8155043: BitMap set operations assume clear bits beyond unaligned end

Be more circumspect in handling of sets with unaligned sizes.

Reviewed-by: stefank, jmasa
This commit is contained in:
Kim Barrett 2016-08-14 21:19:42 -04:00
parent 6758f23018
commit ea503006dd
3 changed files with 536 additions and 83 deletions

View File

@ -376,77 +376,99 @@ void BitMap::par_at_put_large_range(idx_t beg, idx_t end, bool value) {
par_put_range_within_word(bit_index(end_full_word), end, value);
}
inline bm_word_t tail_mask(idx_t tail_bits) {
assert(tail_bits != 0, "precondition"); // Works, but shouldn't be called.
assert(tail_bits < (idx_t)BitsPerWord, "precondition");
return (bm_word_t(1) << tail_bits) - 1;
}
// Get the low tail_bits of value, which is the last partial word of a map.
inline bm_word_t tail_of_map(bm_word_t value, idx_t tail_bits) {
return value & tail_mask(tail_bits);
}
// Compute the new last word of a map with a non-aligned length.
// new_value has the new trailing bits of the map in the low tail_bits.
// old_value is the last word of the map, including bits beyond the end.
// Returns old_value with the low tail_bits replaced by the corresponding
// bits in new_value.
inline bm_word_t merge_tail_of_map(bm_word_t new_value,
bm_word_t old_value,
idx_t tail_bits) {
bm_word_t mask = tail_mask(tail_bits);
return (new_value & mask) | (old_value & ~mask);
}
bool BitMap::contains(const BitMap& other) const {
assert(size() == other.size(), "must have same size");
const bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size_in_words(); index++) {
bm_word_t word_union = dest_map[index] | other_map[index];
// If this has more bits set than dest_map[index], then other is not a
// subset.
if (word_union != dest_map[index]) return false;
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
// false if other bitmap has bits set which are clear in this bitmap.
if ((~dest_map[index] & other_map[index]) != 0) return false;
}
return true;
idx_t rest = bit_in_word(size());
// true unless there is a partial-word tail in which the other
// bitmap has bits set which are clear in this bitmap.
return (rest == 0) || tail_of_map(~dest_map[limit] & other_map[limit], rest) == 0;
}
bool BitMap::intersects(const BitMap& other) const {
assert(size() == other.size(), "must have same size");
const bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size_in_words(); index++) {
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
if ((dest_map[index] & other_map[index]) != 0) return true;
}
// Otherwise, no intersection.
return false;
idx_t rest = bit_in_word(size());
// false unless there is a partial-word tail with non-empty intersection.
return (rest > 0) && tail_of_map(dest_map[limit] & other_map[limit], rest) != 0;
}
void BitMap::set_union(const BitMap& other) {
assert(size() == other.size(), "must have same size");
bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size_in_words(); index++) {
dest_map[index] = dest_map[index] | other_map[index];
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
dest_map[index] |= other_map[index];
}
idx_t rest = bit_in_word(size());
if (rest > 0) {
bm_word_t orig = dest_map[limit];
dest_map[limit] = merge_tail_of_map(orig | other_map[limit], orig, rest);
}
}
void BitMap::set_difference(const BitMap& other) {
assert(size() == other.size(), "must have same size");
bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size_in_words(); index++) {
dest_map[index] = dest_map[index] & ~(other_map[index]);
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
dest_map[index] &= ~other_map[index];
}
idx_t rest = bit_in_word(size());
if (rest > 0) {
bm_word_t orig = dest_map[limit];
dest_map[limit] = merge_tail_of_map(orig & ~other_map[limit], orig, rest);
}
}
void BitMap::set_intersection(const BitMap& other) {
assert(size() == other.size(), "must have same size");
bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size; index++) {
dest_map[index] = dest_map[index] & other_map[index];
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
dest_map[index] &= other_map[index];
}
}
void BitMap::set_intersection_at_offset(const BitMap& other, idx_t offset) {
assert(other.size() >= offset, "offset not in range");
assert(other.size() - offset >= size(), "other not large enough");
// XXX Ideally, we would remove this restriction.
