidet, in, in, mdi, muo)
is semidet.
:- mode fold_up(pred(in, di, uo) is semidet, in, in, di, uo)
is semidet.
:- mode fold_up(pred(in, in, out) is nondet, in, in, in, out)
is nondet.
:- mode fold_up(pred(in, mdi, muo) is nondet, in, in, mdi, muo)
is nondet.
:- mode fold_up(pred(in, di, uo) is cc_multi, in, in, di, uo)
is cc_multi.
:- mode fold_up(pred(in, in, out) is cc_multi, in, in, in, out)
is cc_multi.
% fold_up2(F, Low, High, !Acc1, Acc2) <=>
% list.foldl2(F, Low .. High, !Acc1, !Acc2)
%
% NOTE: fold_up2/7 is undefined if High = max_int.
%
:- pred fold_up2(pred(int, T, T, U, U), int, int, T, T, U, U).
:- mode fold_up2(pred(in, in, out, in, out) is det, in, in, in, out,
in, out) is det.
:- mode fold_up2(pred(in, in, out, mdi, muo) is det, in, in, in, out,
mdi, muo) is det.
:- mode fold_up2(pred(in, in, out, di, uo) is det, in, in, in, out,
di, uo) is det.
:- mode fold_up2(pred(in, di, uo, di, uo) is det, in, in, di, uo,
di, uo) is det.
:- mode fold_up2(pred(in, in, out, array_di, array_uo) is det, in, in,
in, out, array_di, array_uo) is det.
:- mode fold_up2(pred(in, in, out, in, out) is semidet, in, in,
in, out, in, out) is semidet.
:- mode fold_up2(pred(in, in, out, mdi, muo) is semidet, in, in,
in, out, mdi, muo) is semidet.
:- mode fold_up2(pred(in, in, out, di, uo) is semidet, in, in,
in, out, di, uo) is semidet.
:- mode fold_up2(pred(in, in, out, in, out) is nondet, in, in,
in, out, in, out) is nondet.
:- mode fold_up2(pred(in, in, out, mdi, muo) is nondet, in, in,
in, out, mdi, muo) is nondet.
% fold_up3(F, Low, High, !Acc1, Acc2, !Acc3) <=>
% list.foldl3(F, Low .. High, !Acc1, !Acc2, !Acc3)
%
% NOTE: fold_up3/9 is undefined if High = max_int.
%
:- pred fold_up3(pred(int, T, T, U, U, V, V), int, int, T, T, U, U, V, V).
:- mode fold_up3(pred(in, in, out, in, out, in, out) is det,
in, in, in, out, in, out, in, out) is det.
:- mode fold_up3(pred(in, in, out, in, out, mdi, muo) is det,
in, in, in, out, in, out, mdi, muo) is det.
:- mode fold_up3(pred(in, in, out, in, out, di, uo) is det,
in, in, in, out, in, out, di, uo) is det.
:- mode fold_up3(pred(in, in, out, di, uo, di, uo) is det,
in, in, in, out, di, uo, di, uo) is det.
:- mode fold_up3(pred(in, in, out, in, out, array_di, array_uo) is det,
in, in, in, out, in, out, array_di, array_uo) is det.
:- mode fold_up3(pred(in, in, out, in, out, in, out) is semidet,
in, in, in, out, in, out, in, out) is semidet.
:- mode fold_up3(pred(in, in, out, in, out, mdi, muo) is semidet,
in, in, in, out, in, out, mdi, muo) is semidet.
:- mode fold_up3(pred(in, in, out, in, out, di, uo) is semidet,
in, in, in, out, in, out, di, uo) is semidet.
:- mode fold_up3(pred(in, in, out, in, out, in, out) is nondet,
in, in, in, out, in, out, in, out) is nondet.
:- mode fold_up3(pred(in, in, out, in, out, mdi, muo) is nondet,
in, in, in, out, in, out, mdi, muo) is nondet.
% fold_down(F, Low, High, Acc) <=> list.foldr(F, Low .. High, Acc)
%
% NOTE: fold_down/4 is undefined if Low = min_int.
%
:- func fold_down(func(int, T) = T, int, int, T) = T.
% fold_down(F, Low, High, !Acc) <=> list.foldr(F, Low .. High, !Acc)
%
% NOTE: fold_down/5 is undefined if Low min_int.
%
:- pred fold_down(pred(int, T, T), int, int, T, T).
:- mode fold_down(pred(in, in, out) is det, in, in, in, out) is det.
:- mode fold_down(pred(in, mdi, muo) is det, in, in, mdi, muo) is det.
:- mode fold_down(pred(in, di, uo) is det, in, in, di, uo) is det.
:- mode fold_down(pred(in, array_di, array_uo) is det, in, in,
array_di, array_uo) is det.
