Re: proposed new module intoverflow

[Paul Eggert]

On 05/06/11 03:41, Bruno Haible wrote:
>    ADD_OVERFLOW (a, b, unsigned int)
> is easier to write and understand than
>    ADD_OVERFLOW (a, b, 0, UINT_MAX)

OK, but "ADD_OVERFLOW (a, b)" is easier yet, no?  And this would
address Ben's comment that the macro should check the types of the
arguments.  If ADD_OVERFLOW works for all combinations of integer
types, the types are never "wrong", so there's no need for it to
report an error when types are "wrong".

Here's a patch to do that.  It uses an INT_ prefix to make it clearer
that it works only for integer arithmetic.  This proposal also uses "SUM"
instead of "ADD", "DIFFERENCE" rather than "SUBTRACT", etc., for
reasons that escape me: I can easily change the names back if that's
what people prefer.

Example usage:

   return INT_ADD_OVERFLOW (a, b) ? 0 : a + b;

This implementation relies heavily on the intprops module, so I
made it part of intprops.  I suppose it could be split out into
a new intoverflow module; I don't have a strong feeling about that
either.

---

intprops: Add support for portable and safe integer overflow checking.
* lib/intprops.h (_GL_INT_CONVERT, _GL_INT_TWOS_COMPLEMENT):
(_GL_INT_SIGNED, _GL_INT_MINIMUM, _GL_INT_MAXIMUM):
(_GL_SIGNED_INT_MINIMUM, INT_SUM_RANGE_OVERFLOW):
(INT_DIFFERENCE_RANGE_OVERFLOW, INT_NEGATIVE_RANGE_OVERFLOW):
(INT_PRODUCT_RANGE_OVERFLOW, INT_REMAINDER_RANGE_OVERFLOW):
(INT_LEFT_SHIFT_RANGE_OVERFLOW, _GL_SUM_OVERFLOW):
(_GL_DIFFERENCE_OVERFLOW, _GL_PRODUCT_OVERFLOW, _GL_QUOTIENT_OVERFLOW):
(_GL_REMAINDER_OVERFLOW, _GL_UNSIGNED_NEG_MULTIPLE, INT_SUM_OVERFLOW):
(INT_DIFFERENCE_OVERFLOW, INT_NEGATIVE_OVERFLOW, INT_PRODUCT_OVERFLOW):
(INT_QUOTIENT_OVERFLOW, INT_REMAINDER_OVERFLOW):
(INT_LEFT_SHIFT_OVERFLOW, _GL_BINARY_OP_OVERFLOW): New macros.
diff --git a/lib/intprops.h b/lib/intprops.h
index 529b0fa..9f7695d 100644
--- a/lib/intprops.h
+++ b/lib/intprops.h
@@ -22,6 +22,11 @@

 #include <limits.h>

+/* Return a integer value, converted to the same type as the integer
+   expression E after integer type promotion.  V is the unconverted value.
+   E should not have side effects.  */
+#define _GL_INT_CONVERT(e, v) ((e) - (e) + (v))
+
 /* The extra casts in the following macros work around compiler bugs,
    e.g., in Cray C 5.0.3.0.  */

@@ -37,13 +42,23 @@
 #define TYPE_ONES_COMPLEMENT(t) ((t) ~ (t) 0 == 0)
 #define TYPE_SIGNED_MAGNITUDE(t) ((t) ~ (t) 0 < (t) -1)

+/* True if the signed integer expression E uses two's complement.  */
+#define _GL_INT_TWOS_COMPLEMENT(e) (~ _GL_INT_CONVERT (e, 0) == -1)
+
 /* True if the arithmetic type T is signed.  */
 #define TYPE_SIGNED(t) (! ((t) 0 < (t) -1))