guarantee((offset % (sizeof(bm_word_t) * BitsPerByte)) == 0,
"Only handle aligned cases so far.");
bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t offset_word_ind = word_index(offset);
idx_t size = size_in_words();
for (idx_t index = 0; index < size; index++) {
dest_map[index] = dest_map[index] & other_map[offset_word_ind + index];
idx_t rest = bit_in_word(size());
if (rest > 0) {
bm_word_t orig = dest_map[limit];
dest_map[limit] = merge_tail_of_map(orig & other_map[limit], orig, rest);
}
}
@ -455,88 +477,111 @@ bool BitMap::set_union_with_result(const BitMap& other) {
bool changed = false;
bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size; index++) {
idx_t temp = dest_map[index] | other_map[index];
changed = changed || (temp != dest_map[index]);
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
bm_word_t orig = dest_map[index];
bm_word_t temp = orig | other_map[index];
changed = changed || (temp != orig);
dest_map[index] = temp;
}
idx_t rest = bit_in_word(size());
if (rest > 0) {
bm_word_t orig = dest_map[limit];
bm_word_t temp = merge_tail_of_map(orig | other_map[limit], orig, rest);
changed = changed || (temp != orig);
dest_map[limit] = temp;
}
return changed;
}
bool BitMap::set_difference_with_result(const BitMap& other) {
assert(size() == other.size(), "must have same size");
bool changed = false;
bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size; index++) {
bm_word_t temp = dest_map[index] & ~(other_map[index]);
changed = changed || (temp != dest_map[index]);
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
bm_word_t orig = dest_map[index];
bm_word_t temp = orig & ~other_map[index];
changed = changed || (temp != orig);
dest_map[index] = temp;
}
idx_t rest = bit_in_word(size());
if (rest > 0) {
bm_word_t orig = dest_map[limit];
bm_word_t temp = merge_tail_of_map(orig & ~other_map[limit], orig, rest);
changed = changed || (temp != orig);
dest_map[limit] = temp;
}
return changed;
}
bool BitMap::set_intersection_with_result(const BitMap& other) {
assert(size() == other.size(), "must have same size");
bool changed = false;
bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size; index++) {
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
bm_word_t orig = dest_map[index];
bm_word_t temp = orig & other_map[index];
changed = changed || (temp != orig);
dest_map[index] = temp;
dest_map[index] = temp;
}
idx_t rest = bit_in_word(size());
if (rest > 0) {
bm_word_t orig = dest_map[limit];
bm_word_t temp = merge_tail_of_map(orig & other_map[limit], orig, rest);
changed = changed || (temp != orig);
dest_map[limit] = temp;
}
return changed;
}
void BitMap::set_from(const BitMap& other) {
assert(size() == other.size(), "must have same size");
bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size; index++) {
dest_map[index] = other_map[index];
idx_t copy_words = word_index(size());
Copy::disjoint_words((HeapWord*)other_map, (HeapWord*)dest_map, copy_words);
idx_t rest = bit_in_word(size());
if (rest > 0) {
dest_map[copy_words] = merge_tail_of_map(other_map[copy_words],
dest_map[copy_words],
rest);
}
}
bool BitMap::is_same(const BitMap& other) {
bool BitMap::is_same(const BitMap& other) const {
assert(size() == other.size(), "must have same size");
bm_word_t* dest_map = map();
const bm_word_t* dest_map = map();
const bm_word_t* other_map = other.map();
idx_t size = size_in_words();
for (idx_t index = 0; index < size; index++) {
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
if (dest_map[index] != other_map[index]) return false;
}
return true;
idx_t rest = bit_in_word(size());
