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Handle assymetric boundaries

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This commit is contained in:
Victor Zverovich 2019-10-20 07:55:05 -07:00
parent 2bc5585ff0
commit e2ea940673
2 changed files with 48 additions and 43 deletions
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84
include/fmt/format-inl.h
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@ -364,29 +364,6 @@ class fp {
static FMT_CONSTEXPR_DECL const uint64_t implicit_bit =
1ull << double_significand_size;
// Assigns d to this and return true iff predecessor is closer than successor.
template <typename Double> bool assign(Double d) {
// Assume double is in the format [sign][exponent][significand].
using limits = std::numeric_limits<Double>;
const int exponent_size =
bits<Double>::value - double_significand_size - 1; // -1 for sign
const uint64_t significand_mask = implicit_bit - 1;
const uint64_t exponent_mask = (~0ull >> 1) & ~significand_mask;
const int exponent_bias = (1 << exponent_size) - limits::max_exponent - 1;
auto u = bit_cast<uint64_t>(d);
f = u & significand_mask;
auto biased_e = (u & exponent_mask) >> double_significand_size;
// Predecessor is closer if d is a normalized power of 2 (f == 0) other than
// the smallest normalized number (biased_e > 1).
bool is_predecessor_closer = f == 0 && biased_e > 1;
if (biased_e != 0)
f += implicit_bit;
else
biased_e = 1; // Subnormals use biased exponent 1 (min exponent).
e = static_cast<int>(biased_e - exponent_bias - double_significand_size);
return is_predecessor_closer;
}
public:
significand_type f;
int e;
@ -417,6 +394,29 @@ class fp {
return value;
}
// Assigns d to this and return true iff predecessor is closer than successor.
template <typename Double> bool assign(Double d) {
// Assume double is in the format [sign][exponent][significand].
using limits = std::numeric_limits<Double>;
const int exponent_size =
bits<Double>::value - double_significand_size - 1; // -1 for sign
const uint64_t significand_mask = implicit_bit - 1;
const uint64_t exponent_mask = (~0ull >> 1) & ~significand_mask;
const int exponent_bias = (1 << exponent_size) - limits::max_exponent - 1;
auto u = bit_cast<uint64_t>(d);
f = u & significand_mask;
auto biased_e = (u & exponent_mask) >> double_significand_size;
// Predecessor is closer if d is a normalized power of 2 (f == 0) other than
// the smallest normalized number (biased_e > 1).
bool is_predecessor_closer = f == 0 && biased_e > 1;
if (biased_e != 0)
f += implicit_bit;
else
biased_e = 1; // Subnormals use biased exponent 1 (min exponent).
e = static_cast<int>(biased_e - exponent_bias - double_significand_size);
return is_predecessor_closer;
}
// Assigns d to this together with computing lower and upper boundaries,
// where a boundary is a value half way between the number and its predecessor
// (lower) or successor (upper). The upper boundary is normalized and lower
@ -779,7 +779,7 @@ enum result {
template <typename Handler>
digits::result grisu_gen_digits(fp value, uint64_t error, int& exp,
Handler& handler) {
fp one(1ull << -value.e, value.e);
const fp one(1ull << -value.e, value.e);
// The integral part of scaled value (p1 in Grisu) = value / one. It cannot be
// zero because it contains a product of two 64-bit numbers with MSB set (due
// to normalization) - 1, shifted right by at most 60 bits.
@ -800,7 +800,7 @@ digits::result grisu_gen_digits(fp value, uint64_t error, int& exp,
digit = integral / divisor;
integral %= divisor;
};
// This optimization by miloyip reduces the number of integer divisions by
// This optimization by Milo Yip reduces the number of integer divisions by
// one per iteration.
switch (exp) {
case 10:
@ -961,27 +961,29 @@ template <int GRISU_VERSION> struct grisu_shortest_handler {
// Formats value using a variation of the Fixed-Precision Positive
// Floating-Point Printout ((FPP)^2) algorithm by Steele & White:
// https://fmt.dev/p372-steele.pdf.
FMT_FUNC void fallback_format(fp value, buffer<char>& buf, int& exp10) {
// Shift to account for unequal gaps when lower boundary is 2 times closer.
// TODO: handle denormals
int shift = 0; // fp_value.f == 1 ? 1 : 0;
template <typename Double>
void fallback_format(Double d, buffer<char>& buf, int& exp10) {
bigint numerator; // 2 * R in (FPP)^2.
bigint denominator; // 2 * S in (FPP)^2.
// lower and upper are differences between value and corresponding boundaries.
bigint lower; // (M^- in (FPP)^2).
bigint upper_store; // upper's value if different from lower.
bigint* upper = nullptr; // (M^+ in (FPP)^2).
// Shift numerator and denominator by an extra bit to make lower and upper
// which are normally half ulp integers. This eliminates multiplication by 2
// during later computations.
uint64_t significand = value.f << (shift + 1);
fp value;
// Shift numerator and denominator by an extra bit or two (if lower boundary
// is closer) to make lower and upper integers. This eliminates multiplication
// by 2 during later computations.
// TODO: handle float
int shift = value.assign(d) ? 2 : 1;
uint64_t significand = value.f << shift;
if (value.e >= 0) {
numerator.assign(significand);
numerator <<= value.e;
lower.assign(1);
lower <<= value.e;
if (shift != 0) {
if (shift != 1) {
upper_store.assign(1);
upper_store <<= value.e + shift;
upper_store <<= value.e + 1;
upper = &upper_store;
}
denominator.assign_pow10(exp10);
@ -989,21 +991,21 @@ FMT_FUNC void fallback_format(fp value, buffer<char>& buf, int& exp10) {
} else if (exp10 < 0) {
numerator.assign_pow10(-exp10);
lower.assign(numerator);
if (shift != 0) {
if (shift != 1) {
upper_store.assign(numerator);
upper_store <<= 1;
upper = &upper_store;
}
numerator *= significand;
denominator.assign(1);
denominator <<= 1 - value.e;
denominator <<= shift - value.e;
} else {
numerator.assign(significand);
denominator.assign_pow10(exp10);
denominator <<= 1 - value.e;
denominator <<= shift - value.e;
lower.assign(1);
if (shift != 0) {
upper_store.assign(1ull << shift);
if (shift != 1) {
upper_store.assign(1ull << 1);
upper = &upper_store;
}
}
@ -1103,7 +1105,7 @@ bool grisu_format(Double value, buffer<char>& buf, int precision,
size = handler.size;
if (result == digits::error) {
exp = exp + size - cached_exp10 - 1;
fallback_format(fp_value, buf, exp);
fallback_format(value, buf, exp);
return true;
}
}

3
test/grisu-test.cc
View File

@ -69,4 +69,7 @@ TEST(GrisuTest, Fallback) {
EXPECT_EQ("2.2506787569811123e-253",
fmt::format("{}", 2.2506787569811123e-253));
EXPECT_EQ("1103618912042992.8", fmt::format("{}", 1103618912042992.8));
// pow(2, -25) - assymetric boundaries:
EXPECT_EQ("2.9802322387695312e-08",
fmt::format("{}", 2.9802322387695312e-08));
}