:- mode fold_down(pred(in, in, out) is semidet, in, in, in, out)
is semidet.
:- mode fold_down(pred(in, mdi, muo) is semidet, in, in, mdi, muo)
is semidet.
:- mode fold_down(pred(in, di, uo) is semidet, in, in, di, uo)
is semidet.
:- mode fold_down(pred(in, in, out) is nondet, in, in, in, out)
is nondet.
:- mode fold_down(pred(in, mdi, muo) is nondet, in, in, mdi, muo)
is nondet.
:- mode fold_down(pred(in, in, out) is cc_multi, in, in, in, out)
is cc_multi.
:- mode fold_down(pred(in, di, uo) is cc_multi, in, in, di, uo)
is cc_multi.
% fold_down2(F, Low, High, !Acc1, !Acc2) <=>
% list.foldr2(F, Low .. High, !Acc1, Acc2).
%
% NOTE: fold_down2/7 is undefined if Low = min_int.
%
:- pred fold_down2(pred(int, T, T, U, U), int, int, T, T, U, U).
:- mode fold_down2(pred(in, in, out, in, out) is det, in, in, in, out,
in, out) is det.
:- mode fold_down2(pred(in, in, out, mdi, muo) is det, in, in, in, out,
mdi, muo) is det.
:- mode fold_down2(pred(in, in, out, di, uo) is det, in, in, in, out,
di, uo) is det.
:- mode fold_down2(pred(in, di, uo, di, uo) is det, in, in, di, uo,
di, uo) is det.
:- mode fold_down2(pred(in, in, out, array_di, array_uo) is det, in, in,
in, out, array_di, array_uo) is det.
:- mode fold_down2(pred(in, in, out, in, out) is semidet, in, in,
in, out, in, out) is semidet.
:- mode fold_down2(pred(in, in, out, di, uo) is semidet, in, in,
in, out, di, uo) is semidet.
:- mode fold_down2(pred(in, in, out, in, out) is nondet, in, in,
in, out, in, out) is nondet.
:- mode fold_down2(pred(in, in, out, mdi, muo) is nondet, in, in,
in, out, mdi, muo) is nondet.
% fold_up3(F, Low, High, !Acc1, Acc2, !Acc3) <=>
% list.foldr3(F, Low .. High, !Acc1, !Acc2, !Acc3)
%
% NOTE: fold_down3/9 is undefined if Low = min_int.
%
:- pred fold_down3(pred(int, T, T, U, U, V, V), int, int, T, T, U, U, V, V).
:- mode fold_down3(pred(in, in, out, in, out, in, out) is det,
in, in, in, out, in, out, in, out) is det.
:- mode fold_down3(pred(in, in, out, in, out, mdi, muo) is det,
in, in, in, out, in, out, mdi, muo) is det.
:- mode fold_down3(pred(in, in, out, in, out, di, uo) is det,
in, in, in, out, in, out, di, uo) is det.
:- mode fold_down3(pred(in, in, out, di, uo, di, uo) is det,
in, in, in, out, di, uo, di, uo) is det.
:- mode fold_down3(pred(in, in, out, in, out, array_di, array_uo) is det,
in, in, in, out, in, out, array_di, array_uo) is det.
:- mode fold_down3(pred(in, in, out, in, out, in, out) is semidet,
in, in, in, out, in, out, in, out) is semidet.
:- mode fold_down3(pred(in, in, out, in, out, mdi, muo) is semidet,
in, in, in, out, in, out, mdi, muo) is semidet.
:- mode fold_down3(pred(in, in, out, in, out, di, uo) is semidet,
in, in, in, out, in, out, di, uo) is semidet.
:- mode fold_down3(pred(in, in, out, in, out, in, out) is nondet,
in, in, in, out, in, out, in, out) is nondet.
:- mode fold_down3(pred(in, in, out, in, out, mdi, muo) is nondet,
in, in, in, out, in, out, mdi, muo) is nondet.
%--------------------------------------------------%
% nondet_int_in_range(Low, High, I):
%
% On successive successes, set I to every integer from Low to High.
%
:- pred nondet_int_in_range(int::in, int::in, int::out) is nondet.
% all_true_in_range(P, Low, High):
% True iff P is true for every integer in Low to High.
%
% NOTE: all_true_in_range/3 is undefined if High = max_int.
%
:- pred all_true_in_range(pred(int)::in(pred(in) is semidet),
int::in, int::in) is semidet.
%--------------------------------------------------%
% Convert an int to a pretty_printer.doc for formatting.
%
:- func int_to_doc(int) = pretty_printer.doc.
%--------------------------------------------------%
%
% Computing hashes of ints.
%
% Compute a hash value for an int.
%
:- func hash(int) = int.
:- pred hash(int::in, int::out) is det.
%--------------------------------------------------%
%--------------------------------------------------%