bool
range_operator_float::fold_range (frange &r, tree type,
const frange &op1, const frange &op2,
- relation_trio) const
+ relation_trio trio) const
{
if (empty_range_varying (r, type, op1, op2))
return true;
bool maybe_nan;
rv_fold (lb, ub, maybe_nan, type,
op1.lower_bound (), op1.upper_bound (),
- op2.lower_bound (), op2.upper_bound ());
+ op2.lower_bound (), op2.upper_bound (), trio.op1_op2 ());
// Handle possible NANs by saturating to the appropriate INF if only
// one end is a NAN. If both ends are a NAN, just return a NAN.
const REAL_VALUE_TYPE &lh_lb ATTRIBUTE_UNUSED,
const REAL_VALUE_TYPE &lh_ub ATTRIBUTE_UNUSED,
const REAL_VALUE_TYPE &rh_lb ATTRIBUTE_UNUSED,
- const REAL_VALUE_TYPE &rh_ub ATTRIBUTE_UNUSED)
- const
+ const REAL_VALUE_TYPE &rh_ub ATTRIBUTE_UNUSED,
+ relation_kind) const
{
lb = dconstninf;
ub = dconstinf;
const REAL_VALUE_TYPE &lh_lb,
const REAL_VALUE_TYPE &lh_ub,
const REAL_VALUE_TYPE &rh_lb,
- const REAL_VALUE_TYPE &rh_ub) const final override
+ const REAL_VALUE_TYPE &rh_ub,
+ relation_kind) const final override
{
frange_arithmetic (PLUS_EXPR, type, lb, lh_lb, rh_lb, dconstninf);
frange_arithmetic (PLUS_EXPR, type, ub, lh_ub, rh_ub, dconstinf);
const REAL_VALUE_TYPE &lh_lb,
const REAL_VALUE_TYPE &lh_ub,
const REAL_VALUE_TYPE &rh_lb,
- const REAL_VALUE_TYPE &rh_ub) const final override
+ const REAL_VALUE_TYPE &rh_ub,
+ relation_kind) const final override
{
frange_arithmetic (MINUS_EXPR, type, lb, lh_lb, rh_ub, dconstninf);
frange_arithmetic (MINUS_EXPR, type, ub, lh_ub, rh_lb, dconstinf);
}
} fop_minus;
+
+class foperator_mult : public range_operator_float
+{
+ void rv_fold (REAL_VALUE_TYPE &lb, REAL_VALUE_TYPE &ub, bool &maybe_nan,
+ tree type,
+ const REAL_VALUE_TYPE &lh_lb,
+ const REAL_VALUE_TYPE &lh_ub,
+ const REAL_VALUE_TYPE &rh_lb,
+ const REAL_VALUE_TYPE &rh_ub,
+ relation_kind kind) const final override
+ {
+ bool is_square
+ = (kind == VREL_EQ
+ && real_equal (&lh_lb, &rh_lb)
+ && real_equal (&lh_ub, &rh_ub)
+ && real_isneg (&lh_lb) == real_isneg (&rh_lb)
+ && real_isneg (&lh_ub) == real_isneg (&rh_ub));
+
+ maybe_nan = false;
+ // x * x never produces a new NAN and we only multiply the same
+ // values, so the 0 * INF problematic cases never appear there.
+ 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))))
+ {
+ real_nan (&lb, "", 0, TYPE_MODE (type));
+ ub = lb;
+ maybe_nan = true;
+ return;
+ }
+
+ // 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)
+ && (real_isinf (&rh_lb) || real_isinf (&rh_ub)))
+ || (real_compare (LE_EXPR, &rh_lb, &dconst0)
+ && real_compare (GE_EXPR, &rh_ub, &dconst0)
+ && (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;
+ }
+
+ // 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 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;
+ }
+
+ // Otherwise one of the multiplicands could be
+ // [0.0, nextafter (0.0, 1.0)] and the [DBL_MAX, INF]
+ // or similarly with different signs. 0.0 * DBL_MAX
+ // 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;
+ }
+ }
+
+ REAL_VALUE_TYPE cp[8];
+ // Do a cross-product.
+ 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)
+ {
+ // For x * x we can just do max (lh_lb * lh_lb, lh_ub * lh_ub)
+ // as maximum and -0.0 as minimum if 0.0 is in the range,
+ // 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);
+ else
+ cp[1] = cp[0];
+ cp[2] = cp[0];
+ cp[5] = cp[4];
+ cp[6] = cp[4];
+ }
+ else
+ {
+ frange_arithmetic (MULT_EXPR, type, cp[1], lh_lb, rh_ub, dconstninf);
+ frange_arithmetic (MULT_EXPR, type, cp[5], lh_lb, rh_ub, dconstinf);
+ frange_arithmetic (MULT_EXPR, type, cp[2], lh_ub, rh_lb, dconstninf);
+ frange_arithmetic (MULT_EXPR, type, cp[6], lh_ub, rh_lb, dconstinf);
+ }
+ 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];
+
+ }
+} fop_mult;
+
// Instantiate a range_op_table for floating point operations.
static floating_op_table global_floating_table;
set (NEGATE_EXPR, fop_negate);
set (PLUS_EXPR, fop_plus);
set (MINUS_EXPR, fop_minus);
+ set (MULT_EXPR, fop_mult);
}
// Return a pointer to the range_operator_float instance, if there is
projects / thirdparty / gcc.git / commitdiff
