Simplify_Div.cpp
#include "Simplify_Internal.h"
namespace Halide {
namespace Internal {
Expr Simplify::visit(const Div *op, ExprInfo *bounds) {
ExprInfo a_bounds, b_bounds;
Expr a = mutate(op->a, &a_bounds);
Expr b = mutate(op->b, &b_bounds);
if (bounds && no_overflow_int(op->type)) {
bounds->min = INT64_MAX;
bounds->max = INT64_MIN;
// Enumerate all possible values for the min and max and take the extreme values.
if (a_bounds.min_defined && b_bounds.min_defined && b_bounds.min != 0) {
int64_t v = div_imp(a_bounds.min, b_bounds.min);
bounds->min = std::min(bounds->min, v);
bounds->max = std::max(bounds->max, v);
}
if (a_bounds.min_defined && b_bounds.max_defined && b_bounds.max != 0) {
int64_t v = div_imp(a_bounds.min, b_bounds.max);
bounds->min = std::min(bounds->min, v);
bounds->max = std::max(bounds->max, v);
}
if (a_bounds.max_defined && b_bounds.max_defined && b_bounds.max != 0) {
int64_t v = div_imp(a_bounds.max, b_bounds.max);
bounds->min = std::min(bounds->min, v);
bounds->max = std::max(bounds->max, v);
}
if (a_bounds.max_defined && b_bounds.min_defined && b_bounds.min != 0) {
int64_t v = div_imp(a_bounds.max, b_bounds.min);
bounds->min = std::min(bounds->min, v);
bounds->max = std::max(bounds->max, v);
}
const bool b_positive = b_bounds.min_defined && b_bounds.min > 0;
const bool b_negative = b_bounds.max_defined && b_bounds.max < 0;
if ((b_positive && !b_bounds.max_defined) ||
(b_negative && !b_bounds.min_defined)) {
// Take limit as b -> +/- infinity
int64_t v = 0;
bounds->min = std::min(bounds->min, v);
bounds->max = std::max(bounds->max, v);
}
bounds->min_defined = ((a_bounds.min_defined && b_positive) ||
(a_bounds.max_defined && b_negative));
bounds->max_defined = ((a_bounds.max_defined && b_positive) ||
(a_bounds.min_defined && b_negative));
// That's as far as we can get knowing the sign of the
// denominator. For bounded numerators, we additionally know
// that div can't make anything larger in magnitude, so we can
// take the intersection with that.
if (a_bounds.max_defined && a_bounds.min_defined) {
int64_t v = std::max(a_bounds.max, -a_bounds.min);
if (bounds->min_defined) {
bounds->min = std::max(bounds->min, -v);
} else {
bounds->min = -v;
}
if (bounds->max_defined) {
bounds->max = std::min(bounds->max, v);
} else {
bounds->max = v;
}
bounds->min_defined = bounds->max_defined = true;
}
// Bounded numerator divided by constantish
// denominator can sometimes collapse things to a
// constant at this point
if (bounds->min_defined &&
bounds->max_defined &&
bounds->max == bounds->min) {
if (op->type.can_represent(bounds->min)) {
return make_const(op->type, bounds->min);
} else {
// Even though this is 'no-overflow-int', if the result
// we calculate can't fit into the destination type,
// we're better off returning an overflow condition than
// a known-wrong value. (Note that no_overflow_int() should
// only be true for signed integers.)
internal_assert(op->type.is_int());
clear_bounds_info(bounds);
return make_signed_integer_overflow(op->type);
}
}
// Code downstream can use min/max in calculated-but-unused arithmetic
// that can lead to UB (and thus, flaky failures under ASAN/UBSAN)
// if we leave them set to INT64_MAX/INT64_MIN; normalize to zero to avoid this.
