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+@node Integer Properties
+@section Integer Properties
+
+@c Copyright (C) 2011 Free Software Foundation, Inc.
+
+@c Permission is granted to copy, distribute and/or modify this document
+@c under the terms of the GNU Free Documentation License, Version 1.3 or
+@c any later version published by the Free Software Foundation; with no
+@c Invariant Sections, with no Front-Cover Texts, and with no Back-Cover
+@c Texts.  A copy of the license is included in the ``GNU Free
+@c Documentation License'' file as part of this distribution.
+
+@c Written by Paul Eggert.
+
+@cindex integer properties
+
+The @code{intprops} module consists of an include file @code{<intprops.h>}
+that defines several macros useful for testing properties of integer
+types.
+
+@cindex integer overflow
+@cindex overflow, integer
+
+Integer overflow is a common source of problems in programs written in
+C and other languages.  In some cases, such as signed integer
+arithmetic in C programs, the resulting behavior is undefined, and
+practical platforms do not always behave as if integers wrap around
+reliably.  In other cases, such as unsigned integer arithmetic in C,
+the resulting behavior is well-defined, but programs may still
+misbehave badly after overflow occurs.
+
+Many techniques have been proposed to attack these problems.  These
+include precondition testing, GCC's @option{-ftrapv} option, GCC's
+no-undefined-overflow branch, the As-if Infinitely Ranged (AIR) model
+implemented in Clang, saturation semantics where overflow reliably
+yields an extreme value, the RICH static transformer to an
+overflow-checking variant, and special testing methods.  For more
+information about these techniques, see: Dannenberg R, Dormann W,
+Keaton D @emph{et al.},
+@url{http://www.sei.cmu.edu/library/abstracts/reports/10tn008.cfm,
+As-if Infinitely Ranged integer model -- 2nd ed.}, Software Engineering
+Institute Technical Note CMU/SEI-2010-TN-008, April 2010.
+
+Gnulib supports the precondition testing technique, as this is easy to
+support portably.  There are two families of precondition tests: the
+first, for integer ranges, has a simple and straightforward implementation,
+while the second, for integer types, is easier to use.
+
+@menu
+* Integer Type Determination::  Whether a type has integer properties.
+* Integer Bounds::              Bounds on integer values and representations.
+* Integer Range Overflow::      Integer overflow checking if bounds are known.
+* Integer Type Overflow::       General integer overflow checking.
+@end menu
+
+@node Integer Type Determination
+@subsection Integer Type Determination
+
+@findex TYPE_IS_INTEGER
+@code{TYPE_IS_INTEGER (@var{t})} expands to a constant
+expression that is 1 if the arithmetic type @var{t} is an integer type.
+@code{_Bool} counts as an integer type.
+
+@findex TYPE_SIGNED
+@code{TYPE_SIGNED (@var{t})} expands to a constant expression
+that is 1 if the arithmetic type @var{t} is a signed integer type or a
+floating type.  If @var{t} is an integer type, @code{TYPE_SIGNED (@var{t})}
+expands to an integer constant expression.
+
+Example usage:
+
+@example
+#include <intprops.h>
+#include <time.h>
+enum
+@{
+  time_t_is_signed_integer =
+    TYPE_IS_INTEGER (time_t) && TYPE_SIGNED (time_t)
+@};
+@end example
+
+@node Integer Bounds
+@subsection Integer Bounds
+
+@cindex integer bounds
+
+@findex INT_BUFSIZE_BOUND
+@code{INT_BUFSIZE_BOUND (@var{t})} expands to an integer constant
+expression that is a bound on the size of the string representing an
+integer type or expression @var{t} in decimal notation, including the
+terminating null character and any leading @code{-} character.  For
+example, if @code{INT_STRLEN_BOUND (int)} is 12, any value of type
+@code{int} can be represented in 12 bytes or less, including the
+terminating null.  The bound is not necessarily tight.
+
+Example usage:
+
+@example
+#include <intprops.h>
+#include <stdio.h>
+int
+int_strlen (int i)
+@{
+  char buf[INT_BUFSIZE_BOUND (int)];
+  return sprintf (buf, "%d", i);
+@}
+@end example
+
+@findex INT_STRLEN_BOUND
+@code{INT_STRLEN_BOUND (@var{t})} expands to an integer constant
+expression that is a bound on the length of the string representing an
+integer type or expression @var{t} in decimal notation, including any
+leading @code{-} character.  This is one less than
+@code{INT_BUFSIZE_BOUND (@var{t})}.
+
+@findex TYPE_MINIMUM
+@findex TYPE_MAXIMUM
+@code{TYPE_MINIMUM (@var{t})} and @code{TYPE_MAXIMUM (@var{t})} expand
+to integer constant expressions equal to the minimum and maximum
+values of the integer type @var{t}.  These expressions are of the type
+@var{t} (or more precisely, the type @var{t} after integer
+promotions).
