/* intprops.h -- properties of integer types

   Copyright (C) 2001-2017 Free Software Foundation, Inc.

   This program is free software: you can redistribute it and/or modify it

   under the terms of the GNU Lesser General Public License as published

   by the Free Software Foundation; either version 2.1 of the License, or

   (at your option) any later version.

   This program is distributed in the hope that it will be useful,

   but WITHOUT ANY WARRANTY; without even the implied warranty of

   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

   GNU Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public License

   along with this program.  If not, see <http://www.gnu.org/licenses/>.  */

/* Written by Paul Eggert.  */

#ifndef _GL_INTPROPS_H

#define _GL_INTPROPS_H

#include <limits.h>

/* Return a value with the common real type of E and V and the value of V.  */

#define _GL_INT_CONVERT(e, v) (0 * (e) + (v))

/* Act like _GL_INT_CONVERT (E, -V) but work around a bug in IRIX 6.5 cc; see

   <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00406.html>.  */

#define _GL_INT_NEGATE_CONVERT(e, v) (0 * (e) - (v))

/* The extra casts in the following macros work around compiler bugs,

   e.g., in Cray C 5.0.3.0.  */

/* True if the arithmetic type T is an integer type.  bool counts as

   an integer.  */

#define TYPE_IS_INTEGER(t) ((t) 1.5 == 1)

/* True if the real type T is signed.  */

#define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))

/* Return 1 if the real expression E, after promotion, has a

   signed or floating type.  */

#define EXPR_SIGNED(e) (_GL_INT_NEGATE_CONVERT (e, 1) < 0)

/* Minimum and maximum values for integer types and expressions.  */

/* The width in bits of the integer type or expression T.

   Padding bits are not supported; this is checked at compile-time below.  */

#define TYPE_WIDTH(t) (sizeof (t) * CHAR_BIT)

/* The maximum and minimum values for the integer type T.  */

#define TYPE_MINIMUM(t) ((t) ~ TYPE_MAXIMUM (t))

#define TYPE_MAXIMUM(t)                                                 \

  ((t) (! TYPE_SIGNED (t)                                               \

        ? (t) -1                                                        \

        : ((((t) 1 << (TYPE_WIDTH (t) - 2)) - 1) * 2 + 1)))

/* The maximum and minimum values for the type of the expression E,

   after integer promotion.  E should not have side effects.  */

#define _GL_INT_MINIMUM(e)                                              \

  (EXPR_SIGNED (e)                                                      \

   ? ~ _GL_SIGNED_INT_MAXIMUM (e)                                       \

   : _GL_INT_CONVERT (e, 0))

#define _GL_INT_MAXIMUM(e)                                              \

  (EXPR_SIGNED (e)                                                      \

   ? _GL_SIGNED_INT_MAXIMUM (e)                                         \

   : _GL_INT_NEGATE_CONVERT (e, 1))

#define _GL_SIGNED_INT_MAXIMUM(e)                                       \

  (((_GL_INT_CONVERT (e, 1) << (TYPE_WIDTH ((e) + 0) - 2)) - 1) * 2 + 1)

/* Work around OpenVMS incompatibility with C99.  */

#if !defined LLONG_MAX && defined __INT64_MAX

# define LLONG_MAX __INT64_MAX

# define LLONG_MIN __INT64_MIN

#endif

/* This include file assumes that signed types are two's complement without

   padding bits; the above macros have undefined behavior otherwise.

   If this is a problem for you, please let us know how to fix it for your host.

   This assumption is tested by the intprops-tests module.  */

/* Does the __typeof__ keyword work?  This could be done by

   'configure', but for now it's easier to do it by hand.  */

#if (2 <= __GNUC__ \

     || (1210 <= __IBMC__ && defined __IBM__TYPEOF__) \

     || (0x5110 <= __SUNPRO_C && !__STDC__))

# define _GL_HAVE___TYPEOF__ 1

#else

# define _GL_HAVE___TYPEOF__ 0

#endif

/* Return 1 if the integer type or expression T might be signed.  Return 0

   if it is definitely unsigned.  This macro does not evaluate its argument,

   and expands to an integer constant expression.  */

#if _GL_HAVE___TYPEOF__

# define _GL_SIGNED_TYPE_OR_EXPR(t) TYPE_SIGNED (__typeof__ (t))

#else

# define _GL_SIGNED_TYPE_OR_EXPR(t) 1

#endif

/* Bound on length of the string representing an unsigned integer

   value representable in B bits.  log10 (2.0) < 146/485.  The

   smallest value of B where this bound is not tight is 2621.  */

#define INT_BITS_STRLEN_BOUND(b) (((b) * 146 + 484) / 485)

/* Bound on length of the string representing an integer type or expression T.

