simstr/src/sstring.cpp

/*
 * (c) Проект "SimStr", Александр Орефков orefkov@gmail.com
 * ver. 1.0
 * Реализация строковых функций
 */
#include "simstr/simple_unicode.h"
#include "simstr/sstring.h"
#include <simdutf.h>

namespace simstr {

template class sstring<u8s>;
template class sstring<uws>;
template class sstring<u16s>;
template class sstring<u32s>;

// from sqlite.c
/*
** Notes On Invalid UTF-8:
**
**  *  This routine never allows a 7-bit character (0x00 through 0x7f) to
**     be encoded as a multi-byte character.  Any multi-byte character that
**     attempts to encode a value between 0x00 and 0x7f is rendered as 0xfffd.
**
**  *  This routine never allows a UTF16 surrogate value to be encoded.
**     If a multi-byte character attempts to encode a value between
**     0xd800 and 0xe000 then it is rendered as 0xfffd.
**
**  *  Bytes in the range of 0x80 through 0xbf which occur as the first
**     byte of a character are interpreted as single-byte characters
**     and rendered as themselves even though they are technically
**     invalid characters.
**
**  *  This routine accepts over-length UTF8 encodings
**     for unicode values 0x80 and greater.  It does not change over-length
**     encodings to 0xfffd as some systems recommend.
*/
static const uu8s sqlite3Utf8Trans1[] = {
    0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15,
    0x16, 0x17, 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f, 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b,
    0x0c, 0x0d, 0x0e, 0x0f, 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x00, 0x01, 0x02, 0x03, 0x00, 0x01, 0x00, 0x00,
};

u32s readUtf8Symbol(const uu8s*& ptr, const uu8s* end) {
    u32s us = static_cast<u32s>(*ptr++);
    if (us >= 0xC0) {
        us = sqlite3Utf8Trans1[us - 0xC0];
        while (ptr < end && (*ptr & 0xC0) == 0x80)
            us = (us << 6) + (0x3F & *(ptr++));
        if (us < 0x80 || (us & 0xFFFFF800) == 0xD800 || (us & 0xFFFFFFFE) == 0xFFFE) {
            us = 0xFFFD;
        }
    }
    return us;
}

void writeUtf8Symbol(uu8s*& write, u32s us) {
    using u8 = uu8s;
    if (us <= 0x80)
        *write++ = (u8)us;
    else if (us < 0x00800) {
        *write++ = 0xC0 + (u8)((us >> 6) & 0x1F);
        *write++ = 0x80 + (u8)(us & 0x3F);
    } else if (us < 0x10000) {
        *write++ = 0xE0 + (u8)((us >> 12) & 0x0F);
        *write++ = 0x80 + (u8)((us >> 6) & 0x3F);
        *write++ = 0x80 + (u8)(us & 0x3F);
    } else {
        *write++ = 0xF0 + (u8)((us >> 18) & 0x07);
        *write++ = 0x80 + (u8)((us >> 12) & 0x3F);
        *write++ = 0x80 + (u8)((us >> 6) & 0x3F);
        *write++ = 0x80 + (u8)(us & 0x3F);
    }
}

u32s readUtf16Symbol(const u16s*& ptr, const u16s* end) {
    u32s us = static_cast<u32s>(*ptr++);
    if (us >= 0xD800) {
        if (us < 0xDC00 && ptr < end) {
            if (u32s s = static_cast<u32s>(*ptr++); s >= 0xDC00 && s < 0xE000) {
                return ((us & 0x3ff) << 10) + (s & 0x3ff) + 0x10000;
            }
        }
        return 0xFFFD;
    }
    return us;
}

void writeUtf16Symbol(u16s*& ptr, u32s s) {
    if (s < 0x10000) {
        *ptr++ = static_cast<u16s>(s);
    } else {
        s -= 0x10000;
        *ptr++ = 0xD800 + ((s >> 10) & 0x3FF);
        *ptr++ = 0xDC00 + (s & 0x3FF);
    }
}

size_t utf8len(u32s us) {
    if (us <= 0x80)
        return 1;
    else if (us < 0x00800)
        return 2;
    else if (us < 0x10000)
        return 3;
    else
        return 4;
}

SIMSTR_API size_t utf_convert_selector<u8s, u16s>::need_len(const u8s*src, size_t srcLen) {
    return simdutf::utf16_length_from_utf8(src, srcLen);
}

SIMSTR_API size_t utf_convert_selector<u8s, u16s>::convert(const u8s* src, size_t srcLen, u16s* dest) {
    return simdutf::convert_utf8_to_utf16(src, srcLen, dest);
}

SIMSTR_API size_t utf_convert_selector<u8s, u32s>::need_len(const u8s*src, size_t srcLen) {
    return simdutf::utf32_length_from_utf8(src, srcLen);
}

SIMSTR_API size_t utf_convert_selector<u8s, u32s>::convert(const u8s* src, size_t srcLen, u32s* dest) {
    return simdutf::convert_utf8_to_utf32(src, srcLen, dest);
}

SIMSTR_API size_t utf_convert_selector<u16s, u8s>::need_len(const u16s*src, size_t srcLen) {
    return simdutf::utf8_length_from_utf16(src, srcLen);
}

SIMSTR_API size_t utf_convert_selector<u16s, u8s>::convert(const u16s* src, size_t srcLen, u8s* dest) {
    return simdutf::convert_utf16_to_utf8(src, srcLen, dest);
}

SIMSTR_API size_t utf_convert_selector<u16s, u32s>::need_len(const u16s*src, size_t srcLen) {
    return simdutf::utf32_length_from_utf16(src, srcLen);
}

SIMSTR_API size_t utf_convert_selector<u16s, u32s>::convert(const u16s* src, size_t srcLen, u32s* dest) {
    return simdutf::convert_utf16_to_utf32(src, srcLen, dest);
}

SIMSTR_API size_t utf_convert_selector<u32s, u8s>::need_len(const u32s*src, size_t srcLen) {
    return simdutf::utf8_length_from_utf32(src, srcLen);
}

SIMSTR_API size_t utf_convert_selector<u32s, u8s>::convert(const u32s* src, size_t srcLen, u8s* dest) {
    return simdutf::convert_utf32_to_utf8(src, srcLen, dest);
}

SIMSTR_API size_t utf_convert_selector<u32s, u16s>::need_len(const u32s*src, size_t srcLen) {
    return simdutf::utf16_length_from_utf32(src, srcLen);
}