+
+Example usage:
+
+@example
+#include <stdint.h>
+#include <sys/types.h>
+#include <intprops.h>
+int
+in_off_t_range (intmax_t a)
+@{
+  return TYPE_MINIMUM (off_t) <= a && a <= TYPE_MAXIMUM (off_t);
+@}
+@end example
+
+@node Integer Range Overflow
+@subsection Integer Range Overflow
+
+@cindex integer range overflow
+@cindex overflow, integer range
+
+These macros yield 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.  They expand to
+integer constant expresssions if their arguments are.  Their
+implementations are simple and straightforward, but they are typically
+harder to use than the integer type overflow macros.  @xref{Integer
+Type Overflow}.
+
+Although the implementation of these macros is similar to that
+suggested in Seacord R, The CERT C Secure Coding Standard (2009,
+revised 2011), in its two sections
+``@url{https://www.securecoding.cert.org/confluence/display/seccode/INT30-C.+Ensure+that+unsigned+integer+operations+do+not+wrap,
+INT30-C. Ensure that unsigned integer operations do not wrap}'' and
+``@url{https://www.securecoding.cert.org/confluence/display/seccode/INT32-C.+Ensure+that+operations+on+signed+integers+do+not+result+in+overflow,
+INT32-C. Ensure that operations on signed integers do not result in
+overflow}'', Gnulib's implementation was derived independently of
+CERT's suggestions.
+
+Example usage:
+
+@example
+#include <intprops.h>
+void
+print_product (long int a, long int b)
+@{
+  if (INT_MULTIPLY_RANGE_OVERFLOW (a, b, LONG_MIN, LONG_MAX))
+    printf ("multiply would overflow");
+  else
+    printf ("product is %ld", a * b);
+@}
+@end example
+
+@noindent
+These macros have the following restrictions:
+
+@itemize @bullet
+@item
+Their arguments must be integer expressions.
+
+@item
+They may evaluate their arguments zero or multiple times, so
+the arguments should not have side effects.
+
+@item
+The arithmetic arguments (including the @var{min} and @var{max}
+arguments) must be of the same integer type after the usual arithmetic
+conversions, and the type must have minimum value @var{min} and
+maximum @var{max}.  Unsigned values should use a zero @var{min} of the
+proper type, for example, @code{(unsigned int) 0}.
+@end itemize
+
+These macros are tuned for constant @var{min} and @var{max}.  For
+commutative operations such as @code{@var{a} + @var{b}}, they are also
+tuned for constant @var{b}.
+
+@table @code
+@item INT_ADD_RANGE_OVERFLOW (@var{a}, @var{b}, @var{min}, @var{max})
+@findex INT_ADD_RANGE_OVERFLOW
+Yield 1 if @code{@var{a} + @var{b}} would overflow in
+[@var{min},@var{max}] integer arithmetic.  See above for restrictions.
+
+@item INT_SUBTRACT_RANGE_OVERFLOW (@var{a}, @var{b}, @var{min}, @var{max})
+@findex INT_SUBTRACT_RANGE_OVERFLOW
+Yield 1 if @code{@var{a} - @var{b}} would overflow in
+[@var{min},@var{max}] integer arithmetic.  See above for restrictions.
+
+@item INT_NEGATE_RANGE_OVERFLOW (@var{a}, @var{min}, @var{max})
+@findex INT_NEGATE_RANGE_OVERFLOW
+Yield 1 if @code{-@var{a}} would overflow in [@var{min},@var{max}]
+integer arithmetic.  See above for restrictions.
+
+@item INT_MULTIPLY_RANGE_OVERFLOW (@var{a}, @var{b}, @var{min}, @var{max})
+@findex INT_MULTIPLY_RANGE_OVERFLOW
+Yield 1 if @code{@var{a} * @var{b}} would overflow in
+[@var{min},@var{max}] integer arithmetic.  See above for restrictions.
+
+@item INT_DIVIDE_RANGE_OVERFLOW (@var{a}, @var{b}, @var{min}, @var{max})
+@findex INT_DIVIDE_RANGE_OVERFLOW
+Yield 1 if @code{@var{a} / @var{b}} would overflow in
+[@var{min},@var{max}] integer arithmetic.  See above for restrictions.
+Division overflow can happen on two's complement hosts when dividing
+the most negative integer by @minus{}1.  This macro does not check for
+division by zero.
+
+@item INT_REMAINDER_RANGE_OVERFLOW (@var{a}, @var{b}, @var{min}, @var{max})
+@findex INT_REMAINDER_RANGE_OVERFLOW
+Yield 1 if @code{@var{a} % @var{b}} would overflow in
+[@var{min},@var{max}] integer arithmetic.  See above for restrictions.