return (rest == 0) || (tail_of_map(dest_map[limit] ^ other_map[limit], rest) == 0);
}
bool BitMap::is_full() const {
const bm_word_t* word = map();
idx_t rest = size();
for (; rest >= (idx_t) BitsPerWord; rest -= BitsPerWord) {
if (*word != ~(bm_word_t)0) return false;
word++;
const bm_word_t* words = map();
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
if (~words[index] != 0) return false;
}
return rest == 0 || (*word | ~right_n_bits((int)rest)) == ~(bm_word_t)0;
idx_t rest = bit_in_word(size());
return (rest == 0) || (tail_of_map(~words[limit], rest) == 0);
}
bool BitMap::is_empty() const {
const bm_word_t* word = map();
idx_t rest = size();
for (; rest >= (idx_t) BitsPerWord; rest -= BitsPerWord) {
if (*word != 0) return false;
word++;
const bm_word_t* words = map();
idx_t limit = word_index(size());
for (idx_t index = 0; index < limit; ++index) {
if (words[index] != 0) return false;
}
return rest == 0 || (*word & right_n_bits((int)rest)) == 0;
idx_t rest = bit_in_word(size());
return (rest == 0) || (tail_of_map(words[limit], rest) == 0);
}
void BitMap::clear_large() {

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@ -284,18 +284,9 @@ class BitMap VALUE_OBJ_CLASS_SPEC {
bool set_difference_with_result(const BitMap& bits);
bool set_intersection_with_result(const BitMap& bits);
// Requires the submap of "bits" starting at offset to be at least as
// large as "this". Modifies "this" to be the intersection of its
// current contents and the submap of "bits" starting at "offset" of the
// same length as "this."
// (For expedience, currently requires the offset to be aligned to the
// bitsize of a uintptr_t. This should go away in the future though it
// will probably remain a good case to optimize.)
void set_intersection_at_offset(const BitMap& bits, idx_t offset);
void set_from(const BitMap& bits);
bool is_same(const BitMap& bits);
bool is_same(const BitMap& bits) const;
// Test if all bits are set or cleared
bool is_full() const;

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@ -0,0 +1,417 @@
/*
* Copyright (c) 2016, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*
*/
#include "precompiled.hpp"
#include "utilities/bitMap.inline.hpp"
#include "utilities/copy.hpp"
#include "utilities/debug.hpp"
#include "utilities/globalDefinitions.hpp"
#include <stdlib.h>
#include "unittest.hpp"
typedef BitMap::idx_t idx_t;
typedef BitMap::bm_word_t bm_word_t;
class BitMapMemory {
private:
idx_t _words;
bm_word_t* _memory;
public:
BitMapMemory(idx_t bits) :
_words(BitMap::calc_size_in_words(bits)),
_memory(static_cast<bm_word_t*>(malloc(_words * sizeof(bm_word_t))))
{ }
~BitMapMemory() {
free(_memory);
}
BitMapView make_view(idx_t bits, bm_word_t value) {
vmassert(BitMap::calc_size_in_words(bits) <= _words, "invalid request");
STATIC_ASSERT(sizeof(bm_word_t) == sizeof(HeapWord));
Copy::fill_to_aligned_words((HeapWord*)_memory, _words, value);
return BitMapView(_memory, bits);
}
bm_word_t* memory() { return _memory; }
};
const idx_t aligned_size = 4 * BitsPerWord;
const idx_t unaligned_size = aligned_size - (BitsPerWord / 2);
static bm_word_t make_even_bits() {
bm_word_t result = 1;
while (true) {
bm_word_t next = (result << 2) | 1;
if (next == result) {
return result;
}
result = next;
}
}
const bm_word_t even_bits = make_even_bits();
const bm_word_t odd_bits = ~even_bits;
const bm_word_t one_bits = ~bm_word_t(0);
const bm_word_t zero_bits = 0;
// Scoped set a clear bit and restore to clear.
class WithBitSet {
private:
BitMap& _bm;
idx_t _index;
public:
WithBitSet(BitMap& bm, idx_t index) : _bm(bm), _index(index) {
// Failure may indicate test bug; can't use ASSERT_xxx in constructor.