SIMSTR_API size_t utf_convert_selector<u32s, u16s>::convert(const u32s* src, size_t srcLen, u16s* dest) {
    return simdutf::convert_utf32_to_utf16(src, srcLen, dest);
}

inline u32s makeLowerU(u32s s) {
    if (isAsciiUpper(s))
        return s | 0x20;
    else if (s > 127 && s < 0x10000)
        return simpleUnicodeLower(static_cast<uint16_t>(s));
    else
        return s;
}

inline u32s makeUpperU(u32s s) {
    if (isAsciiLower(s))
        return s & ~0x20;
    else if (s > 127 && s < 0x10000)
        return simpleUnicodeUpper(static_cast<uint16_t>(s));
    else
        return s;
}

inline u32s makeFoldU(u32s s) {
    if (isAsciiUpper(s))
        return s | 0x20;
    else if (s > 127 && s < 0x10000)
        return simpleUnicodeFold(static_cast<uint16_t>(s));
    else
        return s;
}

/*
* Поиск utf-8 symbols, которые меняют свою длину при upper/lower преобразовании
* вот они нашлись
* "İiıIſSȺⱥȾⱦɐⱯɑⱭɫⱢɱⱮɽⱤẞßιΙΩωKkÅåⱢɫⱤɽⱥȺⱦȾⱭɑⱮɱⱯɐ"
   l2u ıIſSɐⱯɑⱭɫⱢɱⱮɽⱤιΙⱥȺⱦȾ
   u2l İiȺⱥȾⱦẞßΩωKkÅåⱢɫⱤɽⱭɑⱮɱⱯɐ
void findStrange() {
    u16s badsL2U[100], * pBadslu = badsL2U;
    u16s badsU2L[100], * pBadsul = badsU2L;
    uu8s buf[20];
    size_t allToUpper = 0, allToLower = 0, lowerbadshorter = 0, upperbadshorter = 0, lowerbadlonger = 0, upperbadlonger = 0;
    for (u32s s = 128; s <= 0xFFFF; s++) {
        u16s upper = makeUpperU(s);
        if (upper != s) {
            allToUpper++;
            uu8s* pTest = buf;
            writeUtf8Symbol(pTest, s);
            size_t len1 = pTest - buf;
            pTest = buf;
            writeUtf8Symbol(pTest, upper);
            size_t len2 = pTest - buf;
            if (len1 != len2) {
                *pBadslu++ = s;
                *pBadslu++ = upper;
                if (len1 > len2) {
                    upperbadshorter++;
                } else if (len1 < len2) {
                    upperbadlonger++;
                }
            }
        }
        u16s lower = makeLowerU(s);
        if (lower != s) {
            allToLower++;
            uu8s* pTest = buf;
            writeUtf8Symbol(pTest, s);
            size_t len1 = pTest - buf;
            pTest = buf;
            writeUtf8Symbol(pTest, lower);
            size_t len2 = pTest - buf;
            if (len1 != len2) {
                *pBadsul++ = s;
                *pBadsul++ = lower;
                if (len1 > len2) {
                    lowerbadshorter++;
                } else if (len1 < len2) {
                    lowerbadlonger++;
                }
            }
        }
    }
    *pBadsul = 0;
    *pBadslu = 0;
    return;
}
*/

template<auto Op>
size_t utf8_case_change(const u8s*& src, size_t len, u8s*& dest, size_t lenBuffer) {
    // Допущение для оптимизации - считается, что выделенный буфер записи всегда не меньше длины буфера чтения
    // и что буфер записи не начинается внутри буфера чтения
    // то есть если символ считан, и длина записываемого символа не больше считанного, то он поместится в буфер записи
    // и не перетрет символы, которые еще не прочитали
    // По другому работать откажемся
    if (lenBuffer < len || (dest > src && dest < src + len))
        return len;
    const uu8s *beginReadPos = reinterpret_cast<const uu8s*>(src), *readPos = beginReadPos, *endReadPos = beginReadPos + len,
                    *readFromPos = readPos;
    uu8s *beginWritePos = reinterpret_cast<uu8s*>(dest), *writePos = beginWritePos, *endWritePos = writePos + lenBuffer, *tempWrite;

    size_t state = 0, writedSymbolLen, needExtraLen = 0;
    u32s readedSymbol, writedSymbol;
    lstringa<4096> tempStore;

