return true;
}
+// True if [lb, ub] is [+-0, +-0].
+static bool
+zero_p (const REAL_VALUE_TYPE &lb, const REAL_VALUE_TYPE &ub)
+{
+ return real_iszero (&lb) && real_iszero (&ub);
+}
+
+// True if +0 or -0 is in [lb, ub] range.
+static bool
+contains_zero_p (const REAL_VALUE_TYPE &lb, const REAL_VALUE_TYPE &ub)
+{
+ return (real_compare (LE_EXPR, &lb, &dconst0)
+ && real_compare (GE_EXPR, &ub, &dconst0));
+}
+
+// True if [lb, ub] is [-INF, -INF] or [+INF, +INF].
+static bool
+singleton_inf_p (const REAL_VALUE_TYPE &lb, const REAL_VALUE_TYPE &ub)
+{
+ return real_isinf (&lb) && real_isinf (&ub, real_isneg (&lb));
+}
+
+// Return -1 if binary op result must have sign bit set,
+// 1 if binary op result must have sign bit clear,
+// 0 otherwise.
+// Sign bit of binary op result is exclusive or of the
+// operand's sign bits.
+static int
+signbit_known_p (const REAL_VALUE_TYPE &lh_lb, const REAL_VALUE_TYPE &lh_ub,
+ const REAL_VALUE_TYPE &rh_lb, const REAL_VALUE_TYPE &rh_ub)
+{
+ if (real_isneg (&lh_lb) == real_isneg (&lh_ub)
+ && real_isneg (&rh_lb) == real_isneg (&rh_ub))
+ {
+ if (real_isneg (&lh_lb) == real_isneg (&rh_ub))
+ return 1;
+ else
+ return -1;
+ }
+ return 0;
+}
+
+// Set [lb, ub] to [-0, -0], [-0, +0] or [+0, +0] depending on
+// signbit_known.
+static void
+zero_range (REAL_VALUE_TYPE &lb, REAL_VALUE_TYPE &ub, int signbit_known)
+{
+ ub = lb = dconst0;
+ if (signbit_known <= 0)
+ lb = real_value_negate (&dconst0);
+ if (signbit_known < 0)
+ ub = lb;
+}
+
+// Set [lb, ub] to [-INF, -INF], [-INF, +INF] or [+INF, +INF] depending on
+// signbit_known.
+static void
+inf_range (REAL_VALUE_TYPE &lb, REAL_VALUE_TYPE &ub, int signbit_known)
+{
+ if (signbit_known > 0)
+ ub = lb = dconstinf;
+ else if (signbit_known < 0)
+ ub = lb = dconstninf;
+ else
+ {
+ lb = dconstninf;
+ ub = dconstinf;
+ }
+}
+
+// Set [lb, ub] to [-INF, -0], [-INF, +INF] or [+0, +INF] depending on
+// signbit_known.
+static void
+zero_to_inf_range (REAL_VALUE_TYPE &lb, REAL_VALUE_TYPE &ub, int signbit_known)
+{
+ if (signbit_known > 0)
+ {
+ lb = dconst0;
+ ub = dconstinf;
+ }
+ else if (signbit_known < 0)
+ {
+ lb = dconstninf;
+ ub = real_value_negate (&dconst0);
+ }
+ else
+ {
+ lb = dconstninf;
+ ub = dconstinf;
+ }
+}
+
class foperator_plus : public range_operator_float
{
void rv_fold (REAL_VALUE_TYPE &lb, REAL_VALUE_TYPE &ub, bool &maybe_nan,
} fop_minus;
-class foperator_mult : public range_operator_float
+class foperator_mult_div_base : public range_operator_float
+{
+protected:
+ // Given CP[0] to CP[3] floating point values rounded to -INF,
+ // set LB to the smallest of them (treating -0 as smaller to +0).
+ // Given CP[4] to CP[7] floating point values rounded to +INF,
+ // set UB to the largest of them (treating -0 as smaller to +0).
+ static void find_range (REAL_VALUE_TYPE &lb, REAL_VALUE_TYPE &ub,
+ const REAL_VALUE_TYPE (&cp)[8])
+ {
+ lb = cp[0];
+ ub = cp[4];
+ for (int i = 1; i < 4; ++i)
+ {
+ if (real_less (&cp[i], &lb)
+ || (real_iszero (&lb) && real_isnegzero (&cp[i])))
+ lb = cp[i];
+ if (real_less (&ub, &cp[i + 4])
+ || (real_isnegzero (&ub) && real_iszero (&cp[i + 4])))
+ ub = cp[i + 4];
+ }
+ }
+};
+
+
+class foperator_mult : public foperator_mult_div_base
{
void rv_fold (REAL_VALUE_TYPE &lb, REAL_VALUE_TYPE &ub, bool &maybe_nan,
tree type,
if (!is_square)
{
// [+-0, +-0] * [+INF,+INF] (or [-INF,-INF] or swapped is a known NAN.
