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Optimize digit printing algorithm
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@jk-jeon
jk-jeon committed Feb 12, 2022
1 parent 8864215 commit b75d296
Showing 1 changed file with 95 additions and 102 deletions.
197 changes: 95 additions & 102 deletions source/dragonbox_to_chars.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -48,6 +48,13 @@ namespace jkj::dragonbox {

// These digit generation routines are inspired by James Anhalt's itoa algorithm:
// https://github.com/jeaiii/itoa
// The main idea is for given n, find y such that floor(10^k * y / 2^32) = n holds,
// where k is an appropriate integer depending on the length of n.
// For example, if n = 1234567, we set k = 6. In this case, we have
// floor(y / 2^32) = 1,
// floor(10^2 * (y mod 2^32) / 2^32) = 23,
// floor(10^2 * (10^2 * y mod 2^32) / 2^32) = 45, and
// floor(10^2 * (10^4 * y mod 2^32) / 2^32) = 67.

template <>
char* to_chars<float, default_float_traits<float>>(std::uint32_t s32, int exponent,
Expand Down Expand Up @@ -123,26 +130,25 @@ namespace jkj::dragonbox {
exponent += 5;
}

std::memcpy(buffer, &radix_100_table[second_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[third_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer + 0, &radix_100_table[second_two_digits * 2], 2);
std::memcpy(buffer + 2, &radix_100_table[third_two_digits * 2], 2);
buffer += 4;
}
}
else if (s32 < 1'0000'0000) {
// 140737489 = ceil(2^47 / 100'0000)
auto constexpr mask = (std::numeric_limits<std::uint64_t>::max() >> (64 - 47));
auto prod = s32 * std::uint64_t(140737489);
auto first_two_digits = std::uint32_t(prod >> 47);
// 281474978 = ceil(2^48 / 100'0000) + 1
auto prod = s32 * std::uint64_t(281474978);
prod >>= 16;
auto first_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto second_two_digits = std::uint32_t(prod >> 47);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto second_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto third_two_digits = std::uint32_t(prod >> 47);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto third_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto fourth_two_digits = std::uint32_t(prod >> 47);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto fourth_two_digits = std::uint32_t(prod >> 32);

if (first_two_digits < 10) {
// 7 digits.
Expand All @@ -160,45 +166,40 @@ namespace jkj::dragonbox {
exponent += 7;
}

std::memcpy(buffer, &radix_100_table[second_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[third_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[fourth_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer + 0, &radix_100_table[second_two_digits * 2], 2);
std::memcpy(buffer + 2, &radix_100_table[third_two_digits * 2], 2);
std::memcpy(buffer + 4, &radix_100_table[fourth_two_digits * 2], 2);
buffer += 6;
}
else {
// 9 digits.
// 1441151881 = ceil(2^57 / 1'0000'0000)
auto constexpr mask = (std::numeric_limits<std::uint64_t>::max() >> (64 - 57));
auto prod = s32 * std::uint64_t(1441151881);
auto first_digit = std::uint8_t(prod >> 57);
// 2882303763 = ceil(2^58 / 1'0000'0000) + 1
auto prod = s32 * std::uint64_t(2882303763);
prod >>= 26;
auto first_digit = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto second_two_digits = std::uint32_t(prod >> 57);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto second_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto third_two_digits = std::uint32_t(prod >> 57);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto third_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto fourth_two_digits = std::uint32_t(prod >> 57);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto fourth_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto fifth_two_digits = std::uint32_t(prod >> 57);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto fifth_two_digits = std::uint32_t(prod >> 32);

buffer[0] = char('0' + first_digit);
buffer[1] = '.';
buffer += 2;
exponent += 8;

std::memcpy(buffer, &radix_100_table[second_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[third_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[fourth_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[fifth_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer + 0, &radix_100_table[second_two_digits * 2], 2);
std::memcpy(buffer + 2, &radix_100_table[third_two_digits * 2], 2);
std::memcpy(buffer + 4, &radix_100_table[fourth_two_digits * 2], 2);
std::memcpy(buffer + 6, &radix_100_table[fifth_two_digits * 2], 2);
buffer += 8;
}