   Subtract 1 for the sign bit if T is signed, and then add 1 more for

   a minus sign if needed.

   Because _GL_SIGNED_TYPE_OR_EXPR sometimes returns 0 when its argument is

   signed, this macro may overestimate the true bound by one byte when

   applied to unsigned types of size 2, 4, 16, ... bytes.  */

#define INT_STRLEN_BOUND(t)                                     \

  (INT_BITS_STRLEN_BOUND (TYPE_WIDTH (t) - _GL_SIGNED_TYPE_OR_EXPR (t)) \

   + _GL_SIGNED_TYPE_OR_EXPR (t))

/* Bound on buffer size needed to represent an integer type or expression T,

   including the terminating null.  */

#define INT_BUFSIZE_BOUND(t) (INT_STRLEN_BOUND (t) + 1)

/* Range overflow checks.

   The INT_<op>_RANGE_OVERFLOW macros return 1 if the corresponding C

   operators might not yield numerically correct answers due to

   arithmetic overflow.  They do not rely on undefined or

   implementation-defined behavior.  Their implementations are simple

   and straightforward, but they are a bit harder to use than the

   INT_<op>_OVERFLOW macros described below.

   Example usage:

     long int i = ...;

     long int j = ...;

     if (INT_MULTIPLY_RANGE_OVERFLOW (i, j, LONG_MIN, LONG_MAX))

       printf ("multiply would overflow");

     else

       printf ("product is %ld", i * j);

   Restrictions on *_RANGE_OVERFLOW macros:

   These macros do not check for all possible numerical problems or

   undefined or unspecified behavior: they do not check for division

   by zero, for bad shift counts, or for shifting negative numbers.

   These macros may evaluate their arguments zero or multiple times,

   so the arguments should not have side effects.  The arithmetic

   arguments (including the MIN and MAX arguments) must be of the same

   integer type after the usual arithmetic conversions, and the type

   must have minimum value MIN and maximum MAX.  Unsigned types should

   use a zero MIN of the proper type.

   These macros are tuned for constant MIN and MAX.  For commutative

   operations such as A + B, they are also tuned for constant B.  */

/* Return 1 if A + B would overflow in [MIN,MAX] arithmetic.

   See above for restrictions.  */

#define INT_ADD_RANGE_OVERFLOW(a, b, min, max)          \

  ((b) < 0                                              \

   ? (a) < (min) - (b)                                  \

   : (max) - (b) < (a))

/* Return 1 if A - B would overflow in [MIN,MAX] arithmetic.

   See above for restrictions.  */

#define INT_SUBTRACT_RANGE_OVERFLOW(a, b, min, max)     \

  ((b) < 0                                              \

   ? (max) + (b) < (a)                                  \

   : (a) < (min) + (b))

/* Return 1 if - A would overflow in [MIN,MAX] arithmetic.

   See above for restrictions.  */

#define INT_NEGATE_RANGE_OVERFLOW(a, min, max)          \

  ((min) < 0                                            \

   ? (a) < - (max)                                      \

   : 0 < (a))

/* Return 1 if A * B would overflow in [MIN,MAX] arithmetic.

   See above for restrictions.  Avoid && and || as they tickle

   bugs in Sun C 5.11 2010/08/13 and other compilers; see

   <http://lists.gnu.org/archive/html/bug-gnulib/2011-05/msg00401.html>.  */

#define INT_MULTIPLY_RANGE_OVERFLOW(a, b, min, max)     \

  ((b) < 0                                              \

   ? ((a) < 0                                           \

      ? (a) < (max) / (b)                               \

      : (b) == -1                                       \

      ? 0                                               \

      : (min) / (b) < (a))                              \

   : (b) == 0                                           \

   ? 0                                                  \

   : ((a) < 0                                           \

      ? (a) < (min) / (b)                               \

      : (max) / (b) < (a)))

/* Return 1 if A / B would overflow in [MIN,MAX] arithmetic.

