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Fix APInt long division algorithm
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 llvm-svn: 235699
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Pawel Bylica
parent
60d2b0d189
commit
f959036c26
@ -1586,28 +1586,18 @@ static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
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// this step is actually negative, (u[j+n]...u[j]) should be left as the
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// true value plus b**(n+1), namely as the b's complement of
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// the true value, and a "borrow" to the left should be remembered.
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bool isNeg = false;
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int64_t borrow = 0;
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for (unsigned i = 0; i < n; ++i) {
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uint64_t u_tmp = (uint64_t(u[j+i+1]) << 32) | uint64_t(u[j+i]);
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uint64_t subtrahend = uint64_t(qp) * uint64_t(v[i]);
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bool borrow = subtrahend > u_tmp;
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DEBUG(dbgs() << "KnuthDiv: u_tmp = " << u_tmp
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<< ", subtrahend = " << subtrahend
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uint64_t p = uint64_t(qp) * uint64_t(v[i]);
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int64_t subres = int64_t(u[j+i]) - borrow - (unsigned)p;
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u[j+i] = (unsigned)subres;
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borrow = (p >> 32) - (subres >> 32);
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DEBUG(dbgs() << "KnuthDiv: u[j+i] = " << u[j+i]
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<< ", borrow = " << borrow << '\n');
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uint64_t result = u_tmp - subtrahend;
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unsigned k = j + i;
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u[k++] = (unsigned)result; // subtraction low word
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u[k++] = (unsigned)(result >> 32); // subtraction high word
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while (borrow && k <= m+n) { // deal with borrow to the left
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borrow = u[k] == 0;
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u[k]--;
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k++;
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}
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isNeg |= borrow;
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DEBUG(dbgs() << "KnuthDiv: u[j+i] = " << u[j+i]
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<< ", u[j+i+1] = " << u[j+i+1] << '\n');
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}
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bool isNeg = u[j+n] < borrow;
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u[j+n] -= (unsigned)borrow;
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DEBUG(dbgs() << "KnuthDiv: after subtraction:");
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DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
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DEBUG(dbgs() << '\n');
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@ -209,217 +209,101 @@ TEST(APIntTest, i1) {
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}
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}
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TEST(APIntTest, divrem_big1) {
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// Tests KnuthDiv rare step D6
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APInt a{256, "1ffffffffffffffff", 16};
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APInt b{256, "1ffffffffffffffff", 16};
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APInt c{256, 0};
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// Tests different div/rem varaints using scheme (a * b + c) / a
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void testDiv(APInt a, APInt b, APInt c) {
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ASSERT_TRUE(a.uge(b)); // Must: a >= b
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ASSERT_TRUE(a.ugt(c)); // Must: a > c
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auto p = a * b + c;
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auto q = p.udiv(a);
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auto r = p.urem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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EXPECT_EQ(b, q);
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EXPECT_EQ(c, r);
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APInt::udivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.udiv(b);
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r = p.urem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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APInt::udivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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EXPECT_EQ(b, q);
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EXPECT_EQ(c, r);
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q = p.sdiv(a);
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r = p.srem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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EXPECT_EQ(b, q);
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EXPECT_EQ(c, r);
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APInt::sdivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.sdiv(b);
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r = p.srem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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APInt::sdivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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EXPECT_EQ(b, q);
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EXPECT_EQ(c, r);
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if (b.ugt(c)) { // Test also symmetric case
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q = p.udiv(b);
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r = p.urem(b);
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EXPECT_EQ(a, q);
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EXPECT_EQ(c, r);
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APInt::udivrem(p, b, q, r);
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EXPECT_EQ(a, q);
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EXPECT_EQ(c, r);
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q = p.sdiv(b);
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r = p.srem(b);
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EXPECT_EQ(a, q);
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EXPECT_EQ(c, r);
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APInt::sdivrem(p, b, q, r);
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EXPECT_EQ(a, q);
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EXPECT_EQ(c, r);
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}
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}
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TEST(APIntTest, divrem_big1) {
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// Tests KnuthDiv rare step D6
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testDiv({256, "1ffffffffffffffff", 16},
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{256, "1ffffffffffffffff", 16},
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{256, 0});
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}
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TEST(APIntTest, divrem_big2) {
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// Tests KnuthDiv rare step D6
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APInt a{1024, "111111ffffffffffffffff"
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"ffffffffffffffffffffffffffffffff"
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"fffffffffffffffffffffffffffffccf"
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"ffffffffffffffffffffffffffffff00", 16};
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APInt b{1024, "112233ceff"
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"cecece000000ffffffffffffffffffff"
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"ffffffffffffffffffffffffffffffff"
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"ffffffffffffffffffffffffffffffff"
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"ffffffffffffffffffffffffffffff33", 16};
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APInt c{1024, 7919};
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auto p = a * b + c;
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auto q = p.udiv(a);
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auto r = p.urem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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APInt::udivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.udiv(b);
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r = p.urem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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APInt::udivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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q = p.sdiv(a);
