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Fix APInt long division algorithm

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Summary: This patch fixes step D4 of Knuth's division algorithm implementation. Negative sign of the step result was not always detected due to incorrect "borrow" handling.

Test Plan: Unit test that reveals the bug included.

Reviewers: chandlerc, yaron.keren

Reviewed By: yaron.keren

Subscribers: llvm-commits

Differential Revision: http://reviews.llvm.org/D9196

git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@235699 91177308-0d34-0410-b5e6-96231b3b80d8
This commit is contained in:
Pawel Bylica 2015-04-24 07:38:39 +00:00
parent a9a01d9879
commit 9ee9f1a334
2 changed files with 75 additions and 201 deletions
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28
lib/Support/APInt.cpp
View File

@ -1586,28 +1586,18 @@ static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
// this step is actually negative, (u[j+n]...u[j]) should be left as the
// true value plus b**(n+1), namely as the b's complement of
// the true value, and a "borrow" to the left should be remembered.
bool isNeg = false;
int64_t borrow = 0;
for (unsigned i = 0; i < n; ++i) {
uint64_t u_tmp = (uint64_t(u[j+i+1]) << 32) | uint64_t(u[j+i]);
uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
bool borrow = subtrahend > u_tmp;
DEBUG(dbgs() << "KnuthDiv: u_tmp = " << u_tmp
<< ", subtrahend = " << subtrahend
uint64_t p = uint64_t(qp) * uint64_t(v[i]);
int64_t subres = int64_t(u[j+i]) - borrow - (unsigned)p;
u[j+i] = (unsigned)subres;
borrow = (p >> 32) - (subres >> 32);
DEBUG(dbgs() << "KnuthDiv: u[j+i] = " << u[j+i]
<< ", borrow = " << borrow << '\n');
uint64_t result = u_tmp - subtrahend;
unsigned k = j + i;
u[k++] = (unsigned)result; // subtraction low word
u[k++] = (unsigned)(result >> 32); // subtraction high word
while (borrow && k <= m+n) { // deal with borrow to the left
borrow = u[k] == 0;
u[k]--;
k++;
}
isNeg |= borrow;
DEBUG(dbgs() << "KnuthDiv: u[j+i] = " << u[j+i]
<< ", u[j+i+1] = " << u[j+i+1] << '\n');
}
bool isNeg = u[j+n] < borrow;
u[j+n] -= (unsigned)borrow;
DEBUG(dbgs() << "KnuthDiv: after subtraction:");
DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
DEBUG(dbgs() << '\n');