+Remainder overflow can happen on two's complement hosts when dividing
+the most negative integer by @minus{}1; although the mathematical
+result is always 0, in practice some implementations trap, so this
+counts as an overflow.  This macro does not check for division by
+zero.
+
+@item INT_LEFT_SHIFT_RANGE_OVERFLOW (@var{a}, @var{b}, @var{min}, @var{max})
+@findex INT_LEFT_SHIFT_RANGE_OVERFLOW
+Yield 1 if @code{@var{a} << @var{b}} would overflow in
+[@var{min},@var{max}] integer arithmetic.  See above for restrictions.
+Here, @var{min} and @var{max} are for @var{a} only, and @var{b} need
+not be of the same type as the other arguments.  The C standard says
+that behavior is undefined for shifts unless 0@leq{}@var{b}<@var{w}
+where @var{w} is @var{a}'s word width, and that when @var{a} is negative
+then @code{@var{a} << @var{b}} has undefined behavior and
+@code{@var{a} >> @var{b}} has implementation-defined behavior, but
+this macro does not check these other restrictions.
+@end table
+
+@node Integer Type Overflow
+@subsection Integer Type Overflow
+
+@cindex integer type overflow
+@cindex overflow, integer type
+
+These macros yield 1 if the corresponding C operators might not yield
+numerically correct answers due to arithmetic overflow of an integer
+type.  They work correctly on all known practical hosts, and do not
+rely on undefined behavior due to signed arithmetic overflow.  They
+expand to integer constant expresssions if their arguments are.  They
+are easier to use than the integer range overflow macros
+(@pxref{Integer Range Overflow}).
+
+Example usage:
+
+@example
+#include <intprops.h>
+void
+print_product (long int a, long int b)
+@{
+  if (INT_MULTIPLY_OVERFLOW (a, b))
+    printf ("multiply would overflow");
+  else
+    printf ("product is %ld", a * b);
+@}
+@end example
+
+@noindent
+These macros have the following restrictions:
+
+@itemize @bullet
+@item
+Their arguments must be integer expressions.
+
+@item
+They may evaluate their arguments zero or multiple times, so the
+arguments should not have side effects.
+@end itemize
+
+These macros are tuned for their last argument being a constant.
+
+@table @code
+@item INT_ADD_OVERFLOW (@var{a}, @var{b})
+@findex INT_ADD_OVERFLOW
+Yield 1 if @code{@var{a} + @var{b}} would overflow.  See above for
+restrictions.
+
+@item INT_SUBTRACT_OVERFLOW (@var{a}, @var{b})
+@findex INT_SUBTRACT_OVERFLOW
+Yield 1 if @code{@var{a} - @var{b}} would overflow.  See above for
+restrictions.
+
+@item INT_NEGATE_OVERFLOW (@var{a})
+@findex INT_NEGATE_OVERFLOW
+Yields 1 if @code{-@var{a}} would overflow.  See above for restrictions.
+
+@item INT_MULTIPLY_OVERFLOW (@var{a}, @var{b})
+@findex INT_MULTIPLY_OVERFLOW
+Yield 1 if @code{@var{a} * @var{b}} would overflow.  See above for
+restrictions.
+
+@item INT_DIVIDE_OVERFLOW (@var{a}, @var{b})
+@findex INT_DIVIDE_OVERFLOW
+Yields 1 if @code{@var{a} / @var{b}} would overflow.  See above for
+restrictions.  Division overflow can happen on two's complement hosts
+when dividing the most negative integer by @minus{}1.  This macro does
+not check for division by zero.
+
+@item INT_REMAINDER_OVERFLOW (@var{a}, @var{b})
+@findex INT_REMAINDER_OVERFLOW
+Yield 1 if @code{@var{a} % @var{b}} would overflow.  See above for
+restrictions.  Remainder overflow can happen on two's complement hosts
+when dividing the most negative integer by @minus{}1; although the
+mathematical result is always 0, in practice some implementations
+trap, so this counts as an overflow.  This macro does not check for
+division by zero.
+
+@item INT_LEFT_SHIFT_OVERFLOW (@var{a}, @var{b})
+@findex INT_LEFT_SHIFT_OVERFLOW
+Yield 1 if @code{@var{a} << @var{b}} would overflow.  See above for
+restrictions.  The C standard says that behavior is undefined for
+shifts unless 0@leq{}@var{b}<@var{w} where @var{w} is @var{a}'s word
+width, and that when @var{a} is negative then @code{@var{a} <<
+@var{b}} has undefined behavior and @code{@var{a} >> @var{b}} has
+implementation-defined behavior, but this macro does not check these
+other restrictions.
+@end table