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Fix a bug for right_closed_directed rounding mode
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@jk-jeon
jk-jeon committed May 27, 2021
1 parent 71e6536 commit b6cc3f2
Showing 1 changed file with 37 additions and 9 deletions.
46 changes: 37 additions & 9 deletions include/dragonbox/dragonbox.h
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Original file line number Diff line number Diff line change
Expand Up @@ -2469,6 +2469,34 @@ namespace jkj::dragonbox {
exponent += exponent_bias - significand_bits;

// Shorter interval case; proceed like Schubfach.
// One might think this condition is wrong,
// since when exponent_bits == 1 and two_fc == 0,
// the interval is actullay regular.
// However, it turns out that this seemingly wrong condition
// is actually fine, because the end result is anyway the same.
//
// [binary32]
// floor( (fc-1/2) * 2^e ) = 1.175'494'28... * 10^-38
// floor( (fc-1/4) * 2^e ) = 1.175'494'31... * 10^-38
// floor( fc * 2^e ) = 1.175'494'35... * 10^-38
// floor( (fc+1/2) * 2^e ) = 1.175'494'42... * 10^-38
//
// Hence, shorter_interval_case will return 1.175'494'4 * 10^-38.
// 1.175'494'3 * 10^-38 is also a correct shortest representation
// that will be rejected if we assume shorter interval,
// but 1.175'494'4 * 10^-38 is closer to the true value so it doesn't matter.
//
// [binary64]
// floor( (fc-1/2) * 2^e ) = 2.225'073'858'507'201'13... * 10^-308
// floor( (fc-1/4) * 2^e ) = 2.225'073'858'507'201'25... * 10^-308
// floor( fc * 2^e ) = 2.225'073'858'507'201'38... * 10^-308
// floor( (fc+1/2) * 2^e ) = 2.225'073'858'507'201'63... * 10^-308
//
// Hence, shorter_interval_case will return 2.225'073'858'507'201'4 * 10^-308.
// This is indeed of the shortest length, and it is the unique one
// closest to the true value among valid representations of the same length.
static_assert(std::is_same_v<format, ieee754_binary32> ||
std::is_same_v<format, ieee754_binary64>);
if (two_fc == 0) {
shorter_interval_case<TrailingZeroPolicy,
BinaryToDecimalRoundingPolicy, CachePolicy>(
Expand Down Expand Up @@ -2739,7 +2767,6 @@ namespace jkj::dragonbox {
//////////////////////////////////////////////////////////////////////

constexpr auto big_divisor = compute_power<kappa + 1>(std::uint32_t(10));
constexpr auto small_divisor = compute_power<kappa>(std::uint32_t(10));

// Using an upper bound on xi, we might be able to optimize the division
// better than the compiler; we are computing xi / big_divisor here.
Expand Down Expand Up @@ -2801,7 +2828,7 @@ namespace jkj::dragonbox {
bool closer_boundary = false;
if (exponent != 0) {
exponent += exponent_bias - significand_bits;
if (significand == 0) {
if (significand == 0 && exponent != 1) {
closer_boundary = true;
}
significand |= (carrier_uint(1) << significand_bits);
Expand Down Expand Up @@ -3046,7 +3073,8 @@ namespace jkj::dragonbox {
}
}

static std::uint32_t compute_delta(cache_entry_type const& cache, int beta_minus_1) noexcept
static constexpr std::uint32_t compute_delta(
cache_entry_type const& cache, int beta_minus_1) noexcept
{
if constexpr (std::is_same_v<format, ieee754_binary32>) {
return std::uint32_t(cache >> (cache_bits - 1 - beta_minus_1));
Expand Down Expand Up @@ -3074,7 +3102,7 @@ namespace jkj::dragonbox {
}
}

static carrier_uint compute_left_endpoint_for_shorter_interval_case(
static constexpr carrier_uint compute_left_endpoint_for_shorter_interval_case(
cache_entry_type const& cache, int beta_minus_1) noexcept
{
if constexpr (std::is_same_v<format, ieee754_binary32>) {
Expand All @@ -3089,7 +3117,7 @@ namespace jkj::dragonbox {
}
}

static carrier_uint compute_right_endpoint_for_shorter_interval_case(
static constexpr carrier_uint compute_right_endpoint_for_shorter_interval_case(
cache_entry_type const& cache, int beta_minus_1) noexcept
{
if constexpr (std::is_same_v<format, ieee754_binary32>) {
Expand All @@ -3104,7 +3132,7 @@ namespace jkj::dragonbox {
}
}

static carrier_uint compute_round_up_for_shorter_interval_case(
static constexpr carrier_uint compute_round_up_for_shorter_interval_case(
cache_entry_type const& cache, int beta_minus_1) noexcept
{
if constexpr (std::is_same_v<format, ieee754_binary32>) {
Expand All @@ -3116,12 +3144,12 @@ namespace jkj::dragonbox {
}
}

static bool is_right_endpoint_integer_shorter_interval(int exponent) noexcept {
static constexpr bool is_right_endpoint_integer_shorter_interval(int exponent) noexcept {
return exponent >= case_shorter_interval_right_endpoint_lower_threshold &&
exponent <= case_shorter_interval_right_endpoint_upper_threshold;
}

static bool is_left_endpoint_integer_shorter_interval(int exponent) noexcept {
static constexpr bool is_left_endpoint_integer_shorter_interval(int exponent) noexcept {
return exponent >= case_shorter_interval_left_endpoint_lower_threshold &&
exponent <= case_shorter_interval_left_endpoint_upper_threshold;
}
Expand Down Expand Up @@ -3338,7 +3366,7 @@ namespace jkj::dragonbox {
////////////////////////////////////////////////////////////////////////////////////////

template <class Float, class FloatTraits = default_float_traits<Float>, class... Policies>
JKJ_SAFEBUFFERS JKJ_FORCEINLINE auto to_decimal(Float x, Policies... policies)
JKJ_FORCEINLINE JKJ_SAFEBUFFERS auto to_decimal(Float x, Policies... policies)
{
// Build policy holder type.
using namespace detail::policy_impl;
Expand Down

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