EXPECT_FALSE(_bm.at(_index));
bm.set_bit(_index);
}
~WithBitSet() {
_bm.clear_bit(_index);
}
};
// Scoped clear a set bit and restore to set.
class WithBitClear {
private:
BitMap& _bm;
idx_t _index;
public:
WithBitClear(BitMap& bm, idx_t index) : _bm(bm), _index(index) {
// Failure may indicate test bug; can't use ASSERT_xxx in constructor.
EXPECT_TRUE(_bm.at(_index));
bm.clear_bit(_index);
}
~WithBitClear() {
_bm.set_bit(_index);
}
};
//////////////////////////////////////////////////////////////////////////////
// bool is_same(const BitMap& bits);
TEST(BitMap, is_same__aligned) {
BitMapMemory mx(aligned_size);
BitMapMemory my(aligned_size);
BitMapView x = mx.make_view(aligned_size, even_bits);
BitMapView y = my.make_view(aligned_size, even_bits);
EXPECT_TRUE(x.is_same(y));
WithBitClear wbc(x, aligned_size / 2);
EXPECT_FALSE(x.is_same(y));
}
TEST(BitMap, is_same__unaligned) {
BitMapMemory mx(aligned_size);
BitMapMemory my(aligned_size);
BitMapView x = mx.make_view(unaligned_size, even_bits);
BitMapView y = my.make_view(unaligned_size, even_bits);
// Check that a difference beyond the end of x/y doesn't count.
{
BitMapView aligned = BitMapView(mx.memory(), aligned_size);
const idx_t index = aligned_size - 2;
STATIC_ASSERT(unaligned_size <= index);
WithBitClear wbc(aligned, index);
EXPECT_TRUE(x.is_same(y));
}
// Check that a difference in the final partial word does count.
{
idx_t index = unaligned_size - 2;
ASSERT_LE(BitMap::word_align_down(unaligned_size), index);
WithBitClear wbc(y, index);
EXPECT_FALSE(x.is_same(y));
}
}
//////////////////////////////////////////////////////////////////////////////
// bool is_full();
// bool is_empty();
TEST(BitMap, is_full_or_empty__aligned) {
BitMapMemory mx(aligned_size);
{
BitMapView x = mx.make_view(aligned_size, even_bits);
EXPECT_FALSE(x.is_full());
EXPECT_FALSE(x.is_empty());
}
{
BitMapView x = mx.make_view(aligned_size, zero_bits);
EXPECT_FALSE(x.is_full());
EXPECT_TRUE(x.is_empty());
}
{
BitMapView x = mx.make_view(aligned_size, one_bits);
EXPECT_TRUE(x.is_full());
EXPECT_FALSE(x.is_empty());
}
}
TEST(BitMap, is_full__unaligned) {
BitMapMemory mx(aligned_size);
BitMapView x = mx.make_view(unaligned_size, one_bits);
EXPECT_TRUE(x.is_full());
// Check that a missing bit beyond the end doesn't count.
{
idx_t index = aligned_size - 1;
BitMapView aligned = BitMapView(mx.memory(), aligned_size);
WithBitClear wcb(aligned, index);
EXPECT_FALSE(aligned.is_full());
EXPECT_TRUE(x.is_full());
}
// Check that a missing bit in the final partial word does count.
{
WithBitClear wcb(x, unaligned_size - 1);
EXPECT_FALSE(x.is_full());
}
}
TEST(BitMap, is_empty__unaligned) {
BitMapMemory mx(aligned_size);
BitMapView x = mx.make_view(unaligned_size, zero_bits);
EXPECT_TRUE(x.is_empty());
// Check that a set bit beyond the end doesn't count.
