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Implement add_compare

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This commit is contained in:
Victor Zverovich 2019-10-13 07:08:39 -07:00
parent 3a15ea3ea5
commit 5e58eb97b1
2 changed files with 84 additions and 21 deletions
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79
include/fmt/format-inl.h
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@ -534,17 +534,15 @@ class bigint {
int num_lhs_bigits = lhs.num_bigits(), num_rhs_bigits = rhs.num_bigits();
if (num_lhs_bigits != num_rhs_bigits)
return num_lhs_bigits > num_rhs_bigits ? 1 : -1;
int lhs_bigit_index = static_cast<int>(lhs.bigits_.size()) - 1;
int rhs_bigit_index = static_cast<int>(rhs.bigits_.size()) - 1;
int end = lhs_bigit_index - rhs_bigit_index;
int i = static_cast<int>(lhs.bigits_.size()) - 1;
int j = static_cast<int>(rhs.bigits_.size()) - 1;
int end = i - j;
if (end < 0) end = 0;
for (; lhs_bigit_index >= end; --lhs_bigit_index, --rhs_bigit_index) {
bigit lhs_bigit = lhs.bigits_[lhs_bigit_index];
bigit rhs_bigit = rhs.bigits_[rhs_bigit_index];
for (; i >= end; --i, --j) {
bigit lhs_bigit = lhs.bigits_[i], rhs_bigit = rhs.bigits_[j];
if (lhs_bigit != rhs_bigit) return lhs_bigit > rhs_bigit ? 1 : -1;
}
if (lhs_bigit_index != rhs_bigit_index)
return lhs_bigit_index > rhs_bigit_index ? 1 : -1;
if (i != j) return i > j ? 1 : -1;
return 0;
}
@ -605,6 +603,30 @@ class bigint {
return compare(lhs, rhs) >= 0;
}
// Returns compare(lhs1 + lhs2, rhs).
friend int add_compare(const bigint& lhs1, const bigint& lhs2,
const bigint& rhs) {
int max_lhs_bigits = (std::max)(lhs1.num_bigits(), lhs2.num_bigits());
int num_rhs_bigits = rhs.num_bigits();
if (max_lhs_bigits + 1 < num_rhs_bigits) return -1;
if (max_lhs_bigits > num_rhs_bigits) return 1;
auto get_bigit = [](const bigint& n, int i) -> bigit {
return i >= n.exp_ && i < n.num_bigits() ? n.bigits_[i - n.exp_] : 0;
};
double_bigit borrow = 0;
int min_exp = (std::min)((std::min)(lhs1.exp_, lhs2.exp_), rhs.exp_);
for (int i = num_rhs_bigits - 1; i >= min_exp; --i) {
double_bigit sum =
static_cast<double_bigit>(get_bigit(lhs1, i)) + get_bigit(lhs2, i);
bigit rhs_bigit = get_bigit(rhs, i);
if (sum > rhs_bigit + borrow) return 1;
borrow = rhs_bigit + borrow - sum;
if (borrow > 1) return -1;
borrow <<= bigit_bits;
}
return borrow != 0 ? -1 : 0;
}
// Assigns pow(10, exp) to this bigint.
void assign_pow10(int exp) {
assert(exp >= 0);
@ -900,17 +922,17 @@ template <int GRISU_VERSION> struct grisu_shortest_handler {
// Format value using a variation of the Fixed-Precision Positive Floating-Point
// Printout ((FPP)^2) algorithm by Steele & White.
template <typename Double> FMT_FUNC void fallback_format(Double v, int exp10) {
(void)exp10;
template <typename Double>
FMT_FUNC void fallback_format(Double v, buffer<char>& buf, int& exp10) {
fp fp_value(v);
// Shift to account for unequal gaps when lower boundary is 2 times closer.
// TODO: handle denormals
int shift = fp_value.f == 1 ? 1 : 0;
// Shift value and pow10 by an extra bit to make lower and upper which are
// half ulp integers. This eliminates multiplication by 2 during later
// computations in (FPP)^2.
bigint value(fp_value.f << (shift + 1)); // R in (FPP)^2.
bigint pow10(1 << (shift + 1)); // S in (FPP)^2.
// computations.
bigint value(fp_value.f << (shift + 1)); // 2 * R in (FPP)^2.
bigint pow10(1 << (shift + 1)); // 2 * S in (FPP)^2.
bigint lower(1); // M^- in (FPP)^2.
bigint upper(1 << shift); // M^+ in (FPP)^2.
if (fp_value.e >= 0) {
@ -921,16 +943,30 @@ template <typename Double> FMT_FUNC void fallback_format(Double v, int exp10) {
pow10 <<= -fp_value.e;
// TODO: fixup
}
// fp_value = value / pow10.
while (value /* + upper */ >= pow10) pow10 *= 10;
do {
// fp_value == value / pow10.
int exp = 0;
while (add_compare(value, upper, pow10) >= 0) {
pow10 *= 10;
++exp;
}
int num_digits = 0;
char* data = buf.data();
for (;;) {
value *= 10;
int digit = value.divmod_assign(pow10);
(void)digit;
lower *= 10;
upper *= 10;
} while (value >= lower && value <= pow10 /* - upper */);
// TODO
bool low = value < lower;
bool high = add_compare(value, upper, pow10) > 0; // value + upper > pow10
if (low || high) {
if (!low) ++digit;
data[num_digits++] = static_cast<char>('0' + digit);
buf.resize(num_digits);
exp10 = exp - num_digits;
return;
}
data[num_digits++] = static_cast<char>('0' + digit);
}
}
template <typename Double,
@ -986,8 +1022,9 @@ FMT_API bool grisu_format(Double value, buffer<char>& buf, int precision,
result = grisu_gen_digits(upper, upper.f - lower.f, exp, handler);
size = handler.size;
if (result == digits::error) {
fallback_format(value, exp - cached_exp10);
return false;
exp -= cached_exp10;
fallback_format(value, buf, exp);
return true;
}
} else {
++lower.f; // \tilde{M}^- + 1 ulp -> M^-_{\uparrow}.