    while (readPos < endReadPos) {
        readedSymbol = readUtf8Symbol(readPos, endReadPos), writedSymbol = Op(readedSymbol);
        writedSymbolLen = utf8len(writedSymbol);
        switch (state) {
        case 0: // начальное состояние
            // Так как выделенный буфер записи всегда не меньше длины буфера чтения
            // то если символ считан, и длина записываемого символа не больше считанного,
            // то он поместится в буфер записи, можно не проверять
            // оптимизация для inplace конвертации в идеальном случае
            if (writePos == readFromPos && readedSymbol == writedSymbol) {
                writePos    = const_cast<uu8s*>(readPos);
                readFromPos = readPos;
                continue;
            }
            if (writePos + writedSymbolLen <= endWritePos && (writePos > readPos || writePos + writedSymbolLen <= readPos)) {
                // всё отлично
                writeUtf8Symbol(writePos, writedSymbol);
            } else {
                state = 1;
                goto state1;
            }
            break;
        case 1:
        state1:
            // До этого когда-то был считан символ, при записи ставший длиннее.
            // Можно его писать, но надо проверять, что записываемый символ:
            // - не перезатрёт читаемые
            // - не выйдет за границы буфера записи
            // - восстановит обычный режим, если записываемый символ короче прочитанного
            if (writePos + writedSymbolLen > endWritePos) {
                // Записываемый символ не поместится в буфер записи
                // Запомним, где это произошло, подсчитаем символы далее
                src          = reinterpret_cast<const u8s*>(readFromPos);
                dest         = reinterpret_cast<u8s*>(writePos);
                needExtraLen = 0;
                state        = 2;
                goto state2;
            } else if (writePos < readPos && writePos + writedSymbolLen > readPos) {
                // Совсем плохой случай - записываемый символ перезатрет следующий читаемый
                // Запомним, где это произошло, подсчитаем символы далее
                src          = reinterpret_cast<const u8s*>(readFromPos);
                dest         = reinterpret_cast<u8s*>(writePos);
                needExtraLen = 0;
                if (lenBuffer > len) {
                    // считаем, что это второй вызов, и места в буфере в итоге хватит
                    // поэтому будем сохранять считанные символы в свой буфер, а потом скопируем их в результат
                    tempWrite = reinterpret_cast<uu8s*>(tempStore.reserve(lenBuffer - static_cast<size_t>(writePos - beginWritePos)));
                    state     = 3;
                    goto state3;
                } else {
                    // Это первый вызов, будем просто считать нужное место
                    state = 2;
                    goto state2;
                }
            } else {
                // Можем записать прочитанный символ
                writeUtf8Symbol(writePos, writedSymbol);
                // Возможно, мы выровнялись по прочитанным/записанным байтам, тогда можно снова писать в буфер
                // в обычном состоянии
                size_t allReaded = static_cast<size_t>(readPos - beginReadPos);
                size_t allWrite  = static_cast<size_t>(writePos - beginWritePos);
                if (allReaded >= allWrite) {
                    // вернулись в обычное состояние
                    state = 0;
                }
            }
            break;
        case 2:
        state2:
            // Место в буфере кончилось, просто считаем нужное место
            needExtraLen += writedSymbolLen;
            break;
        case 3:
        state3:
            // Был прочитан удлинившийся символ, который мог перезатереть читаемые.
            // Конец буфера записи не достигнут, но писать туда нельзя.
            // При этом известно, что место в буфере выделено
            // с нужным запасом, и сейчас мы просто запоминаем считанные символы, чтобы
            // потом вписать их когда позволит указатель чтения
            if (writePos + writedSymbolLen <= readPos || readPos == endReadPos) {
                // Опа, символ стал короче и снова влезает в буфер. Или все прочитали, можно записывать
                std::char_traits<u8s>::copy(dest, tempStore.symbols(), needExtraLen);
                writeUtf8Symbol(writePos, writedSymbol);
                state = 0;
            } else {
                if (writePos + writedSymbolLen > endWritePos) {
                    // Таки всё-равно не влезем в буфер
                    state = 2;
                    goto state2;
                }
                writeUtf8Symbol(tempWrite, writedSymbol);
                writePos += writedSymbolLen;
                needExtraLen += writedSymbolLen;
            }
            break;
        }
        readFromPos = readPos;
    }
    if (state == 0 || state == 1) {
        // все отлично, можно возвращать получившуюся длину
        src  = reinterpret_cast<const u8s*>(readFromPos);
        dest = reinterpret_cast<u8s*>(writePos);
        return static_cast<size_t>(writePos - beginWritePos);
    } else {
        size_t writedCount = static_cast<size_t>(dest - (u8s*)beginWritePos);
        size_t needBuffer  = writedCount + needExtraLen;
        if (needBuffer <= lenBuffer) {
            // значит попали во 2ое состояние и считали символы, так как перезатирали читаемые
            // но видимо потом попались укоротившиеся и по итогу всё-равно все влезет, только
            // нужно временно сохранять символы. Запустим еще раз
            size_t readedCount = static_cast<size_t>((uu8s*)src - beginReadPos);
            len -= readedCount;
            lenBuffer -= writedCount; // по идее они должны быть одинаковые
            utf8_case_change<Op>(src, len, dest, lenBuffer + 1);
        }
        // в dest и src уже сохранены последние позиции. Вернем нужную длину
        return needBuffer;
    }
}

SIMSTR_API size_t unicode_traits<u8s>::upper(const u8s*& src, size_t len, u8s*& dest, size_t lenBuffer) {
    return utf8_case_change<makeUpperU>(src, len, dest, lenBuffer);
}

SIMSTR_API size_t unicode_traits<u8s>::lower(const u8s*& src, size_t len, u8s*& dest, size_t lenBuffer) {
    return utf8_case_change<makeLowerU>(src, len, dest, lenBuffer);
}

template<auto Op>
void utf16_change_case(const u16s* src, size_t len, u16s* dest) {
    if (dest != src) {
        // не inplace - надо писать все символы
        for (size_t l = 0; l < len; l++)
            dest[l] = static_cast<u16s>(Op(src[l]));
    } else {
        // inplace - будем писать только измененные символы
        for (size_t l = 0; l < len; l++) {
            u16s s = src[l], s1 = static_cast<u16s>(Op(s));
            if (s != s1)
                dest[l] = s1;
        }
    }
}

void unicode_traits<u16s>::upper(const u16s* src, size_t len, u16s* dest) {
    utf16_change_case<makeUpperU>(src, len, dest);
}

void unicode_traits<u16s>::lower(const u16s* src, size_t len, u16s* dest) {
    utf16_change_case<makeLowerU>(src, len, dest);
}

template<auto Op>
void utf32_change_case(const u32s* src, size_t len, u32s* dest) {
    if (dest != src) {
        // не inplace - надо писать все символы
        for (size_t l = 0; l < len; l++)
            *dest++ = Op(*src++);
    } else {
        // inplace - будем писать только измененные символы
        for (size_t l = 0; l < len; l++, src++, dest++) {
            u32s s = *src, s1 = Op(s);
            if (s != s1)
                *dest = s1;
        }
    }
}

SIMSTR_API void unicode_traits<u32s>::upper(const u32s* src, size_t len, u32s* dest) {
    utf32_change_case<makeUpperU>(src, len, dest);
}

SIMSTR_API void unicode_traits<u32s>::lower(const u32s* src, size_t len, u32s* dest) {
    utf32_change_case<makeLowerU>(src, len, dest);
}

SIMSTR_API int unicode_traits<u8s>::compareiu(const u8s* text1, size_t len1, const u8s* text2, size_t len2) {
    if (!len1) {
        return len2 == 0 ? 0 : -1;
    } else if (!len2)
        return 1;
    const uu8s *ptr1 = reinterpret_cast<const uu8s*>(text1), *ptr2 = reinterpret_cast<const uu8s*>(text2),
                    *ptr1End = ptr1 + len1, *ptr2End = ptr2 + len2;

    for (;;) {
        u32s s1 = makeFoldU(readUtf8Symbol(ptr1, ptr1End)), s2 = makeFoldU(readUtf8Symbol(ptr2, ptr2End));
        if (s1 > s2)
            return 1;
        else if (s1 < s2)
            return -1;
        else if (ptr1 >= ptr1End)
            return ptr2 >= ptr2End ? 0 : -1;
        else if (ptr2 >= ptr2End)
            return 1;
    }
}