{
idx_t index = aligned_size - 1;
BitMapView aligned = BitMapView(mx.memory(), aligned_size);
WithBitSet wbs(aligned, index);
EXPECT_FALSE(aligned.is_empty());
EXPECT_TRUE(x.is_empty());
}
// Check that a set bit in the final partial word does count.
{
WithBitSet wbs(x, unaligned_size - 1);
EXPECT_FALSE(x.is_empty());
}
}
//////////////////////////////////////////////////////////////////////////////
// bool contains(const BitMap& bits);
TEST(BitMap, contains__aligned) {
BitMapMemory mx(aligned_size);
BitMapMemory my(aligned_size);
BitMapView x = mx.make_view(aligned_size, even_bits);
BitMapView y = my.make_view(aligned_size, even_bits);
EXPECT_TRUE(x.contains(y));
WithBitClear wbc(x, aligned_size / 2);
EXPECT_FALSE(x.contains(y));
}
TEST(BitMap, contains__unaligned) {
BitMapMemory mx(aligned_size);
BitMapMemory my(aligned_size);
BitMapView x = mx.make_view(unaligned_size, even_bits);
BitMapView y = my.make_view(unaligned_size, even_bits);
// Check that a missing bit beyond the end of x doesn't count.
{
BitMapView aligned = BitMapView(mx.memory(), aligned_size);
const idx_t index = aligned_size - 2;
STATIC_ASSERT(unaligned_size <= index);
WithBitClear wbc(aligned, index);
EXPECT_TRUE(x.contains(y));
}
// Check that a missing bit in the final partial word does count.
{
idx_t index = unaligned_size - 2;
ASSERT_LE(BitMap::word_align_down(unaligned_size), index);
WithBitClear wbc(x, index);
EXPECT_FALSE(x.contains(y));
}
}
//////////////////////////////////////////////////////////////////////////////
// bool intersects(const BitMap& bits);
TEST(BitMap, intersects__aligned) {
BitMapMemory mx(aligned_size);
BitMapMemory my(aligned_size);
BitMapView x = mx.make_view(aligned_size, even_bits);
BitMapView y = my.make_view(aligned_size, zero_bits);
EXPECT_FALSE(x.intersects(y));
ASSERT_TRUE(x.at(aligned_size / 2));
WithBitSet wbs(y, aligned_size / 2);
EXPECT_TRUE(x.intersects(y));
}
TEST(BitMap, intersects__unaligned) {
BitMapMemory mx(aligned_size);
BitMapMemory my(aligned_size);
BitMapView x = mx.make_view(unaligned_size, even_bits);
BitMapView y = my.make_view(unaligned_size, zero_bits);
EXPECT_FALSE(x.intersects(y));
// Check that adding a bit beyond the end of y doesn't count.
{
BitMapView aligned_x = BitMapView(mx.memory(), aligned_size);
BitMapView aligned_y = BitMapView(my.memory(), aligned_size);
const idx_t index = aligned_size - 2;
STATIC_ASSERT(unaligned_size <= index);
ASSERT_TRUE(aligned_x.at(index));
WithBitSet wbs(aligned_y, index);
EXPECT_FALSE(x.intersects(y));
}
// Check that adding a bit in the final partial word does count.