if (!bounds->min_defined) {
bounds->min = 0;
}
if (!bounds->max_defined) {
bounds->max = 0;
}
bounds->alignment = a_bounds.alignment / b_bounds.alignment;
bounds->trim_bounds_using_alignment();
}
bool denominator_non_zero =
(no_overflow_int(op->type) &&
((b_bounds.min_defined && b_bounds.min > 0) ||
(b_bounds.max_defined && b_bounds.max < 0) ||
(b_bounds.alignment.remainder != 0)));
if (may_simplify(op->type)) {
int lanes = op->type.lanes();
auto rewrite = IRMatcher::rewriter(IRMatcher::div(a, b), op->type);
if (rewrite(IRMatcher::Overflow() / x, a) ||
rewrite(x / IRMatcher::Overflow(), b) ||
rewrite(x / 1, x) ||
(!op->type.is_float() && rewrite(x / 0, 0)) ||
(!op->type.is_float() && denominator_non_zero && rewrite(x / x, 1)) ||
rewrite(0 / x, 0) ||
false) {
return rewrite.result;
}
int a_mod = a_bounds.alignment.modulus;
int a_rem = a_bounds.alignment.remainder;
// clang-format off
if (EVAL_IN_LAMBDA
(rewrite(c0 / c1, fold(c0 / c1)) ||
rewrite(broadcast(x, c0) / broadcast(y, c0), broadcast(x / y, c0)) ||
rewrite(select(x, c0, c1) / c2, select(x, fold(c0/c2), fold(c1/c2))) ||
(!op->type.is_float() &&
rewrite(x / x, select(x == 0, 0, 1))) ||
(no_overflow(op->type) &&
(// Fold repeated division
rewrite((x / c0) / c2, x / fold(c0 * c2), c0 > 0 && c2 > 0 && !overflows(c0 * c2)) ||
rewrite((x / c0 + c1) / c2, (x + fold(c1 * c0)) / fold(c0 * c2), c0 > 0 && c2 > 0 && !overflows(c0 * c2) && !overflows(c0 * c1)) ||
rewrite((x * c0) / c1, x / fold(c1 / c0), c1 % c0 == 0 && c0 > 0 && c1 / c0 != 0) ||
// Pull out terms that are a multiple of the denominator
rewrite((x * c0) / c1, x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(min((x * c0), c1) / c2, min(x * fold(c0 / c2), fold(c1 / c2)), c0 % c2 == 0 && c2 > 0) ||
rewrite(max((x * c0), c1) / c2, max(x * fold(c0 / c2), fold(c1 / c2)), c0 % c2 == 0 && c2 > 0) ||
rewrite((x * c0 + y) / c1, y / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((x * c0 - y) / c0, x + (0 - y) / c0) ||
rewrite((x * c1 - y) / c0, (0 - y) / c0 - x, c0 + c1 == 0) ||
rewrite((y + x * c0) / c1, y / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((y - x * c0) / c1, y / c1 - x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(((x * c0 + y) + z) / c1, (y + z) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(((x * c0 - y) + z) / c1, (z - y) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(((x * c0 + y) - z) / c1, (y - z) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(((x * c0 - y) - z) / c0, x + (0 - y - z) / c0) ||
rewrite(((x * c1 - y) - z) / c0, (0 - y - z) / c0 - x, c0 + c1 == 0) ||
rewrite(((y + x * c0) + z) / c1, (y + z) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(((y + x * c0) - z) / c1, (y - z) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(((y - x * c0) - z) / c1, (y - z) / c1 - x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(((y - x * c0) + z) / c1, (y + z) / c1 - x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((z + (x * c0 + y)) / c1, (z + y) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((z + (x * c0 - y)) / c1, (z - y) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((z - (x * c0 - y)) / c1, (z + y) / c1 - x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((z - (x * c0 + y)) / c1, (z - y) / c1 + x * fold(-c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((z + (y + x * c0)) / c1, (z + y) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((z - (y + x * c0)) / c1, (z - y) / c1 + x * fold(-c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((z + (y - x * c0)) / c1, (z + y) / c1 - x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((z - (y - x * c0)) / c1, (z - y) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
// For the next depth, stick to addition
rewrite((((x * c0 + y) + z) + w) / c1, (y + z + w) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((((y + x * c0) + z) + w) / c1, (y + z + w) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(((z + (x * c0 + y)) + w) / c1, (y + z + w) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite(((z + (y + x * c0)) + w) / c1, (y + z + w) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((w + ((x * c0 + y) + z)) / c1, (y + z + w) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((w + ((y + x * c0) + z)) / c1, (y + z + w) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((w + (z + (x * c0 + y))) / c1, (y + z + w) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
rewrite((w + (z + (y + x * c0))) / c1, (y + z + w) / c1 + x * fold(c0 / c1), c0 % c1 == 0 && c1 > 0) ||
/** In (x + c0) / c1, when can we pull the constant
addition out of the numerator? An obvious answer is
the constant is a multiple of the denominator, but
there are other cases too. The condition for the
rewrite to be correct is:
(x + c0) / c1 == x / c1 + c2
Say we know (x + c0) = a_mod * y + a_rem
(a_mod * y + a_rem) / c1 == (a_mod * y + a_rem - c0) / c1 + c2
If a_mod % c1 == 0, we can subtract the term in y
from both sides and get:
a_rem / c1 == (a_rem - c0) / c1 + c2
c2 == a_rem / c1 - (a_rem - c0) / c1
This is a sufficient and necessary condition for the case when x_mod % c1 == 0.