- if ((real_iszero (&lh_lb)
- && real_iszero (&lh_ub)
- && real_isinf (&rh_lb)
- && real_isinf (&rh_ub, real_isneg (&rh_lb)))
- || (real_iszero (&rh_lb)
- && real_iszero (&rh_ub)
- && real_isinf (&lh_lb)
- && real_isinf (&lh_ub, real_isneg (&lh_lb))))
+ if ((zero_p (lh_lb, lh_ub) && singleton_inf_p (rh_lb, rh_ub))
+ || (zero_p (rh_lb, rh_ub) && singleton_inf_p (lh_lb, lh_ub)))
{
real_nan (&lb, "", 0, TYPE_MODE (type));
ub = lb;
// Otherwise, if one range includes zero and the other ends with +-INF,
// it is a maybe NAN.
- if ((real_compare (LE_EXPR, &lh_lb, &dconst0)
- && real_compare (GE_EXPR, &lh_ub, &dconst0)
+ if ((contains_zero_p (lh_lb, lh_ub)
&& (real_isinf (&rh_lb) || real_isinf (&rh_ub)))
- || (real_compare (LE_EXPR, &rh_lb, &dconst0)
- && real_compare (GE_EXPR, &rh_ub, &dconst0)
+ || (contains_zero_p (rh_lb, rh_ub)
&& (real_isinf (&lh_lb) || real_isinf (&lh_ub))))
{
maybe_nan = true;
- bool must_have_signbit_zero = false;
- bool must_have_signbit_nonzero = false;
- if (real_isneg (&lh_lb) == real_isneg (&lh_ub)
- && real_isneg (&rh_lb) == real_isneg (&rh_ub))
- {
- if (real_isneg (&lh_lb) == real_isneg (&rh_ub))
- must_have_signbit_zero = true;
- else
- must_have_signbit_nonzero = true;
- }
+ int signbit_known = signbit_known_p (lh_lb, lh_ub, rh_lb, rh_ub);
// If one of the ranges that includes INF is singleton
// and the other range includes zero, the resulting
// range is INF and NAN, because the 0 * INF boundary
// case will be NAN, but already nextafter (0, 1) * INF
// is INF.
- if ((real_isinf (&lh_lb)
- && real_isinf (&lh_ub, real_isneg (&lh_lb)))
- || (real_isinf (&rh_lb)
- && real_isinf (&rh_ub, real_isneg (&rh_lb))))
- {
- // If all the boundary signs are the same, [+INF, +INF].
- if (must_have_signbit_zero)
- ub = lb = dconstinf;
- // If the two multiplicands have always different sign,
- // [-INF, -INF].
- else if (must_have_signbit_nonzero)
- ub = lb = dconstninf;
- // Otherwise -> [-INF, +INF] (-INF or +INF).
- else
- {
- lb = dconstninf;
- ub = dconstinf;
- }
- return;
- }
+ if (singleton_inf_p (lh_lb, lh_ub)
+ || singleton_inf_p (rh_lb, rh_ub))
+ return inf_range (lb, ub, signbit_known);
// If one of the multiplicands must be zero, the resulting
// range is +-0 and NAN.
- if ((real_iszero (&lh_lb) && real_iszero (&lh_ub))
- || (real_iszero (&rh_lb) && real_iszero (&rh_ub)))
- {
- ub = lb = dconst0;
- // If all the boundary signs are the same, [+0.0, +0.0].
- if (must_have_signbit_zero)
- ;
- // If divisor and dividend must have different signs,
- // [-0.0, -0.0].
- else if (must_have_signbit_nonzero)
- ub = lb = real_value_negate (&dconst0);
- // Otherwise -> [-0.0, +0.0].
- else
- lb = real_value_negate (&dconst0);
- return;
- }
+ if (zero_p (lh_lb, lh_ub) || zero_p (rh_lb, rh_ub))
+ return zero_range (lb, ub, signbit_known);
// Otherwise one of the multiplicands could be
// [0.0, nextafter (0.0, 1.0)] and the [DBL_MAX, INF]
// is still 0.0, nextafter (0.0, 1.0) * INF is still INF,
// so if the signs are always the same or always different,
// result is [+0.0, +INF] or [-INF, -0.0], otherwise VARYING.