SIMSTR_API int unicode_traits<u16s>::compareiu(const u16s* text1, size_t len1, const u16s* text2, size_t len2) {
    if (!len1) {
        return len2 == 0 ? 0 : -1;
    } else if (!len2)
        return 1;
    const u16s *ptr1End = text1 + len1, *ptr2End = text2 + len2;

    for (;;) {
        u32s s1 = makeFoldU(readUtf16Symbol(text1, ptr1End)), s2 = makeFoldU(readUtf16Symbol(text2, ptr2End));
        if (s1 > s2)
            return 1;
        else if (s1 < s2)
            return -1;
        else if (text1 >= ptr1End)
            return text2 >= ptr2End ? 0 : -1;
        else if (text2 >= ptr2End)
            return 1;
    }
}

SIMSTR_API int unicode_traits<u32s>::compareiu(const u32s* text1, size_t len1, const u32s* text2, size_t len2) {
    if (!len1) {
        return len2 == 0 ? 0 : -1;
    } else if (!len2)
        return 1;
    const u32s *ptr1End = text1 + len1, *ptr2End = text2 + len2;

    for (;;) {
        u32s s1 = makeFoldU(*text1++), s2 = makeFoldU(*text2++);
        if (s1 > s2)
            return 1;
        else if (s1 < s2)
            return -1;
        else if (text1 > ptr1End)
            return text2 >= ptr2End ? 0 : -1;
        else if (text2 > ptr2End)
            return 1;
    }
}

SIMSTR_API size_t unicode_traits<u8s>::hashia(const u8s* src, size_t l) {
    size_t h = fnv::basis;
    for (size_t i = 0; i < l; i++) {
        h = (h ^ (uu8s)makeAsciiLower(src[i])) * fnv::prime;
    }
    return h;
}

SIMSTR_API size_t unicode_traits<u8s>::hashiu(const u8s* src, size_t l) {
    size_t h = fnv::basis;
    const uu8s *ptr = (const uu8s*)src, *pEnd = ptr + l;

    while (ptr < pEnd) {
        h = (h ^ makeFoldU(readUtf8Symbol(ptr, pEnd))) * fnv::prime;
    }
    return h;
}

SIMSTR_API size_t unicode_traits<u16s>::hashia(const u16s* src, size_t l) {
    size_t h = fnv::basis;
    for (size_t i = 0; i < l; i++) {
        h = (h ^ makeAsciiLower(src[i])) * fnv::prime;
    }
    return h;
}

SIMSTR_API size_t unicode_traits<u16s>::hashiu(const u16s* src, size_t l) {
    size_t h = fnv::basis;
    const u16s* pEnd = src + l;

    while (src < pEnd) {
        h = (h ^ makeFoldU(readUtf16Symbol(src, pEnd))) * fnv::prime;
    }
    return h;
}

SIMSTR_API size_t unicode_traits<u32s>::hashia(const u32s* src, size_t l) {
    size_t h = fnv::basis;
    for (size_t i = 0; i < l; i++) {
        h = (h ^ makeAsciiLower(src[i])) * fnv::prime;
    }
    return h;
}

SIMSTR_API size_t unicode_traits<u32s>::hashiu(const u32s* src, size_t l) {
    size_t h = fnv::basis;
    for (size_t i = 0; i < l; i++) {
        h = (h ^ makeFoldU(src[i])) * fnv::prime;
    }
    return h;
}

namespace {
// Based on simdjson sources https://github.com/simdjson/simdjson/blob/667d0ed3c77f55cbda2082b034168d69898d1f88/include/simdjson/compile_time_json-inl.h#L189

// Counts the number of leading zeros in a 64-bit integer.
int leading_zeroes(uint64_t input_num) {

#if defined __has_builtin
#  if __has_builtin (__builtin_clzll)
#   define HAS_BLT_CLZ
#  endif
#endif
#ifdef HAS_BLT_CLZ
    return __builtin_clzll(input_num);
#else
    int last_bit = 0;

    if (input_num & uint64_t(0xffffffff00000000)) {
        input_num >>= 32;
        last_bit |= 32;
    }
    if (input_num & uint64_t(0xffff0000)) {
        input_num >>= 16;
        last_bit |= 16;
    }
    if (input_num & uint64_t(0xff00)) {
        input_num >>= 8;
        last_bit |= 8;
    }
    if (input_num & uint64_t(0xf0)) {
        input_num >>= 4;
        last_bit |= 4;
    }
    if (input_num & uint64_t(0xc)) {
        input_num >>= 2;
        last_bit |= 2;
    }
    if (input_num & uint64_t(0x2)) { /* input_num >>=  1; */
        last_bit |= 1;
    }
    return 63 - last_bit;
#endif
}

// Multiplies two 32-bit unsigned integers and returns a 64-bit result.
uint64_t emulu(uint32_t x, uint32_t y) {
    return x * (uint64_t)y;
}

uint64_t umul128_generic(uint64_t ab, uint64_t cd, uint64_t* hi) {
    uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd);
    uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd);
    uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32));
    uint64_t adbc_carry = (uint64_t)(adbc < ad);
    uint64_t lo = bd + (adbc << 32);
    *hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) + (adbc_carry << 32) + (uint64_t)(lo < bd);
    return lo;
}

// Represents a 128-bit unsigned integer as two 64-bit parts.
// We have a value128 struct elsewhere in the simdjson, but we
// use a separate one here for clarity.
struct value128 {
    uint64_t low;
    uint64_t high;

    constexpr value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
    constexpr value128() : low(0), high(0) {}
};

// Multiplies two 64-bit integers and returns a 128-bit result as value128.
value128 full_multiplication(uint64_t a, uint64_t b) {
    value128 answer;
    answer.low = umul128_generic(a, b, &answer.high);
    return answer;
}

// Converts mantissa and exponent to a double, considering the sign.
double to_double(uint64_t mantissa, int64_t exponent, bool negative) {
    uint64_t sign_bit = negative ? (1ULL << 63) : 0;
    uint64_t exponent_bits = (uint64_t(exponent) & 0x7FF) << 52;
    uint64_t bits = sign_bit | exponent_bits | (mantissa & ((1ULL << 52) - 1));
    return std::bit_cast<double>(bits);
}

constexpr int smallest_power = -342;
constexpr int largest_power = 308;

// Precomputed powers of ten from 10^0 to 10^22. These
// can be represented exactly using the double type.
const double power_of_ten[] = {
    1e0,  1e1,  1e2,  1e3,  1e4,  1e5,  1e6,  1e7,  1e8,  1e9,  1e10, 1e11,
    1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22
};

