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+/* intprops.h -- properties of integer types
+
+   Copyright (C) 2001-2022 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 <https://www.gnu.org/licenses/>.  */
+
+#ifndef _GL_INTPROPS_H
+#define _GL_INTPROPS_H
+
+#include "intprops-internal.h"
+
+/* 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) _GL_TYPE_SIGNED (t)
+
+/* Return 1 if the real expression E, after promotion, has a
+   signed or floating type.  Do not evaluate E.  */
+#define EXPR_SIGNED(e) _GL_EXPR_SIGNED (e)
+
+
+/* Minimum and maximum values for integer types and expressions.  */
+
+/* The width in bits of the integer type or expression T.
+   Do not evaluate T.  T must not be a bit-field expression.
+   Padding bits are not supported; this is checked at compile-time below.  */
+#define TYPE_WIDTH(t) _GL_TYPE_WIDTH (t)
+
+/* 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)))
+
+/* 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.
+   T must not be a bit-field expression.
+
+   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 1 when its argument is
+   unsigned, 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.  T must not be a bit-field expression.  */
+#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 overflow arithmetically when given the same arguments.
+   These macros do not rely on undefined or implementation-defined behavior.
+   Although their implementations are simple and straightforward,
+   they are harder to use and may be less efficient than the
+   INT_<op>_WRAPV, INT_<op>_OK, and 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.
+
+   Because all arguments are subject to integer promotions, these
+   macros typically do not work on types narrower than 'int'.
+
+   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)          \
+  _GL_INT_NEGATE_RANGE_OVERFLOW (a, min, max)
+
+/* 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
+   <https://lists.gnu.org/r/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))
+
+/* 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 compute the low-order bits of the sum,
+   difference, and product of two C integers, and return 1 if these
+   low-order bits are not numerically correct.
+   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 *.
+
+   Because the WRAPV macros convert the result, they report overflow
+   in different circumstances than the OVERFLOW macros do.  For
+   example, in the typical case with 16-bit 'short' and 32-bit 'int',
+   if A, B and *R are all of type 'short' then INT_ADD_OVERFLOW (A, B)
+   returns false because the addition cannot overflow after A and B
+   are converted to 'int', whereas INT_ADD_WRAPV (A, B, R) returns
+   true or false depending on whether the sum fits into 'short'.
+
+   These macros are tuned for their last input argument being a constant.
+
+   A, B, and *R should be integers; they need not be the same type,
+   and they need not be all signed or all unsigned.
+   However, none of the integer types should be bit-precise,
+   and *R's type should not be char, bool, or an enumeration type.
+
+   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)
+#define INT_NEGATE_OVERFLOW(a) _GL_INT_NEGATE_OVERFLOW (a)
+#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 (_GL_INT_CONVERT (a, b)), \
+                      _GL_INT_MAXIMUM (_GL_INT_CONVERT (a, b)))
+
+/* 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_ADD_WRAPV (a, b, r)
+#define INT_SUBTRACT_WRAPV(a, b, r) _GL_INT_SUBTRACT_WRAPV (a, b, r)
+#define INT_MULTIPLY_WRAPV(a, b, r) _GL_INT_MULTIPLY_WRAPV (a, b, r)
+
+/* The following macros compute A + B, A - B, and A * B, respectively.
+   If no overflow occurs, they set *R to the result and return 1;
+   otherwise, they return 0 and may modify *R.
+
+   Example usage:
+
+     long int result;
+     if (INT_ADD_OK (a, b, &result))
+       printf ("result is %ld\n", result);
+     else
+       printf ("overflow\n");
+
+   A, B, and *R should be integers; they need not be the same type,
+   and they need not be all signed or all unsigned.
+   However, none of the integer types should be bit-precise,
+   and *R's type should not be char, bool, or an enumeration type.
+
+   These macros work correctly on all known practical hosts, and do not rely
+   on undefined behavior due to signed arithmetic overflow.
+
+   These macros are not constant expressions.
+
+   These macros may evaluate their arguments zero or multiple times, so the
+   arguments should not have side effects.
+
+   These macros are tuned for B being a constant.  */
+
+#define INT_ADD_OK(a, b, r) (! INT_ADD_WRAPV (a, b, r))
+#define INT_SUBTRACT_OK(a, b, r) (! INT_SUBTRACT_WRAPV (a, b, r))
+#define INT_MULTIPLY_OK(a, b, r) (! INT_MULTIPLY_WRAPV (a, b, r))
+
+#endif /* _GL_INTPROPS_H */