{
idx_t index = unaligned_size - 2;
ASSERT_LE(BitMap::word_align_down(unaligned_size), index);
ASSERT_TRUE(x.at(index));
WithBitSet wbs(y, index);
EXPECT_TRUE(x.intersects(y));
}
}
//////////////////////////////////////////////////////////////////////////////
// void set_from(const BitMap& bits);
// void set_union(const BitMap& bits);
// void set_difference(const BitMap& bits);
// void set_intersection(const BitMap& bits);
//
// bool set_union_with_result(const BitMap& bits);
// bool set_difference_with_result(const BitMap& bits);
// bool set_intersection_with_result(const BitMap& bits);
static void check_tail_unmodified(BitMapMemory& mem,
idx_t bits,
bm_word_t fill_word) {
if (!BitMap::is_word_aligned(bits)) {
idx_t last_word_bit_index = BitMap::word_align_down(bits);
idx_t last_word_index = BitMap::calc_size_in_words(last_word_bit_index);
bm_word_t last_word = mem.memory()[last_word_index];
idx_t shift = bits - last_word_bit_index;
EXPECT_EQ(fill_word >> shift, last_word >> shift);
}
}
static void check_mod_setop(void (BitMap::*f)(const BitMap&),
idx_t bits,
bm_word_t wx,
bm_word_t wy,
bm_word_t wexp) {
BitMapMemory mx(bits);
BitMapMemory my(bits);
BitMapMemory mexp(bits);
BitMapView x = mx.make_view(bits, wx);
BitMapView y = my.make_view(bits, wy);
BitMapView exp = mexp.make_view(bits, wexp);
(x.*f)(y);
EXPECT_TRUE(exp.is_same(x));
check_tail_unmodified(mx, bits, wx);
}
static void check_mod_setop_with_result(bool (BitMap::*f)(const BitMap&),
idx_t bits,
bm_word_t wx,
bm_word_t wy,
bm_word_t wexp) {
BitMapMemory mx(bits);
BitMapMemory my(bits);
BitMapMemory mexp(bits);
BitMapView x = mx.make_view(bits, wx);
BitMapView y = my.make_view(bits, wy);
BitMapView exp = mexp.make_view(bits, wexp);
bool value = (x.*f)(y);
EXPECT_EQ(value, wx != wexp);
EXPECT_TRUE(exp.is_same(x));
check_tail_unmodified(mx, bits, wx);
}
#define CHECK_MOD_SETOP_AUX(checker, name, x, y, exp) \
TEST(BitMap, name ## __ ## x ## _ ## y) { \
checker(&BitMap::name, aligned_size, \
x ## _bits, y ## _bits, exp ## _bits); \
checker(&BitMap::name, unaligned_size, \
x ## _bits, y ## _bits, exp ## _bits); \
}
#define CHECK_MOD_SETOP(name, x, y, exp) \
CHECK_MOD_SETOP_AUX(check_mod_setop, name, x, y, exp)
#define CHECK_MOD_SETOP_WITH_RESULT(name, x, y, exp) \
CHECK_MOD_SETOP_AUX(check_mod_setop_with_result, name, x, y, exp)
#define CHECK_MOD_SETOPS(name, x, y, exp) \
CHECK_MOD_SETOP(name, x, y, exp) \
CHECK_MOD_SETOP_WITH_RESULT(name ## _with_result, x, y, exp)
CHECK_MOD_SETOP(set_from, even, even, even)
CHECK_MOD_SETOP(set_from, even, odd, odd)
CHECK_MOD_SETOP(set_from, even, one, one)
CHECK_MOD_SETOP(set_from, even, zero, zero)
CHECK_MOD_SETOPS(set_union, even, even, even)
CHECK_MOD_SETOPS(set_union, even, odd, one)
CHECK_MOD_SETOPS(set_union, even, one, one)
CHECK_MOD_SETOPS(set_union, even, zero, even)
CHECK_MOD_SETOPS(set_difference, even, even, zero)
CHECK_MOD_SETOPS(set_difference, even, odd, even)
CHECK_MOD_SETOPS(set_difference, even, one, zero)
CHECK_MOD_SETOPS(set_difference, even, zero, even)
CHECK_MOD_SETOPS(set_intersection, even, even, even)
CHECK_MOD_SETOPS(set_intersection, even, odd, zero)
CHECK_MOD_SETOPS(set_intersection, even, one, even)
CHECK_MOD_SETOPS(set_intersection, even, zero, zero)