#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