/**
 * When mapping numbers from decimal to binary,
 * we go from w * 10^q to m * 2^p but we have
 * 10^q = 5^q * 2^q, so effectively
 * we are trying to match
 * w * 2^q * 5^q to m * 2^p. Thus the powers of two
 * are not a concern since they can be represented
 * exactly using the binary notation, only the powers of five
 * affect the binary significand.
 */
// The truncated powers of five from 5^-342 all the way to 5^308
// The mantissa is truncated to 128 bits, and
// never rounded up. Uses about 10KB.
const uint64_t power_of_five_128[]= {
    0xeef453d6923bd65a,0x113faa2906a13b3f,
    0x9558b4661b6565f8,0x4ac7ca59a424c507,
    0xbaaee17fa23ebf76,0x5d79bcf00d2df649,
    0xe95a99df8ace6f53,0xf4d82c2c107973dc,
    0x91d8a02bb6c10594,0x79071b9b8a4be869,
    0xb64ec836a47146f9,0x9748e2826cdee284,
    0xe3e27a444d8d98b7,0xfd1b1b2308169b25,
    0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7,
    0xb208ef855c969f4f,0xbdbd2d335e51a935,
    0xde8b2b66b3bc4723,0xad2c788035e61382,
    0x8b16fb203055ac76,0x4c3bcb5021afcc31,
    0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d,
    0xd953e8624b85dd78,0xd71d6dad34a2af0d,
    0x87d4713d6f33aa6b,0x8672648c40e5ad68,
    0xa9c98d8ccb009506,0x680efdaf511f18c2,
    0xd43bf0effdc0ba48,0x212bd1b2566def2,
    0x84a57695fe98746d,0x14bb630f7604b57,
    0xa5ced43b7e3e9188,0x419ea3bd35385e2d,
    0xcf42894a5dce35ea,0x52064cac828675b9,
    0x818995ce7aa0e1b2,0x7343efebd1940993,
    0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8,
    0xca66fa129f9b60a6,0xd41a26e077774ef6,
    0xfd00b897478238d0,0x8920b098955522b4,
    0x9e20735e8cb16382,0x55b46e5f5d5535b0,
    0xc5a890362fddbc62,0xeb2189f734aa831d,
    0xf712b443bbd52b7b,0xa5e9ec7501d523e4,
    0x9a6bb0aa55653b2d,0x47b233c92125366e,
    0xc1069cd4eabe89f8,0x999ec0bb696e840a,
    0xf148440a256e2c76,0xc00670ea43ca250d,
    0x96cd2a865764dbca,0x380406926a5e5728,
    0xbc807527ed3e12bc,0xc605083704f5ecf2,
    0xeba09271e88d976b,0xf7864a44c633682e,
    0x93445b8731587ea3,0x7ab3ee6afbe0211d,
    0xb8157268fdae9e4c,0x5960ea05bad82964,
    0xe61acf033d1a45df,0x6fb92487298e33bd,
    0x8fd0c16206306bab,0xa5d3b6d479f8e056,
    0xb3c4f1ba87bc8696,0x8f48a4899877186c,
    0xe0b62e2929aba83c,0x331acdabfe94de87,
    0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14,
    0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9,
    0xdb71e91432b1a24a,0xc9e82cd9f69d6150,
    0x892731ac9faf056e,0xbe311c083a225cd2,
    0xab70fe17c79ac6ca,0x6dbd630a48aaf406,
    0xd64d3d9db981787d,0x92cbbccdad5b108,
    0x85f0468293f0eb4e,0x25bbf56008c58ea5,
    0xa76c582338ed2621,0xaf2af2b80af6f24e,
    0xd1476e2c07286faa,0x1af5af660db4aee1,
    0x82cca4db847945ca,0x50d98d9fc890ed4d,
    0xa37fce126597973c,0xe50ff107bab528a0,
    0xcc5fc196fefd7d0c,0x1e53ed49a96272c8,
    0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a,
    0x9faacf3df73609b1,0x77b191618c54e9ac,
    0xc795830d75038c1d,0xd59df5b9ef6a2417,
    0xf97ae3d0d2446f25,0x4b0573286b44ad1d,
    0x9becce62836ac577,0x4ee367f9430aec32,
    0xc2e801fb244576d5,0x229c41f793cda73f,
    0xf3a20279ed56d48a,0x6b43527578c1110f,
    0x9845418c345644d6,0x830a13896b78aaa9,
    0xbe5691ef416bd60c,0x23cc986bc656d553,
    0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8,
    0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9,
    0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53,
    0xe858ad248f5c22c9,0xd1b3400f8f9cff68,
    0x91376c36d99995be,0x23100809b9c21fa1,
    0xb58547448ffffb2d,0xabd40a0c2832a78a,
    0xe2e69915b3fff9f9,0x16c90c8f323f516c,
    0x8dd01fad907ffc3b,0xae3da7d97f6792e3,
    0xb1442798f49ffb4a,0x99cd11cfdf41779c,
    0xdd95317f31c7fa1d,0x40405643d711d583,
    0x8a7d3eef7f1cfc52,0x482835ea666b2572,
    0xad1c8eab5ee43b66,0xda3243650005eecf,
    0xd863b256369d4a40,0x90bed43e40076a82,
    0x873e4f75e2224e68,0x5a7744a6e804a291,
    0xa90de3535aaae202,0x711515d0a205cb36,
    0xd3515c2831559a83,0xd5a5b44ca873e03,
    0x8412d9991ed58091,0xe858790afe9486c2,
    0xa5178fff668ae0b6,0x626e974dbe39a872,
    0xce5d73ff402d98e3,0xfb0a3d212dc8128f,
    0x80fa687f881c7f8e,0x7ce66634bc9d0b99,
    0xa139029f6a239f72,0x1c1fffc1ebc44e80,
    0xc987434744ac874e,0xa327ffb266b56220,
    0xfbe9141915d7a922,0x4bf1ff9f0062baa8,
    0x9d71ac8fada6c9b5,0x6f773fc3603db4a9,
    0xc4ce17b399107c22,0xcb550fb4384d21d3,
    0xf6019da07f549b2b,0x7e2a53a146606a48,
    0x99c102844f94e0fb,0x2eda7444cbfc426d,
    0xc0314325637a1939,0xfa911155fefb5308,
    0xf03d93eebc589f88,0x793555ab7eba27ca,
    0x96267c7535b763b5,0x4bc1558b2f3458de,
    0xbbb01b9283253ca2,0x9eb1aaedfb016f16,
    0xea9c227723ee8bcb,0x465e15a979c1cadc,
    0x92a1958a7675175f,0xbfacd89ec191ec9,
    0xb749faed14125d36,0xcef980ec671f667b,
    0xe51c79a85916f484,0x82b7e12780e7401a,
    0x8f31cc0937ae58d2,0xd1b2ecb8b0908810,
    0xb2fe3f0b8599ef07,0x861fa7e6dcb4aa15,
    0xdfbdcece67006ac9,0x67a791e093e1d49a,
    0x8bd6a141006042bd,0xe0c8bb2c5c6d24e0,
    0xaecc49914078536d,0x58fae9f773886e18,
    0xda7f5bf590966848,0xaf39a475506a899e,
    0x888f99797a5e012d,0x6d8406c952429603,
    0xaab37fd7d8f58178,0xc8e5087ba6d33b83,
    0xd5605fcdcf32e1d6,0xfb1e4a9a90880a64,
    0x855c3be0a17fcd26,0x5cf2eea09a55067f,
    0xa6b34ad8c9dfc06f,0xf42faa48c0ea481e,
