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Add compressed cache for binary32
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Compressed table size is 48 + 14 = 62 bytes.
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@jk-jeon
jk-jeon committed Apr 10, 2024
1 parent c6152a8 commit 3b1663c
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Showing 3 changed files with 307 additions and 114 deletions.
119 changes: 115 additions & 4 deletions include/dragonbox/dragonbox.h
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Original file line number Diff line number Diff line change
Expand Up @@ -217,6 +217,7 @@ namespace jkj {

// <cstdint>
using JKJ_STD_REPLACEMENT_NAMESPACE::int_least32_t;
using JKJ_STD_REPLACEMENT_NAMESPACE::uint_least16_t;
using JKJ_STD_REPLACEMENT_NAMESPACE::uint_least32_t;
using JKJ_STD_REPLACEMENT_NAMESPACE::uint_least64_t;
// We need UINT32_C and UINT64_C macros too, but again there is nothing to do here.
Expand Down Expand Up @@ -1782,6 +1783,102 @@ namespace jkj {
}
};

template <class Dummy>
struct compressed_cache_holder<ieee754_binary32, Dummy> {
using cache_entry_type = cache_holder<ieee754_binary32>::cache_entry_type;
static constexpr int cache_bits = cache_holder<ieee754_binary32>::cache_bits;
static constexpr int min_k = cache_holder<ieee754_binary32>::min_k;
static constexpr int max_k = cache_holder<ieee754_binary32>::max_k;
static constexpr int compression_ratio = 13;
static constexpr detail::stdr::size_t compressed_table_size =
detail::stdr::size_t((max_k - min_k + compression_ratio) / compression_ratio);
static constexpr detail::stdr::size_t pow5_table_size =
detail::stdr::size_t((compression_ratio + 1) / 2);

struct cache_holder_t {
cache_entry_type table[compressed_table_size];
};
struct pow5_holder_t {
detail::stdr::uint_least16_t table[pow5_table_size];
};

#if JKJ_HAS_CONSTEXPR17
static constexpr cache_holder_t cache JKJ_STATIC_DATA_SECTION = [] {
cache_holder_t res{};
for (detail::stdr::size_t i = 0; i < compressed_table_size; ++i) {
res.table[i] = cache_holder<ieee754_binary32>::cache[i * compression_ratio];
}
return res;
}();
static constexpr pow5_holder_t pow5_table JKJ_STATIC_DATA_SECTION = [] {
pow5_holder_t res{};
detail::stdr::uint_least16_t p = 1;
for (detail::stdr::size_t i = 0; i < pow5_table_size; ++i) {
res.table[i] = p;
p *= 5;
}
return res;
}();
#else
template <detail::stdr::size_t... indices>
static constexpr cache_holder_t make_cache(detail::index_sequence<indices...>) {
return {cache_holder<ieee754_binary32>::cache[indices * compression_ratio]...};
}
static constexpr cache_holder_t cache JKJ_STATIC_DATA_SECTION =
make_cache(detail::make_index_sequence<compressed_table_size>{});

template <detail::stdr::size_t... indices>
static constexpr pow5_holder_t make_pow5_table(detail::index_sequence<indices...>) {
return {detail::compute_power<indices>(detail::stdr::uint_least16_t(5))...};
}
static constexpr pow5_holder_t pow5_table JKJ_STATIC_DATA_SECTION =
make_pow5_table(detail::make_index_sequence<pow5_table_size>{});
#endif

static JKJ_CONSTEXPR20 cache_entry_type get_cache(int k) noexcept {
// Compute the base index.
auto const cache_index =
int(detail::stdr::uint_least32_t(k - min_k) / compression_ratio);
auto const kb = cache_index * compression_ratio + min_k;
auto const offset = k - kb;

// Get the base cache.
auto const base_cache = cache.table[cache_index];

if (offset == 0) {
return base_cache;
}
else {
// Compute the required amount of bit-shift.
auto const alpha =
detail::log::floor_log2_pow10(k) - detail::log::floor_log2_pow10(kb) - offset;
assert(alpha > 0 && alpha < 64);

