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Fix rare case where APInt divide algorithm applied un-needed transformation.

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APInt uses Knuth's D algorithm for long division. In rare cases the
implementation applied a transformation that was not needed.

Added unit tests for long division. KnuthDiv() procedure is fully covered.
There is a case in APInt::divide() that I believe is never used (marked with
a comment) as all users of divide() handle trivial cases earlier.

Patch by Pawel Bylica!

  http://reviews.llvm.org/D8448

llvm-svn: 233312
This commit is contained in:
Yaron Keren 2015-03-26 19:45:19 +00:00
parent d429dd288c
commit 7c2f11d4be
2 changed files with 219 additions and 34 deletions
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53
lib/Support/APInt.cpp
View File

@ -1511,21 +1511,18 @@ static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
assert(u && "Must provide dividend");
assert(v && "Must provide divisor");
assert(q && "Must provide quotient");
assert(u != v && u != q && v != q && "Must us different memory");
assert(u != v && u != q && v != q && "Must use different memory");
assert(n>1 && "n must be > 1");
// Knuth uses the value b as the base of the number system. In our case b
// is 2^31 so we just set it to -1u.
uint64_t b = uint64_t(1) << 32;
// b denotes the base of the number system. In our case b is 2^32.
LLVM_CONSTEXPR uint64_t b = uint64_t(1) << 32;
#if 0
DEBUG(dbgs() << "KnuthDiv: m=" << m << " n=" << n << '\n');
DEBUG(dbgs() << "KnuthDiv: original:");
DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
DEBUG(dbgs() << " by");
DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
DEBUG(dbgs() << '\n');
#endif
// D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
// u and v by d. Note that we have taken Knuth's advice here to use a power
// of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
@ -1550,13 +1547,12 @@ static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
}
}
u[m+n] = u_carry;
#if 0
DEBUG(dbgs() << "KnuthDiv: normal:");
DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
DEBUG(dbgs() << " by");
DEBUG(for (int i = n; i >0; i--) dbgs() << " " << v[i-1]);
DEBUG(dbgs() << '\n');
#endif
// D2. [Initialize j.] Set j to m. This is the loop counter over the places.
int j = m;
@ -1586,46 +1582,35 @@ static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
// (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
// consists of a simple multiplication by a one-place number, combined with
// a subtraction.
// The digits (u[j+n]...u[j]) should be kept positive; if the result of
// 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;
for (unsigned i = 0; i < n; ++i) {
uint64_t u_tmp = uint64_t(u[j+i]) | (uint64_t(u[j+i+1]) << 32);
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
DEBUG(dbgs() << "KnuthDiv: u_tmp = " << u_tmp
<< ", subtrahend = " << subtrahend
<< ", borrow = " << borrow << '\n');
uint64_t result = u_tmp - subtrahend;
unsigned k = j + i;
u[k++] = (unsigned)(result & (b-1)); // subtract low word
u[k++] = (unsigned)(result >> 32); // subtract high word
while (borrow && k <= m+n) { // deal with borrow to the left
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');
DEBUG(dbgs() << "KnuthDiv: u[j+i] = " << u[j+i]
<< ", u[j+i+1] = " << u[j+i+1] << '\n');
}
DEBUG(dbgs() << "KnuthDiv: after subtraction:");
DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
DEBUG(dbgs() << '\n');
// The digits (u[j+n]...u[j]) should be kept positive; if the result of
// 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.
//
if (isNeg) {
bool carry = true; // true because b's complement is "complement + 1"
for (unsigned i = 0; i <= m+n; ++i) {
u[i] = ~u[i] + carry; // b's complement
carry = carry && u[i] == 0;
}
}
DEBUG(dbgs() << "KnuthDiv: after complement:");
DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
DEBUG(dbgs() << '\n');
// D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
// negative, go to step D6; otherwise go on to step D7.
@ -1647,7 +1632,7 @@ static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
u[j+n] += carry;
}
DEBUG(dbgs() << "KnuthDiv: after correction:");
DEBUG(for (int i = m+n; i >=0; i--) dbgs() <<" " << u[i]);
DEBUG(for (int i = m+n; i >=0; i--) dbgs() << " " << u[i]);
DEBUG(dbgs() << "\nKnuthDiv: digit result = " << q[j] << '\n');
// D7. [Loop on j.] Decrease j by one. Now if j >= 0, go back to D3.
@ -1680,9 +1665,7 @@ static void KnuthDiv(unsigned *u, unsigned *v, unsigned *q, unsigned* r,
}
DEBUG(dbgs() << '\n');
}
#if 0
DEBUG(dbgs() << '\n');
#endif
}
void APInt::divide(const APInt LHS, unsigned lhsWords,
@ -1806,6 +1789,8 @@ void APInt::divide(const APInt LHS, unsigned lhsWords,
// The quotient is in Q. Reconstitute the quotient into Quotient's low
// order words.
// This case is currently dead as all users of divide() handle trivial cases
// earlier.
if (lhsWords == 1) {
uint64_t tmp =
uint64_t(Q[0]) | (uint64_t(Q[1]) << (APINT_BITS_PER_WORD / 2));

200
unittests/ADT/APIntTest.cpp
View File

@ -209,6 +209,206 @@ 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};
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_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);
}
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);
}
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);
}
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};
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, fromString) {
EXPECT_EQ(APInt(32, 0), APInt(32, "0", 2));
EXPECT_EQ(APInt(32, 1), APInt(32, "1", 2));