26
test/format-impl-test.cc
View File

@ -95,6 +95,32 @@ TEST(BigIntTest, GreaterEqual) {
EXPECT_TRUE(n4 >= n2);
}
TEST(BigIntTest, AddCompare) {
EXPECT_LT(
add_compare(bigint(0xffffffff), bigint(0xffffffff), bigint(1) <<= 64), 0);
EXPECT_LT(add_compare(bigint(1) <<= 32, bigint(1), bigint(1) <<= 96), 0);
EXPECT_GT(add_compare(bigint(1) <<= 32, bigint(0), bigint(0xffffffff)), 0);
EXPECT_GT(add_compare(bigint(0), bigint(1) <<= 32, bigint(0xffffffff)), 0);
EXPECT_GT(add_compare(bigint(42), bigint(1), bigint(42)), 0);
EXPECT_GT(add_compare(bigint(0xffffffff), bigint(1), bigint(0xffffffff)), 0);
EXPECT_LT(add_compare(bigint(10), bigint(10), bigint(22)), 0);
EXPECT_LT(add_compare(bigint(0x100000010), bigint(0x100000010),
bigint(0x300000010)),
0);
EXPECT_GT(add_compare(bigint(0x1ffffffff), bigint(0x100000002),
bigint(0x300000000)),
0);
EXPECT_EQ(add_compare(bigint(0x1ffffffff), bigint(0x100000002),
bigint(0x300000001)),
0);
EXPECT_LT(add_compare(bigint(0x1ffffffff), bigint(0x100000002),
bigint(0x300000002)),
0);
EXPECT_LT(add_compare(bigint(0x1ffffffff), bigint(0x100000002),
bigint(0x300000003)),
0);
}
TEST(BigIntTest, ShiftLeft) {
bigint n(0x42);
n <<= 0;