- if (must_have_signbit_zero)
- {
- lb = dconst0;
- ub = dconstinf;
- }
- else if (must_have_signbit_nonzero)
- {
- lb = dconstninf;
- ub = real_value_negate (&dconst0);
- }
- else
- {
- lb = dconstninf;
- ub = dconstinf;
- }
- return;
+ return zero_to_inf_range (lb, ub, signbit_known);
}
}
REAL_VALUE_TYPE cp[8];
- // Do a cross-product.
+ // Do a cross-product. At this point none of the multiplications
+ // should produce a NAN.
frange_arithmetic (MULT_EXPR, type, cp[0], lh_lb, rh_lb, dconstninf);
frange_arithmetic (MULT_EXPR, type, cp[4], lh_lb, rh_lb, dconstinf);
if (is_square)
// otherwise min (lh_lb * lh_lb, lh_ub * lh_ub).
// -0.0 rather than 0.0 because VREL_EQ doesn't prove that
// x and y are bitwise equal, just that they compare equal.
- if (real_compare (LE_EXPR, &lh_lb, &dconst0)
- && real_compare (GE_EXPR, &lh_ub, &dconst0))
- cp[1] = real_value_negate (&dconst0);
+ if (contains_zero_p (lh_lb, lh_ub))
+ {
+ if (real_isneg (&lh_lb) == real_isneg (&lh_ub))
+ cp[1] = dconst0;
+ else
+ cp[1] = real_value_negate (&dconst0);
+ }
else
cp[1] = cp[0];
cp[2] = cp[0];
frange_arithmetic (MULT_EXPR, type, cp[3], lh_ub, rh_ub, dconstninf);
frange_arithmetic (MULT_EXPR, type, cp[7], lh_ub, rh_ub, dconstinf);
- for (int i = 1; i < 4; ++i)
- {
- if (real_less (&cp[i], &cp[0])
- || (real_iszero (&cp[0]) && real_isnegzero (&cp[i])))
- std::swap (cp[i], cp[0]);
- if (real_less (&cp[4], &cp[i + 4])
- || (real_isnegzero (&cp[4]) && real_iszero (&cp[i + 4])))
- std::swap (cp[i + 4], cp[4]);
- }
- lb = cp[0];
- ub = cp[4];
-
+ find_range (lb, ub, cp);
}
} fop_mult;
-class foperator_div : public range_operator_float
+
+class foperator_div : public foperator_mult_div_base
{
void rv_fold (REAL_VALUE_TYPE &lb, REAL_VALUE_TYPE &ub, bool &maybe_nan,
tree type,
relation_kind) const final override
{
// +-0.0 / +-0.0 or +-INF / +-INF is a known NAN.
- if ((real_iszero (&lh_lb)
- && real_iszero (&lh_ub)
- && real_iszero (&rh_lb)
- && real_iszero (&rh_ub))
- || (real_isinf (&lh_lb)
- && real_isinf (&lh_ub, real_isneg (&lh_lb))
- && real_isinf (&rh_lb)
- && real_isinf (&rh_ub, real_isneg (&rh_lb))))
+ if ((zero_p (lh_lb, lh_ub) && zero_p (rh_lb, rh_ub))
+ || (singleton_inf_p (lh_lb, lh_ub) || singleton_inf_p (rh_lb, rh_ub)))
{
real_nan (&lb, "", 0, TYPE_MODE (type));
ub = lb;
return;
}
- bool both_maybe_zero = false;
- bool both_maybe_inf = false;
- bool must_have_signbit_zero = false;
- bool must_have_signbit_nonzero = false;
-
// If +-0.0 is in both ranges, it is a maybe NAN.
- if (real_compare (LE_EXPR, &lh_lb, &dconst0)
- && real_compare (GE_EXPR, &lh_ub, &dconst0)
- && real_compare (LE_EXPR, &rh_lb, &dconst0)
- && real_compare (GE_EXPR, &rh_ub, &dconst0))
- {
- both_maybe_zero = true;
- maybe_nan = true;
- }
+ if (contains_zero_p (lh_lb, lh_ub) && contains_zero_p (rh_lb, rh_ub))
+ maybe_nan = true;
// If +-INF is in both ranges, it is a maybe NAN.
else if ((real_isinf (&lh_lb) || real_isinf (&lh_ub))
&& (real_isinf (&rh_lb) || real_isinf (&rh_ub)))
- {
- both_maybe_inf = true;
- maybe_nan = true;
- }
+ maybe_nan = true;
else
maybe_nan = false;
- if (real_isneg (&lh_lb) == real_isneg (&lh_ub)
- && real_isneg (&rh_lb) == real_isneg (&rh_ub))
- {
- if (real_isneg (&lh_lb) == real_isneg (&rh_ub))
- must_have_signbit_zero = true;
- else
- must_have_signbit_nonzero = true;
- }
+ int signbit_known = signbit_known_p (lh_lb, lh_ub, rh_lb, rh_ub);
// If dividend must be zero, the range is just +-0
// (including if the divisor is +-INF).