   See above for restrictions.  Do not check for division by zero.  */

#define INT_DIVIDE_RANGE_OVERFLOW(a, b, min, max)       \

  ((min) < 0 && (b) == -1 && (a) < - (max))

/* Return 1 if A % B would overflow in [MIN,MAX] arithmetic.

   See above for restrictions.  Do not check for division by zero.

   Mathematically, % should never overflow, but on x86-like hosts

   INT_MIN % -1 traps, and the C standard permits this, so treat this

   as an overflow too.  */

#define INT_REMAINDER_RANGE_OVERFLOW(a, b, min, max)    \

  INT_DIVIDE_RANGE_OVERFLOW (a, b, min, max)

/* Return 1 if A << B would overflow in [MIN,MAX] arithmetic.

   See above for restrictions.  Here, MIN and MAX are for A only, and B need

   not be of the same type as the other arguments.  The C standard says that

   behavior is undefined for shifts unless 0 <= B < wordwidth, and that when

   A is negative then A << B has undefined behavior and A >> B has

   implementation-defined behavior, but do not check these other

   restrictions.  */

#define INT_LEFT_SHIFT_RANGE_OVERFLOW(a, b, min, max)   \

  ((a) < 0                                              \

   ? (a) < (min) >> (b)                                 \

   : (max) >> (b) < (a))

/* True if __builtin_add_overflow (A, B, P) works when P is non-null.  */

#if 5 <= __GNUC__ && !defined __ICC

# define _GL_HAS_BUILTIN_OVERFLOW 1

#else

# define _GL_HAS_BUILTIN_OVERFLOW 0

#endif

/* True if __builtin_add_overflow_p (A, B, C) works.  */

#define _GL_HAS_BUILTIN_OVERFLOW_P (7 <= __GNUC__)

/* The _GL*_OVERFLOW macros have the same restrictions as the

   *_RANGE_OVERFLOW macros, except that they do not assume that operands

   (e.g., A and B) have the same type as MIN and MAX.  Instead, they assume

   that the result (e.g., A + B) has that type.  */

#if _GL_HAS_BUILTIN_OVERFLOW_P

# define _GL_ADD_OVERFLOW(a, b, min, max)                               \

   __builtin_add_overflow_p (a, b, (__typeof__ ((a) + (b))) 0)

# define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                          \

   __builtin_sub_overflow_p (a, b, (__typeof__ ((a) - (b))) 0)

# define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                          \

   __builtin_mul_overflow_p (a, b, (__typeof__ ((a) * (b))) 0)

#else

# define _GL_ADD_OVERFLOW(a, b, min, max)                                \

   ((min) < 0 ? INT_ADD_RANGE_OVERFLOW (a, b, min, max)                  \

    : (a) < 0 ? (b) <= (a) + (b)                                         \

    : (b) < 0 ? (a) <= (a) + (b)                                         \

    : (a) + (b) < (b))

# define _GL_SUBTRACT_OVERFLOW(a, b, min, max)                           \

   ((min) < 0 ? INT_SUBTRACT_RANGE_OVERFLOW (a, b, min, max)             \

    : (a) < 0 ? 1                                                        \

    : (b) < 0 ? (a) - (b) <= (a)                                         \

    : (a) < (b))

# define _GL_MULTIPLY_OVERFLOW(a, b, min, max)                           \

   (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \

    || INT_MULTIPLY_RANGE_OVERFLOW (a, b, min, max))

#endif

#define _GL_DIVIDE_OVERFLOW(a, b, min, max)                             \

  ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \

   : (a) < 0 ? (b) <= (a) + (b) - 1                                     \

   : (b) < 0 && (a) + (b) <= (a))

#define _GL_REMAINDER_OVERFLOW(a, b, min, max)                          \

  ((min) < 0 ? (b) == _GL_INT_NEGATE_CONVERT (min, 1) && (a) < - (max)  \

   : (a) < 0 ? (a) % (b) != ((max) - (b) + 1) % (b)                     \

   : (b) < 0 && ! _GL_UNSIGNED_NEG_MULTIPLE (a, b, max))

/* Return a nonzero value if A is a mathematical multiple of B, where

   A is unsigned, B is negative, and MAX is the maximum value of A's

   type.  A's type must be the same as (A % B)'s type.  Normally (A %

   -B == 0) suffices, but things get tricky if -B would overflow.  */

#define _GL_UNSIGNED_NEG_MULTIPLE(a, b, max)                            \

  (((b) < -_GL_SIGNED_INT_MAXIMUM (b)                                   \

    ? (_GL_SIGNED_INT_MAXIMUM (b) == (max)                              \

       ? (a)                                                            \

       : (a) % (_GL_INT_CONVERT (a, _GL_SIGNED_INT_MAXIMUM (b)) + 1))   \

    : (a) % - (b))                                                      \

   == 0)

/* Check for integer overflow, and report low order bits of answer.