    0xd0601d8efc57b08b,0xf13b94daf124da26,
    0x823c12795db6ce57,0x76c53d08d6b70858,
    0xa2cb1717b52481ed,0x54768c4b0c64ca6e,
    0xcb7ddcdda26da268,0xa9942f5dcf7dfd09,
    0xfe5d54150b090b02,0xd3f93b35435d7c4c,
    0x9efa548d26e5a6e1,0xc47bc5014a1a6daf,
    0xc6b8e9b0709f109a,0x359ab6419ca1091b,
    0xf867241c8cc6d4c0,0xc30163d203c94b62,
    0x9b407691d7fc44f8,0x79e0de63425dcf1d,
    0xc21094364dfb5636,0x985915fc12f542e4,
    0xf294b943e17a2bc4,0x3e6f5b7b17b2939d,
    0x979cf3ca6cec5b5a,0xa705992ceecf9c42,
    0xbd8430bd08277231,0x50c6ff782a838353,
    0xece53cec4a314ebd,0xa4f8bf5635246428,
    0x940f4613ae5ed136,0x871b7795e136be99,
    0xb913179899f68584,0x28e2557b59846e3f,
    0xe757dd7ec07426e5,0x331aeada2fe589cf,
    0x9096ea6f3848984f,0x3ff0d2c85def7621,
    0xb4bca50b065abe63,0xfed077a756b53a9,
    0xe1ebce4dc7f16dfb,0xd3e8495912c62894,
    0x8d3360f09cf6e4bd,0x64712dd7abbbd95c,
    0xb080392cc4349dec,0xbd8d794d96aacfb3,
    0xdca04777f541c567,0xecf0d7a0fc5583a0,
    0x89e42caaf9491b60,0xf41686c49db57244,
    0xac5d37d5b79b6239,0x311c2875c522ced5,
    0xd77485cb25823ac7,0x7d633293366b828b,
    0x86a8d39ef77164bc,0xae5dff9c02033197,
    0xa8530886b54dbdeb,0xd9f57f830283fdfc,
    0xd267caa862a12d66,0xd072df63c324fd7b,
    0x8380dea93da4bc60,0x4247cb9e59f71e6d,
    0xa46116538d0deb78,0x52d9be85f074e608,
    0xcd795be870516656,0x67902e276c921f8b,
    0x806bd9714632dff6,0xba1cd8a3db53b6,
    0xa086cfcd97bf97f3,0x80e8a40eccd228a4,
    0xc8a883c0fdaf7df0,0x6122cd128006b2cd,
    0xfad2a4b13d1b5d6c,0x796b805720085f81,
    0x9cc3a6eec6311a63,0xcbe3303674053bb0,
    0xc3f490aa77bd60fc,0xbedbfc4411068a9c,
    0xf4f1b4d515acb93b,0xee92fb5515482d44,
    0x991711052d8bf3c5,0x751bdd152d4d1c4a,
    0xbf5cd54678eef0b6,0xd262d45a78a0635d,
    0xef340a98172aace4,0x86fb897116c87c34,
    0x9580869f0e7aac0e,0xd45d35e6ae3d4da0,
    0xbae0a846d2195712,0x8974836059cca109,
    0xe998d258869facd7,0x2bd1a438703fc94b,
    0x91ff83775423cc06,0x7b6306a34627ddcf,
    0xb67f6455292cbf08,0x1a3bc84c17b1d542,
    0xe41f3d6a7377eeca,0x20caba5f1d9e4a93,
    0x8e938662882af53e,0x547eb47b7282ee9c,
    0xb23867fb2a35b28d,0xe99e619a4f23aa43,
    0xdec681f9f4c31f31,0x6405fa00e2ec94d4,
    0x8b3c113c38f9f37e,0xde83bc408dd3dd04,
    0xae0b158b4738705e,0x9624ab50b148d445,
    0xd98ddaee19068c76,0x3badd624dd9b0957,
    0x87f8a8d4cfa417c9,0xe54ca5d70a80e5d6,
    0xa9f6d30a038d1dbc,0x5e9fcf4ccd211f4c,
    0xd47487cc8470652b,0x7647c3200069671f,
    0x84c8d4dfd2c63f3b,0x29ecd9f40041e073,
    0xa5fb0a17c777cf09,0xf468107100525890,
    0xcf79cc9db955c2cc,0x7182148d4066eeb4,
    0x81ac1fe293d599bf,0xc6f14cd848405530,
    0xa21727db38cb002f,0xb8ada00e5a506a7c,
    0xca9cf1d206fdc03b,0xa6d90811f0e4851c,
    0xfd442e4688bd304a,0x908f4a166d1da663,
    0x9e4a9cec15763e2e,0x9a598e4e043287fe,
    0xc5dd44271ad3cdba,0x40eff1e1853f29fd,
    0xf7549530e188c128,0xd12bee59e68ef47c,
    0x9a94dd3e8cf578b9,0x82bb74f8301958ce,
    0xc13a148e3032d6e7,0xe36a52363c1faf01,
    0xf18899b1bc3f8ca1,0xdc44e6c3cb279ac1,
    0x96f5600f15a7b7e5,0x29ab103a5ef8c0b9,
    0xbcb2b812db11a5de,0x7415d448f6b6f0e7,
    0xebdf661791d60f56,0x111b495b3464ad21,
    0x936b9fcebb25c995,0xcab10dd900beec34,
    0xb84687c269ef3bfb,0x3d5d514f40eea742,
    0xe65829b3046b0afa,0xcb4a5a3112a5112,
    0x8ff71a0fe2c2e6dc,0x47f0e785eaba72ab,
    0xb3f4e093db73a093,0x59ed216765690f56,
    0xe0f218b8d25088b8,0x306869c13ec3532c,
    0x8c974f7383725573,0x1e414218c73a13fb,
    0xafbd2350644eeacf,0xe5d1929ef90898fa,
    0xdbac6c247d62a583,0xdf45f746b74abf39,
    0x894bc396ce5da772,0x6b8bba8c328eb783,
    0xab9eb47c81f5114f,0x66ea92f3f326564,
    0xd686619ba27255a2,0xc80a537b0efefebd,
    0x8613fd0145877585,0xbd06742ce95f5f36,
    0xa798fc4196e952e7,0x2c48113823b73704,
    0xd17f3b51fca3a7a0,0xf75a15862ca504c5,
    0x82ef85133de648c4,0x9a984d73dbe722fb,
    0xa3ab66580d5fdaf5,0xc13e60d0d2e0ebba,
    0xcc963fee10b7d1b3,0x318df905079926a8,
    0xffbbcfe994e5c61f,0xfdf17746497f7052,
    0x9fd561f1fd0f9bd3,0xfeb6ea8bedefa633,
    0xc7caba6e7c5382c8,0xfe64a52ee96b8fc0,
    0xf9bd690a1b68637b,0x3dfdce7aa3c673b0,
    0x9c1661a651213e2d,0x6bea10ca65c084e,
    0xc31bfa0fe5698db8,0x486e494fcff30a62,
    0xf3e2f893dec3f126,0x5a89dba3c3efccfa,
    0x986ddb5c6b3a76b7,0xf89629465a75e01c,
    0xbe89523386091465,0xf6bbb397f1135823,
    0xee2ba6c0678b597f,0x746aa07ded582e2c,
    0x94db483840b717ef,0xa8c2a44eb4571cdc,
    0xba121a4650e4ddeb,0x92f34d62616ce413,
    0xe896a0d7e51e1566,0x77b020baf9c81d17,
    0x915e2486ef32cd60,0xace1474dc1d122e,
    0xb5b5ada8aaff80b8,0xd819992132456ba,
    0xe3231912d5bf60e6,0x10e1fff697ed6c69,
    0x8df5efabc5979c8f,0xca8d3ffa1ef463c1,
    0xb1736b96b6fd83b3,0xbd308ff8a6b17cb2,
    0xddd0467c64bce4a0,0xac7cb3f6d05ddbde,
    0x8aa22c0dbef60ee4,0x6bcdf07a423aa96b,
    0xad4ab7112eb3929d,0x86c16c98d2c953c6,
    0xd89d64d57a607744,0xe871c7bf077ba8b7,
    0x87625f056c7c4a8b,0x11471cd764ad4972,
    0xa93af6c6c79b5d2d,0xd598e40d3dd89bcf,
    0xd389b47879823479,0x4aff1d108d4ec2c3,
    0x843610cb4bf160cb,0xcedf722a585139ba,
    0xa54394fe1eedb8fe,0xc2974eb4ee658828,
    0xce947a3da6a9273e,0x733d226229feea32,
    0x811ccc668829b887,0x806357d5a3f525f,
    0xa163ff802a3426a8,0xca07c2dcb0cf26f7,