248
unittests/ADT/APIntTest.cpp
View File

@ -209,217 +209,101 @@ TEST(APIntTest, i1) {
}
}
TEST(APIntTest, divrem_big1) {
// Tests KnuthDiv rare step D6
APInt a{256, "1ffffffffffffffff", 16};
APInt b{256, "1ffffffffffffffff", 16};
APInt c{256, 0};
// Tests different div/rem varaints using scheme (a * b + c) / a
void testDiv(APInt a, APInt b, APInt c) {
ASSERT_TRUE(a.uge(b)); // Must: a >= b
ASSERT_TRUE(a.ugt(c)); // Must: a > c
auto p = a * b + c;
auto q = p.udiv(a);
auto r = p.urem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
EXPECT_EQ(b, q);
EXPECT_EQ(c, r);
APInt::udivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.udiv(b);
r = p.urem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
APInt::udivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
EXPECT_EQ(b, q);
EXPECT_EQ(c, r);
q = p.sdiv(a);
r = p.srem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
EXPECT_EQ(b, q);
EXPECT_EQ(c, r);
APInt::sdivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.sdiv(b);
r = p.srem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
APInt::sdivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
EXPECT_EQ(b, q);
EXPECT_EQ(c, r);
if (b.ugt(c)) { // Test also symmetric case
q = p.udiv(b);
r = p.urem(b);
EXPECT_EQ(a, q);
EXPECT_EQ(c, r);
APInt::udivrem(p, b, q, r);
EXPECT_EQ(a, q);
EXPECT_EQ(c, r);
q = p.sdiv(b);
r = p.srem(b);
EXPECT_EQ(a, q);
EXPECT_EQ(c, r);
APInt::sdivrem(p, b, q, r);
EXPECT_EQ(a, q);
EXPECT_EQ(c, r);
}
}
TEST(APIntTest, divrem_big1) {
// Tests KnuthDiv rare step D6
testDiv({256, "1ffffffffffffffff", 16},
{256, "1ffffffffffffffff", 16},
{256, 0});
}
TEST(APIntTest, divrem_big2) {
// Tests KnuthDiv rare step D6
APInt a{1024, "111111ffffffffffffffff"
"ffffffffffffffffffffffffffffffff"
"fffffffffffffffffffffffffffffccf"
"ffffffffffffffffffffffffffffff00", 16};
APInt b{1024, "112233ceff"
"cecece000000ffffffffffffffffffff"
"ffffffffffffffffffffffffffffffff"
"ffffffffffffffffffffffffffffffff"
"ffffffffffffffffffffffffffffff33", 16};
APInt c{1024, 7919};
auto p = a * b + c;
auto q = p.udiv(a);
auto r = p.urem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
APInt::udivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.udiv(b);
r = p.urem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
APInt::udivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
q = p.sdiv(a);
r = p.srem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
APInt::sdivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.sdiv(b);
r = p.srem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
APInt::sdivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
testDiv({1024, "112233ceff"
"cecece000000ffffffffffffffffffff"
"ffffffffffffffffffffffffffffffff"
"ffffffffffffffffffffffffffffffff"
"ffffffffffffffffffffffffffffff33", 16},
{1024, "111111ffffffffffffffff"
"ffffffffffffffffffffffffffffffff"
"fffffffffffffffffffffffffffffccf"
"ffffffffffffffffffffffffffffff00", 16},
{1024, 7919});
}
TEST(APIntTest, divrem_big3) {
// Tests KnuthDiv case without shift
APInt a{256, "ffffffffffffff0000000", 16};
APInt b{256, "80000001ffffffffffffffff", 16};
APInt c{256, 4219};
auto p = a * b + c;
auto q = p.udiv(a);
auto r = p.urem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
APInt::udivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.udiv(b);
r = p.urem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
APInt::udivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
q = p.sdiv(a);
r = p.srem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
APInt::sdivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.sdiv(b);
r = p.srem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
APInt::sdivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
testDiv({256, "80000001ffffffffffffffff", 16},
{256, "ffffffffffffff0000000", 16},
{256, 4219});
}
TEST(APIntTest, divrem_big4) {
// Tests heap allocation in divide() enfoced by huge numbers
auto a = APInt{4096, 1}.shl(2000);
auto b = APInt{4096, 5}.shl(2001);
auto c = APInt{4096, 4219*13};
auto p = a * b + c;
auto q = p.udiv(a);
auto r = p.urem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = APInt{1024, 0}; // test non-single word APInt conversion in divide()
r = APInt{1024, 0};
APInt::udivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.udiv(b);
r = p.urem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
q = APInt{1024, 0};
r = APInt{1024, 0};
APInt::udivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
q = p.sdiv(a);
r = p.srem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = APInt{1024, 0};
r = APInt{1024, 0};
APInt::sdivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.sdiv(b);
r = p.srem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
q = APInt{1024, 0};
r = APInt{1024, 0};
APInt::sdivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
testDiv(APInt{4096, 5}.shl(2001),
APInt{4096, 1}.shl(2000),
APInt{4096, 4219*13});
}
TEST(APIntTest, divrem_big5) {
// Tests one word divisor case of divide()
auto a = APInt{1024, 19}.shl(811);
auto b = APInt{1024, 4356013}; // one word
auto c = APInt{1024, 1};
testDiv(APInt{1024, 19}.shl(811),
APInt{1024, 4356013}, // one word
APInt{1024, 1});
}
auto p = a * b + c;
auto q = p.udiv(a);
auto r = p.urem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
APInt::udivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.udiv(b);
r = p.urem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
APInt::udivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
q = p.sdiv(a);
r = p.srem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
APInt::sdivrem(p, a, q, r);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
q = p.sdiv(b);
r = p.srem(b);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
APInt::sdivrem(p, b, q, r);
EXPECT_EQ(q, a);
EXPECT_EQ(r, c);
TEST(APIntTest, divrem_big6) {
// Tests some rare "borrow" cases in D4 step
testDiv(APInt{512, "ffffffffffffffff00000000000000000000000001", 16},
APInt{512, "10000000000000001000000000000001", 16},
APInt{512, "10000000000000000000000000000000", 16});
}
TEST(APIntTest, divrem_big7) {
// Yet another test for KnuthDiv rare step D6.
APInt a{224, "800000008000000200000005", 16};
APInt b{224, "fffffffd", 16};
APInt c{224, "80000000800000010000000f", 16};
auto p = a * b + c;
auto q = p.udiv(a);
auto r = p.urem(a);
EXPECT_EQ(q, b);
EXPECT_EQ(r, c);
testDiv({224, "800000008000000200000005", 16},
{224, "fffffffd", 16},
{224, "80000000800000010000000f", 16});
}
TEST(APIntTest, fromString) {