   The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators

   might not yield numerically correct answers due to arithmetic overflow.

   The INT_<op>_WRAPV macros also store the low-order bits of the answer.

   These macros work correctly on all known practical hosts, and do not rely

   on undefined behavior due to signed arithmetic overflow.

   Example usage, assuming A and B are long int:

     if (INT_MULTIPLY_OVERFLOW (a, b))

       printf ("result would overflow\n");

     else

       printf ("result is %ld (no overflow)\n", a * b);

   Example usage with WRAPV flavor:

     long int result;

     bool overflow = INT_MULTIPLY_WRAPV (a, b, &result);

     printf ("result is %ld (%s)\n", result,

             overflow ? "after overflow" : "no overflow");

   Restrictions on these macros:

   These macros do not check for all possible numerical problems or

   undefined or unspecified behavior: they do not check for division

   by zero, for bad shift counts, or for shifting negative numbers.

   These macros may evaluate their arguments zero or multiple times, so the

   arguments should not have side effects.

   The WRAPV macros are not constant expressions.  They support only

   +, binary -, and *.  The result type must be signed.

   These macros are tuned for their last argument being a constant.

   Return 1 if the integer expressions A * B, A - B, -A, A * B, A / B,

   A % B, and A << B would overflow, respectively.  */

#define INT_ADD_OVERFLOW(a, b) \

  _GL_BINARY_OP_OVERFLOW (a, b, _GL_ADD_OVERFLOW)

#define INT_SUBTRACT_OVERFLOW(a, b) \

  _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUBTRACT_OVERFLOW)

#if _GL_HAS_BUILTIN_OVERFLOW_P

# define INT_NEGATE_OVERFLOW(a) INT_SUBTRACT_OVERFLOW (0, a)

#else

# define INT_NEGATE_OVERFLOW(a) \

   INT_NEGATE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))

#endif

#define INT_MULTIPLY_OVERFLOW(a, b) \

  _GL_BINARY_OP_OVERFLOW (a, b, _GL_MULTIPLY_OVERFLOW)

#define INT_DIVIDE_OVERFLOW(a, b) \

  _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIVIDE_OVERFLOW)

#define INT_REMAINDER_OVERFLOW(a, b) \

  _GL_BINARY_OP_OVERFLOW (a, b, _GL_REMAINDER_OVERFLOW)

#define INT_LEFT_SHIFT_OVERFLOW(a, b) \

  INT_LEFT_SHIFT_RANGE_OVERFLOW (a, b, \

                                 _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))

/* Return 1 if the expression A <op> B would overflow,

   where OP_RESULT_OVERFLOW (A, B, MIN, MAX) does the actual test,

   assuming MIN and MAX are the minimum and maximum for the result type.

   Arguments should be free of side effects.  */

#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \

  op_result_overflow (a, b,                                     \

                      _GL_INT_MINIMUM (0 * (b) + (a)),          \

                      _GL_INT_MAXIMUM (0 * (b) + (a)))

/* Store the low-order bits of A + B, A - B, A * B, respectively, into *R.

   Return 1 if the result overflows.  See above for restrictions.  */

#define INT_ADD_WRAPV(a, b, r) \

  _GL_INT_OP_WRAPV (a, b, r, +, __builtin_add_overflow, INT_ADD_OVERFLOW)

#define INT_SUBTRACT_WRAPV(a, b, r) \

  _GL_INT_OP_WRAPV (a, b, r, -, __builtin_sub_overflow, INT_SUBTRACT_OVERFLOW)

#define INT_MULTIPLY_WRAPV(a, b, r) \

  _GL_INT_OP_WRAPV (a, b, r, *, __builtin_mul_overflow, INT_MULTIPLY_OVERFLOW)