*/
(no_overflow_int(op->type) &&
(rewrite((x + c0) / c1, x / c1 + fold(a_rem / c1 - (a_rem - c0) / c1), a_mod % c1 == 0) ||
/**
Now do the same thing for subtraction from a constant.
(c0 - x) / c1 == c2 - x / c1
where c0 - x == a_mod * y + a_rem
So x = c0 - a_mod * y - a_rem
(a_mod * y + a_rem) / c1 == c2 - (c0 - a_mod * y - a_rem) / c1
If a_mod % c1 == 0, we can pull that term out and cancel it:
a_rem / c1 == c2 - (c0 - a_rem) / c1
c2 == a_rem / c1 + (c0 - a_rem) / c1
*/
rewrite((c0 - x)/c1, fold(a_rem / c1 + (c0 - a_rem) / c1) - x / c1, a_mod % c1 == 0) ||
// We can also pull it out when the constant is a
// multiple of the denominator.
rewrite((x + c0) / c1, x / c1 + fold(c0 / c1), c0 % c1 == 0) ||
rewrite((c0 - x) / c1, fold(c0 / c1) - x / c1, (c0 + 1) % c1 == 0))) ||
(denominator_non_zero &&
(rewrite((x + y)/x, y/x + 1) ||
rewrite((y + x)/x, y/x + 1) ||
rewrite((x - y)/x, (-y)/x + 1) ||
rewrite((y - x)/x, y/x - 1) ||
rewrite(((x + y) + z)/x, (y + z)/x + 1) ||
rewrite(((y + x) + z)/x, (y + z)/x + 1) ||
rewrite((z + (x + y))/x, (z + y)/x + 1) ||
rewrite((z + (y + x))/x, (z + y)/x + 1) ||
rewrite((x*y)/x, y) ||
rewrite((y*x)/x, y) ||
rewrite((x*y + z)/x, y + z/x) ||
rewrite((y*x + z)/x, y + z/x) ||
rewrite((z + x*y)/x, z/x + y) ||
rewrite((z + y*x)/x, z/x + y) ||
rewrite((x*y - z)/x, y + (-z)/x) ||
rewrite((y*x - z)/x, y + (-z)/x) ||
rewrite((z - x*y)/x, z/x - y) ||
rewrite((z - y*x)/x, z/x - y) ||
false)) ||
(op->type.is_float() && rewrite(x/c0, x * fold(1/c0))))) ||
(no_overflow_int(op->type) &&
(
rewrite(ramp(x, c0, lanes) / broadcast(c1, lanes), ramp(x / c1, fold(c0 / c1), lanes), (c0 % c1 == 0)) ||
rewrite(ramp(x, c0, lanes) / broadcast(c1, lanes), broadcast(x / c1, lanes),
// First and last lanes are the same when...
can_prove((x % c1 + c0 * (lanes - 1)) / c1 == 0, this))
)) ||
(no_overflow_scalar_int(op->type) &&
(rewrite(x / -1, -x) ||
(denominator_non_zero && rewrite(c0 / y, select(y < 0, fold(-c0), c0), c0 == -1)) ||
rewrite((x * c0 + c1) / c2,
(x + fold(c1 / c0)) / fold(c2 / c0),
c2 > 0 && c0 > 0 && c2 % c0 == 0) ||
rewrite((x * c0 + c1) / c2,
x * fold(c0 / c2) + fold(c1 / c2),
c2 > 0 && c0 % c2 == 0) ||
// A very specific pattern that comes up in bounds in upsampling code.
rewrite((x % 2 + c0) / 2, x % 2 + fold(c0 / 2), c0 % 2 == 1))))) {
return mutate(rewrite.result, bounds);
}
// clang-format on
}
if (a.same_as(op->a) && b.same_as(op->b)) {
return op;
} else {
return Div::make(a, b);
}
}
} // namespace Internal
} // namespace Halide