    0xc9bcff6034c13052,0xfc89b393dd02f0b5,
    0xfc2c3f3841f17c67,0xbbac2078d443ace2,
    0x9d9ba7832936edc0,0xd54b944b84aa4c0d,
    0xc5029163f384a931,0xa9e795e65d4df11,
    0xf64335bcf065d37d,0x4d4617b5ff4a16d5,
    0x99ea0196163fa42e,0x504bced1bf8e4e45,
    0xc06481fb9bcf8d39,0xe45ec2862f71e1d6,
    0xf07da27a82c37088,0x5d767327bb4e5a4c,
    0x964e858c91ba2655,0x3a6a07f8d510f86f,
    0xbbe226efb628afea,0x890489f70a55368b,
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    0x82a45b450226b39c,0xecc0024661173473,
    0xa34d721642b06084,0x27f002d7f95d0190,
    0xcc20ce9bd35c78a5,0x31ec038df7b441f4,
    0xff290242c83396ce,0x7e67047175a15271,
    0x9f79a169bd203e41,0xf0062c6e984d386,
    0xc75809c42c684dd1,0x52c07b78a3e60868,
    0xf92e0c3537826145,0xa7709a56ccdf8a82,
    0x9bbcc7a142b17ccb,0x88a66076400bb691,
    0xc2abf989935ddbfe,0x6acff893d00ea435,
    0xf356f7ebf83552fe,0x583f6b8c4124d43,
    0x98165af37b2153de,0xc3727a337a8b704a,
    0xbe1bf1b059e9a8d6,0x744f18c0592e4c5c,
    0xeda2ee1c7064130c,0x1162def06f79df73,
    0x9485d4d1c63e8be7,0x8addcb5645ac2ba8,
    0xb9a74a0637ce2ee1,0x6d953e2bd7173692,
    0xe8111c87c5c1ba99,0xc8fa8db6ccdd0437,
    0x910ab1d4db9914a0,0x1d9c9892400a22a2,
    0xb54d5e4a127f59c8,0x2503beb6d00cab4b,
    0xe2a0b5dc971f303a,0x2e44ae64840fd61d,
    0x8da471a9de737e24,0x5ceaecfed289e5d2,
    0xb10d8e1456105dad,0x7425a83e872c5f47,
    0xdd50f1996b947518,0xd12f124e28f77719,
    0x8a5296ffe33cc92f,0x82bd6b70d99aaa6f,
    0xace73cbfdc0bfb7b,0x636cc64d1001550b,
    0xd8210befd30efa5a,0x3c47f7e05401aa4e,
    0x8714a775e3e95c78,0x65acfaec34810a71,
    0xa8d9d1535ce3b396,0x7f1839a741a14d0d,
    0xd31045a8341ca07c,0x1ede48111209a050,
    0x83ea2b892091e44d,0x934aed0aab460432,
    0xa4e4b66b68b65d60,0xf81da84d5617853f,
    0xce1de40642e3f4b9,0x36251260ab9d668e,
    0x80d2ae83e9ce78f3,0xc1d72b7c6b426019,
    0xa1075a24e4421730,0xb24cf65b8612f81f,
    0xc94930ae1d529cfc,0xdee033f26797b627,
    0xfb9b7cd9a4a7443c,0x169840ef017da3b1,
    0x9d412e0806e88aa5,0x8e1f289560ee864e,
    0xc491798a08a2ad4e,0xf1a6f2bab92a27e2,
    0xf5b5d7ec8acb58a2,0xae10af696774b1db,
    0x9991a6f3d6bf1765,0xacca6da1e0a8ef29,
    0xbff610b0cc6edd3f,0x17fd090a58d32af3,
    0xeff394dcff8a948e,0xddfc4b4cef07f5b0,
    0x95f83d0a1fb69cd9,0x4abdaf101564f98e,
    0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1,
    0xea53df5fd18d5513,0x84c86189216dc5ed,
    0x92746b9be2f8552c,0x32fd3cf5b4e49bb4,
    0xb7118682dbb66a77,0x3fbc8c33221dc2a1,
    0xe4d5e82392a40515,0xfabaf3feaa5334a,
    0x8f05b1163ba6832d,0x29cb4d87f2a7400e,
    0xb2c71d5bca9023f8,0x743e20e9ef511012,
    0xdf78e4b2bd342cf6,0x914da9246b255416,
    0x8bab8eefb6409c1a,0x1ad089b6c2f7548e,
    0xae9672aba3d0c320,0xa184ac2473b529b1,
    0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e,
    0x8865899617fb1871,0x7e2fa67c7a658892,
    0xaa7eebfb9df9de8d,0xddbb901b98feeab7,
    0xd51ea6fa85785631,0x552a74227f3ea565,
    0x8533285c936b35de,0xd53a88958f87275f,
    0xa67ff273b8460356,0x8a892abaf368f137,
    0xd01fef10a657842c,0x2d2b7569b0432d85,
    0x8213f56a67f6b29b,0x9c3b29620e29fc73,
    0xa298f2c501f45f42,0x8349f3ba91b47b8f,
    0xcb3f2f7642717713,0x241c70a936219a73,
    0xfe0efb53d30dd4d7,0xed238cd383aa0110,
    0x9ec95d1463e8a506,0xf4363804324a40aa,
    0xc67bb4597ce2ce48,0xb143c6053edcd0d5,
    0xf81aa16fdc1b81da,0xdd94b7868e94050a,
    0x9b10a4e5e9913128,0xca7cf2b4191c8326,
    0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0,
    0xf24a01a73cf2dccf,0xbc633b39673c8cec,
    0x976e41088617ca01,0xd5be0503e085d813,
    0xbd49d14aa79dbc82,0x4b2d8644d8a74e18,
    0xec9c459d51852ba2,0xddf8e7d60ed1219e,
    0x93e1ab8252f33b45,0xcabb90e5c942b503,
    0xb8da1662e7b00a17,0x3d6a751f3b936243,
    0xe7109bfba19c0c9d,0xcc512670a783ad4,
    0x906a617d450187e2,0x27fb2b80668b24c5,
    0xb484f9dc9641e9da,0xb1f9f660802dedf6,
    0xe1a63853bbd26451,0x5e7873f8a0396973,
    0x8d07e33455637eb2,0xdb0b487b6423e1e8,
    0xb049dc016abc5e5f,0x91ce1a9a3d2cda62,
    0xdc5c5301c56b75f7,0x7641a140cc7810fb,
    0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d,
    0xac2820d9623bf429,0x546345fa9fbdcd44,
    0xd732290fbacaf133,0xa97c177947ad4095,
    0x867f59a9d4bed6c0,0x49ed8eabcccc485d,
    0xa81f301449ee8c70,0x5c68f256bfff5a74,
    0xd226fc195c6a2f8c,0x73832eec6fff3111,
    0x83585d8fd9c25db7,0xc831fd53c5ff7eab,
    0xa42e74f3d032f525,0xba3e7ca8b77f5e55,
    0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb,
    0x80444b5e7aa7cf85,0x7980d163cf5b81b3,
    0xa0555e361951c366,0xd7e105bcc332621f,
    0xc86ab5c39fa63440,0x8dd9472bf3fefaa7,
    0xfa856334878fc150,0xb14f98f6f0feb951,
    0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3,
    0xc3b8358109e84f07,0xa862f80ec4700c8,
    0xf4a642e14c6262c8,0xcd27bb612758c0fa,
    0x98e7e9cccfbd7dbd,0x8038d51cb897789c,
    0xbf21e44003acdd2c,0xe0470a63e6bd56c3,
    0xeeea5d5004981478,0x1858ccfce06cac74,
    0x95527a5202df0ccb,0xf37801e0c43ebc8,
    0xbaa718e68396cffd,0xd30560258f54e6ba,
    0xe950df20247c83fd,0x47c6b82ef32a2069,
    0x91d28b7416cdd27e,0x4cdc331d57fa5441,
    0xb6472e511c81471d,0xe0133fe4adf8e952,
    0xe3d8f9e563a198e5,0x58180fddd97723a6,
    0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,
};