/* Nonzero if this compiler has GCC bug 68193 or Clang bug 25390.  See:

   https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68193

   https://llvm.org/bugs/show_bug.cgi?id=25390

   For now, assume all versions of GCC-like compilers generate bogus

   warnings for _Generic.  This matters only for older compilers that

   lack __builtin_add_overflow.  */

#if __GNUC__

# define _GL__GENERIC_BOGUS 1

#else

# define _GL__GENERIC_BOGUS 0

#endif

/* Store the low-order bits of A <op> B into *R, where OP specifies

   the operation.  BUILTIN is the builtin operation, and OVERFLOW the

   overflow predicate.  Return 1 if the result overflows.  See above

   for restrictions.  */

#if _GL_HAS_BUILTIN_OVERFLOW

# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) builtin (a, b, r)

#elif 201112 <= __STDC_VERSION__ && !_GL__GENERIC_BOGUS

# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \

   (_Generic \

    (*(r), \

     signed char: \

       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \

                        signed char, SCHAR_MIN, SCHAR_MAX), \

     short int: \

       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \

                        short int, SHRT_MIN, SHRT_MAX), \

     int: \

       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \

                        int, INT_MIN, INT_MAX), \

     long int: \

       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \

                        long int, LONG_MIN, LONG_MAX), \

     long long int: \

       _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \

                        long long int, LLONG_MIN, LLONG_MAX)))

#else

# define _GL_INT_OP_WRAPV(a, b, r, op, builtin, overflow) \

   (sizeof *(r) == sizeof (signed char) \

    ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \

                       signed char, SCHAR_MIN, SCHAR_MAX) \

    : sizeof *(r) == sizeof (short int) \

    ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \

                       short int, SHRT_MIN, SHRT_MAX) \

    : sizeof *(r) == sizeof (int) \

    ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned int, \

                       int, INT_MIN, INT_MAX) \

    : _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow))

# ifdef LLONG_MAX

#  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \

    (sizeof *(r) == sizeof (long int) \

     ? _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \

                        long int, LONG_MIN, LONG_MAX) \

     : _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long long int, \

                        long long int, LLONG_MIN, LLONG_MAX))

# else

#  define _GL_INT_OP_WRAPV_LONGISH(a, b, r, op, overflow) \

    _GL_INT_OP_CALC (a, b, r, op, overflow, unsigned long int, \

                     long int, LONG_MIN, LONG_MAX)

# endif

#endif

/* Store the low-order bits of A <op> B into *R, where the operation

   is given by OP.  Use the unsigned type UT for calculation to avoid

   overflow problems.  *R's type is T, with extrema TMIN and TMAX.

   T must be a signed integer type.  Return 1 if the result overflows.  */

#define _GL_INT_OP_CALC(a, b, r, op, overflow, ut, t, tmin, tmax) \

  (sizeof ((a) op (b)) < sizeof (t) \

   ? _GL_INT_OP_CALC1 ((t) (a), (t) (b), r, op, overflow, ut, t, tmin, tmax) \

   : _GL_INT_OP_CALC1 (a, b, r, op, overflow, ut, t, tmin, tmax))

#define _GL_INT_OP_CALC1(a, b, r, op, overflow, ut, t, tmin, tmax) \

  ((overflow (a, b) \

    || (EXPR_SIGNED ((a) op (b)) && ((a) op (b)) < (tmin)) \

    || (tmax) < ((a) op (b))) \

   ? (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 1) \

   : (*(r) = _GL_INT_OP_WRAPV_VIA_UNSIGNED (a, b, op, ut, t), 0))

/* Return the low-order bits of A <op> B, where the operation is given

   by OP.  Use the unsigned type UT for calculation to avoid undefined

   behavior on signed integer overflow, and convert the result to type T.

   UT is at least as wide as T and is no narrower than unsigned int,

   T is two's complement, and there is no padding or trap representations.

   Assume that converting UT to T yields the low-order bits, as is

   done in all known two's-complement C compilers.  E.g., see:

   https://gcc.gnu.org/onlinedocs/gcc/Integers-implementation.html

   According to the C standard, converting UT to T yields an

   implementation-defined result or signal for values outside T's

   range.  However, code that works around this theoretical problem

   runs afoul of a compiler bug in Oracle Studio 12.3 x86.  See:

   http://lists.gnu.org/archive/html/bug-gnulib/2017-04/msg00049.html

   As the compiler bug is real, don't try to work around the

   theoretical problem.  */

#define _GL_INT_OP_WRAPV_VIA_UNSIGNED(a, b, op, ut, t) \

  ((t) ((ut) (a) op (ut) (b)))

#endif /* _GL_INTPROPS_H */