// Try to recover the real cache.
constexpr auto pow5_7 = detail::compute_power<7>(detail::stdr::uint_least32_t(5));
auto const pow5 =
offset >= 7
? detail::stdr::uint_least32_t(pow5_7 * pow5_table.table[offset - 7])
: detail::stdr::uint_least32_t(pow5_table.table[offset]);
auto mul_result = detail::wuint::umul128(base_cache, pow5);
auto const recovered_cache = cache_entry_type(
(((mul_result.high() << (64 - alpha)) | (mul_result.low() >> alpha)) + 1) &
UINT64_C(0xffffffffffffffff));
assert(recovered_cache != 0);

return recovered_cache;
}
}
};
#if !JKJ_HAS_INLINE_VARIABLE
template <class Dummy>
constexpr typename compressed_cache_holder<ieee754_binary32, Dummy>::cache_holder_t
compressed_cache_holder<ieee754_binary32, Dummy>::cache;
template <class Dummy>
constexpr typename compressed_cache_holder<ieee754_binary32, Dummy>::pow5_holder_t
compressed_cache_holder<ieee754_binary32, Dummy>::pow5_table;
#endif

template <class Dummy>
struct compressed_cache_holder<ieee754_binary64, Dummy> {
using cache_entry_type = cache_holder<ieee754_binary64>::cache_entry_type;
Expand All @@ -1790,13 +1887,15 @@ namespace jkj {
static constexpr int max_k = cache_holder<ieee754_binary64>::max_k;
static constexpr int compression_ratio = 27;
static constexpr detail::stdr::size_t compressed_table_size =
(max_k - min_k + compression_ratio) / compression_ratio;
detail::stdr::size_t((max_k - min_k + compression_ratio) / compression_ratio);
static constexpr detail::stdr::size_t pow5_table_size =
detail::stdr::size_t(compression_ratio);

struct cache_holder_t {
cache_entry_type table[compressed_table_size];
};
struct pow5_holder_t {
detail::stdr::uint_least64_t table[compression_ratio];
detail::stdr::uint_least64_t table[pow5_table_size];
};

#if JKJ_HAS_CONSTEXPR17
Expand All @@ -1810,7 +1909,7 @@ namespace jkj {
static constexpr pow5_holder_t pow5_table JKJ_STATIC_DATA_SECTION = [] {
pow5_holder_t res{};
detail::stdr::uint_least64_t p = 1;
for (detail::stdr::size_t i = 0; i < compression_ratio; ++i) {
for (detail::stdr::size_t i = 0; i < pow5_table_size; ++i) {
res.table[i] = p;
p *= 5;
}
Expand All @@ -1829,7 +1928,7 @@ namespace jkj {
return {detail::compute_power<indices>(detail::stdr::uint_least64_t(5))...};
}
static constexpr pow5_holder_t pow5_table JKJ_STATIC_DATA_SECTION =
make_pow5_table(detail::make_index_sequence<compression_ratio>{});
make_pow5_table(detail::make_index_sequence<pow5_table_size>{});
#endif

static JKJ_CONSTEXPR20 cache_entry_type get_cache(int k) noexcept {
Expand Down Expand Up @@ -3088,6 +3187,18 @@ namespace jkj {
// 10^-18) and 2f_c = 29711482, e = -80
// (1.2288529832819387448703332688104694625508273020386695861816... *
// 10^-17).
// For the case of compressed cache for binary32, there is another
// exceptional case 2f_c = 33554430, e = -10 (16383.9990234375). In this
// case, the recovered cache is two large to make compute_mul_parity
// mistakenly conclude that z is not an integer, but actually z = 16384 is
// an integer.
JKJ_IF_CONSTEXPR(
stdr::is_same<cache_holder_type,
compressed_cache_holder<ieee754_binary32>>::value) {
if (two_fc == 33554430 && binary_exponent == -10) {
break;
}
}
auto const z_result =
multiplication_traits_::compute_mul_parity(two_fc + 2, cache, beta);
if (z_result.parity || z_result.is_integer) {
Expand Down
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