// If divisor must be +-INF, the range is just +-0
// (including if the dividend is zero).
- if ((real_iszero (&lh_lb) && real_iszero (&lh_ub))
- || real_isinf (&rh_lb, false)
- || real_isinf (&rh_ub, true))
- {
- ub = lb = dconst0;
- // If all the boundary signs are the same, [+0.0, +0.0].
- if (must_have_signbit_zero)
- ;
- // If divisor and dividend must have different signs,
- // [-0.0, -0.0].
- else if (must_have_signbit_nonzero)
- ub = lb = real_value_negate (&dconst0);
- // Otherwise -> [-0.0, +0.0].
- else
- lb = real_value_negate (&dconst0);
- return;
- }
+ if (zero_p (lh_lb, lh_ub) || singleton_inf_p (rh_lb, rh_ub))
+ return zero_range (lb, ub, signbit_known);
// If divisor must be zero, the range is just +-INF
// (including if the dividend is +-INF).
// If dividend must be +-INF, the range is just +-INF
// (including if the dividend is zero).
- if ((real_iszero (&rh_lb) && real_iszero (&rh_ub))
- || real_isinf (&lh_lb, false)
- || real_isinf (&lh_ub, true))
- {
- // If all the boundary signs are the same, [+INF, +INF].
- if (must_have_signbit_zero)
- ub = lb = dconstinf;
- // If divisor and dividend must have different signs,
- // [-INF, -INF].
- else if (must_have_signbit_nonzero)
- ub = lb = dconstninf;
- // Otherwise -> [-INF, +INF] (-INF or +INF).
- else
- {
- lb = dconstninf;
- ub = dconstinf;
- }
- return;
- }
+ if (zero_p (rh_lb, rh_ub) || singleton_inf_p (lh_lb, lh_ub))
+ return inf_range (lb, ub, signbit_known);
// Otherwise if both operands may be zero, divisor could be
// nextafter(0.0, +-1.0) and dividend +-0.0
// signs of divisor and dividend are always the same we have
// [+0.0, +INF], if they are always different we have
// [-INF, -0.0]. If they vary, VARYING.
- if (both_maybe_zero || both_maybe_inf)
- {
- if (must_have_signbit_zero)
- {
- lb = dconst0;
- ub = dconstinf;
- }
- else if (must_have_signbit_nonzero)
- {
- lb = dconstninf;
- ub = real_value_negate (&dconst0);
- }
- else
- {
- lb = dconstninf;
- ub = dconstinf;
- }
- return;
- }
+ if (maybe_nan)
+ return zero_to_inf_range (lb, ub, signbit_known);
REAL_VALUE_TYPE cp[8];
// Do a cross-division. At this point none of the divisions should
// produce a NAN.
- gcc_assert (!maybe_nan);
frange_arithmetic (RDIV_EXPR, type, cp[0], lh_lb, rh_lb, dconstninf);
frange_arithmetic (RDIV_EXPR, type, cp[1], lh_lb, rh_ub, dconstninf);
frange_arithmetic (RDIV_EXPR, type, cp[2], lh_ub, rh_lb, dconstninf);
frange_arithmetic (RDIV_EXPR, type, cp[6], lh_ub, rh_lb, dconstinf);
frange_arithmetic (RDIV_EXPR, type, cp[7], lh_ub, rh_ub, dconstinf);
- for (int i = 1; i < 4; ++i)
- {
- if (real_less (&cp[i], &cp[0])
- || (real_iszero (&cp[0]) && real_isnegzero (&cp[i])))
- std::swap (cp[i], cp[0]);
- if (real_less (&cp[4], &cp[i + 4])
- || (real_isnegzero (&cp[4]) && real_iszero (&cp[i + 4])))
- std::swap (cp[i + 4], cp[4]);
- }
- lb = cp[0];
- ub = cp[4];
+ find_range (lb, ub, cp);
// If divisor may be zero (but is not known to be only zero),
// and dividend can't be zero, the range can go up to -INF or +INF
// depending on the signs.
- if (real_compare (LE_EXPR, &rh_lb, &dconst0)
- && real_compare (GE_EXPR, &rh_ub, &dconst0))
+ if (contains_zero_p (rh_lb, rh_ub))
{
- if (!must_have_signbit_zero)
+ if (signbit_known <= 0)
real_inf (&lb, true);
- if (!must_have_signbit_nonzero)
+ if (signbit_known >= 0)
real_inf (&ub, false);
}
}
git://gcc.gnu.org / gcc.git / commitdiff