// Print exponent and return
Expand Down Expand Up @@ -317,26 +318,25 @@ namespace jkj::dragonbox {
exponent += 5;
}

std::memcpy(buffer, &radix_100_table[second_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[third_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer + 0, &radix_100_table[second_two_digits * 2], 2);
std::memcpy(buffer + 2, &radix_100_table[third_two_digits * 2], 2);
buffer += 4;
}
}
else if (first_block < 1'0000'0000) {
// 140737489 = ceil(2^47 / 100'0000)
auto constexpr mask = (std::numeric_limits<std::uint64_t>::max() >> (64 - 47));
auto prod = first_block * std::uint64_t(140737489);
auto first_two_digits = std::uint32_t(prod >> 47);
// 281474978 = ceil(2^48 / 100'0000) + 1
auto prod = first_block * std::uint64_t(281474978);
prod >>= 16;
auto first_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto second_two_digits = std::uint32_t(prod >> 47);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto second_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto third_two_digits = std::uint32_t(prod >> 47);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto third_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto fourth_two_digits = std::uint32_t(prod >> 47);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto fourth_two_digits = std::uint32_t(prod >> 32);

if (first_two_digits < 10) {
// 7 digits.
Expand All @@ -354,71 +354,64 @@ namespace jkj::dragonbox {
exponent += 7;
}

std::memcpy(buffer, &radix_100_table[second_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[third_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[fourth_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer + 0, &radix_100_table[second_two_digits * 2], 2);
std::memcpy(buffer + 2, &radix_100_table[third_two_digits * 2], 2);
std::memcpy(buffer + 4, &radix_100_table[fourth_two_digits * 2], 2);
buffer += 6;
}
else {
// 9 digits.
// 1441151881 = ceil(2^57 / 1'0000'0000)
auto constexpr mask = (std::numeric_limits<std::uint64_t>::max() >> (64 - 57));
auto prod = first_block * std::uint64_t(1441151881);
auto first_digit = std::uint8_t(prod >> 57);
// 2882303763 = ceil(2^58 / 1'0000'0000) + 1
auto prod = first_block * std::uint64_t(2882303763);
prod >>= 26;
auto first_digit = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto second_two_digits = std::uint32_t(prod >> 57);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto second_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto third_two_digits = std::uint32_t(prod >> 57);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto third_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto fourth_two_digits = std::uint32_t(prod >> 57);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto fourth_two_digits = std::uint32_t(prod >> 32);

prod = (prod & mask) * 100;
auto fifth_two_digits = std::uint32_t(prod >> 57);
prod = std::uint32_t(prod) * std::uint64_t(100);
auto fifth_two_digits = std::uint32_t(prod >> 32);

buffer[0] = char('0' + first_digit);
buffer[1] = '.';
buffer += 2;
exponent += 8;

std::memcpy(buffer, &radix_100_table[second_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[third_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[fourth_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[fifth_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer + 0, &radix_100_table[second_two_digits * 2], 2);
std::memcpy(buffer + 2, &radix_100_table[third_two_digits * 2], 2);
std::memcpy(buffer + 4, &radix_100_table[fourth_two_digits * 2], 2);
std::memcpy(buffer + 6, &radix_100_table[fifth_two_digits * 2], 2);
buffer += 8;
}

// Print second block if necessary.
if (have_second_block) {
// 140737489 = ceil(2^47 / 100'0000)
auto constexpr mask = (std::numeric_limits<std::uint64_t>::max() >> (64 - 47));
auto prod = second_block * std::uint64_t(140737489);
auto first_two_digits = std::uint32_t(prod >> 47);

prod = (prod & mask) * 100;
auto second_two_digits = std::uint32_t(prod >> 47);

prod = (prod & mask) * 100;
auto third_two_digits = std::uint32_t(prod >> 47);

prod = (prod & mask) * 100;
auto fourth_two_digits = std::uint32_t(prod >> 47);

std::memcpy(buffer, &radix_100_table[first_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[second_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[third_two_digits * 2], 2);
buffer += 2;
std::memcpy(buffer, &radix_100_table[fourth_two_digits * 2], 2);
buffer += 2;
// 281474978 = ceil(2^48 / 100'0000) + 1
auto prod = second_block * std::uint64_t(281474978);
prod >>= 16;
prod += 1;
auto first_two_digits = std::uint32_t(prod >> 32);

prod = std::uint32_t(prod) * std::uint64_t(100);
auto second_two_digits = std::uint32_t(prod >> 32);

prod = std::uint32_t(prod) * std::uint64_t(100);
auto third_two_digits = std::uint32_t(prod >> 32);

prod = std::uint32_t(prod) * std::uint64_t(100);
auto fourth_two_digits = std::uint32_t(prod >> 32);

std::memcpy(buffer + 0, &radix_100_table[first_two_digits * 2], 2);
std::memcpy(buffer + 2, &radix_100_table[second_two_digits * 2], 2);
std::memcpy(buffer + 4, &radix_100_table[third_two_digits * 2], 2);
std::memcpy(buffer + 6, &radix_100_table[fourth_two_digits * 2], 2);
buffer += 8;

exponent += 8;
}
Expand Down

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