-/* The maximum and minimum values for the integer type T.  These
+/* Return 1 if the integer expression E, after integer promotion, has
+   a signed type.  E should not have side effects.  */
+#define _GL_INT_SIGNED(e) (_GL_INT_CONVERT (e, -1) < 0)
+
+
+/* Minimum and maximum values for integer types and expressions.  These
    macros have undefined behavior if T is signed and has padding bits.
    If this is a problem for you, please let us know how to fix it for
    your host.  */
+
+/* The maximum and minimum values for the integer type T.  */
 #define TYPE_MINIMUM(t)                                                 \
   ((t) (! TYPE_SIGNED (t)                                               \
         ? (t) 0                                                         \
@@ -55,6 +70,20 @@
         ? (t) -1                                                        \
         : ((((t) 1 << (sizeof (t) * CHAR_BIT - 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)                                              \
+  (_GL_INT_SIGNED (e)                                                   \
+   ? - _GL_INT_TWOS_COMPLEMENT (e) - _GL_SIGNED_INT_MAXIMUM (e)         \
+   : _GL_INT_CONVERT (e, 0))
+#define _GL_INT_MAXIMUM(e)                                              \
+  (_GL_INT_SIGNED (e)                                                   \
+   ? _GL_SIGNED_INT_MAXIMUM (e)                                         \
+   : _GL_INT_CONVERT (e, -1))
+#define _GL_SIGNED_INT_MAXIMUM(e)                                       \
+  (((_GL_INT_CONVERT (e, 1) << (sizeof ((e) + 0) * CHAR_BIT - 2)) - 1) * 2 + 1)
+
+
 /* Return 1 if the __typeof__ keyword works.  This could be done by
    'configure', but for now it's easier to do it by hand.  */
 #if 2 <= __GNUC__ || 0x5110 <= __SUNPRO_C
@@ -93,4 +122,193 @@
    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_PRODUCT_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_SUM_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_DIFFERENCE_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_NEGATIVE_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.  */
+#define INT_PRODUCT_RANGE_OVERFLOW(a, b, min, max)      \
+  ((b) < 0                                              \
+   ? ((a) < 0                                           \
+      ? (a) < (max) / (b)                               \
+      : (b) < -1 && (min) / (b) < (a))                  \
+   : (0 < (b)                                           \
+      && ((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_QUOTIENT_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_QUOTIENT_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.  */
+#define _GL_SUM_OVERFLOW(a, b, min, max)                                \
+  ((min) < 0 ? INT_SUM_RANGE_OVERFLOW (a, b, min, max)                  \
+   : (a) < 0 ? (b) <= (a) + (b)                                         \
+   : (b) < 0 ? (a) <= (a) + (b)                                         \
+   : (a) + (b) < (b))
+#define _GL_DIFFERENCE_OVERFLOW(a, b, min, max)                         \
+  ((min) < 0 ? INT_DIFFERENCE_RANGE_OVERFLOW (a, b, min, max)           \
+   : (a) < 0 ? 1                                                        \
+   : (b) < 0 ? (a) - (b) <= (a)                                         \
+   : (a) < (b))
+#define _GL_PRODUCT_OVERFLOW(a, b, min, max)                            \
+  (((min) == 0 && (((a) < 0 && 0 < (b)) || ((b) < 0 && 0 < (a))))       \
+   || INT_PRODUCT_RANGE_OVERFLOW (a, b, min, max))
+#define _GL_QUOTIENT_OVERFLOW(a, b, min, max)                           \
+  ((min) < 0 ? (b) == _GL_INT_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_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)
+
+
+/* Integer overflow checks.
+
+   The INT_<op>_OVERFLOW macros return 1 if the corresponding C operators
+   might not yield numerically correct answers due to arithmetic overflow.
+   They work correctly on all known practical hosts, and do not rely
+   on undefined behavior due to signed arithmetic overflow.
+
+   Example usage:
+
+     long int i = ...;
+     long int j = ...;
+     if (INT_PRODUCT_OVERFLOW (i, j))
+       printf ("multiply would overflow");
+     else
+       printf ("product is %ld", i * j);
+
+   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.
+
+   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_SUM_OVERFLOW(a, b) \
+  _GL_BINARY_OP_OVERFLOW (a, b, _GL_SUM_OVERFLOW)
+#define INT_DIFFERENCE_OVERFLOW(a, b) \
+  _GL_BINARY_OP_OVERFLOW (a, b, _GL_DIFFERENCE_OVERFLOW)
+#define INT_NEGATIVE_OVERFLOW(a) \
+  INT_NEGATIVE_RANGE_OVERFLOW (a, _GL_INT_MINIMUM (a), _GL_INT_MAXIMUM (a))
+#define INT_PRODUCT_OVERFLOW(a, b) \
+  _GL_BINARY_OP_OVERFLOW (a, b, _GL_PRODUCT_OVERFLOW)
+#define INT_QUOTIENT_OVERFLOW(a, b) \
+  _GL_BINARY_OP_OVERFLOW (a, b, _GL_QUOTIENT_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.
+
+   This macro assumes that A | B is a valid integer if both A and B are,
+   which is true of all known practical hosts.  If this is a problem
+   for you, please let us know how to fix it for your host.  */
+#define _GL_BINARY_OP_OVERFLOW(a, b, op_result_overflow)        \
+  op_result_overflow (a, b,                                     \
+                      _GL_INT_MINIMUM ((a) | (b)),              \
+                      _GL_INT_MAXIMUM ((a) | (b)))
+
 #endif /* _GL_INTPROPS_H */