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r = p.srem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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APInt::sdivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.sdiv(b);
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r = p.srem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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APInt::sdivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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testDiv({1024, "112233ceff"
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"cecece000000ffffffffffffffffffff"
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"ffffffffffffffffffffffffffffffff"
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"ffffffffffffffffffffffffffffffff"
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"ffffffffffffffffffffffffffffff33", 16},
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{1024, "111111ffffffffffffffff"
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"ffffffffffffffffffffffffffffffff"
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"fffffffffffffffffffffffffffffccf"
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"ffffffffffffffffffffffffffffff00", 16},
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{1024, 7919});
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}
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TEST(APIntTest, divrem_big3) {
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// Tests KnuthDiv case without shift
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APInt a{256, "ffffffffffffff0000000", 16};
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APInt b{256, "80000001ffffffffffffffff", 16};
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APInt c{256, 4219};
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auto p = a * b + c;
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auto q = p.udiv(a);
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auto r = p.urem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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APInt::udivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.udiv(b);
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r = p.urem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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APInt::udivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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q = p.sdiv(a);
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r = p.srem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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APInt::sdivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.sdiv(b);
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r = p.srem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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APInt::sdivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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testDiv({256, "80000001ffffffffffffffff", 16},
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{256, "ffffffffffffff0000000", 16},
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{256, 4219});
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}
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TEST(APIntTest, divrem_big4) {
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// Tests heap allocation in divide() enfoced by huge numbers
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auto a = APInt{4096, 1}.shl(2000);
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auto b = APInt{4096, 5}.shl(2001);
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auto c = APInt{4096, 4219*13};
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auto p = a * b + c;
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auto q = p.udiv(a);
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auto r = p.urem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = APInt{1024, 0}; // test non-single word APInt conversion in divide()
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r = APInt{1024, 0};
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APInt::udivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.udiv(b);
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r = p.urem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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q = APInt{1024, 0};
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r = APInt{1024, 0};
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APInt::udivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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q = p.sdiv(a);
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r = p.srem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = APInt{1024, 0};
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r = APInt{1024, 0};
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APInt::sdivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.sdiv(b);
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r = p.srem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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q = APInt{1024, 0};
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r = APInt{1024, 0};
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APInt::sdivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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testDiv(APInt{4096, 5}.shl(2001),
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APInt{4096, 1}.shl(2000),
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APInt{4096, 4219*13});
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}
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TEST(APIntTest, divrem_big5) {
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// Tests one word divisor case of divide()
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auto a = APInt{1024, 19}.shl(811);
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auto b = APInt{1024, 4356013}; // one word
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auto c = APInt{1024, 1};
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testDiv(APInt{1024, 19}.shl(811),
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APInt{1024, 4356013}, // one word
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APInt{1024, 1});
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}
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auto p = a * b + c;
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auto q = p.udiv(a);
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auto r = p.urem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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APInt::udivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.udiv(b);
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r = p.urem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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APInt::udivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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q = p.sdiv(a);
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r = p.srem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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APInt::sdivrem(p, a, q, r);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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q = p.sdiv(b);
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r = p.srem(b);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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APInt::sdivrem(p, b, q, r);
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EXPECT_EQ(q, a);
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EXPECT_EQ(r, c);
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TEST(APIntTest, divrem_big6) {
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// Tests some rare "borrow" cases in D4 step
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testDiv(APInt{512, "ffffffffffffffff00000000000000000000000001", 16},
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APInt{512, "10000000000000001000000000000001", 16},
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APInt{512, "10000000000000000000000000000000", 16});
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}
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TEST(APIntTest, divrem_big7) {
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// Yet another test for KnuthDiv rare step D6.
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APInt a{224, "800000008000000200000005", 16};
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APInt b{224, "fffffffd", 16};
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APInt c{224, "80000000800000010000000f", 16};
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auto p = a * b + c;
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auto q = p.udiv(a);
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auto r = p.urem(a);
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EXPECT_EQ(q, b);
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EXPECT_EQ(r, c);
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testDiv({224, "800000008000000200000005", 16},
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{224, "fffffffd", 16},
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{224, "80000000800000010000000f", 16});
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}
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TEST(APIntTest, fromString) {
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