// Attempts to compute i * 10^(power) exactly; and if "negative" is
// true, negate the result.
// Returns true on success, false on failure.
// Failure suggests and invalid input or out-of-range result.
bool compute_float_64(int64_t power, uint64_t i, bool negative, double& d) {
    if (i == 0) {
        d = negative ? -0.0 : 0.0;
        return true;
    }
    int64_t exponent = (((152170 + 65536) * power) >> 16) + 1024 + 63;
    int lz = leading_zeroes(i);
    i <<= lz;
    const uint32_t index = 2 * uint32_t(power - smallest_power);
    value128 firstproduct = full_multiplication(i, power_of_five_128[index]);
    if ((firstproduct.high & 0x1FF) == 0x1FF) {
        value128 secondproduct = full_multiplication(i, power_of_five_128[index + 1]);
        firstproduct.low += secondproduct.high;
        if (secondproduct.high > firstproduct.low) {
            firstproduct.high++;
        }
    }
    uint64_t lower = firstproduct.low;
    uint64_t upper = firstproduct.high;
    uint64_t upperbit = upper >> 63;
    uint64_t mantissa = upper >> (upperbit + 9);
    lz += int(1 ^ upperbit);
    int64_t real_exponent = exponent - lz;
    if (real_exponent <= 0) {
        if (-real_exponent + 1 >= 64) {
            d = negative ? -0.0 : 0.0;
            return true;
        }
        mantissa >>= -real_exponent + 1;
        mantissa += (mantissa & 1);
        mantissa >>= 1;
        real_exponent = (mantissa < (uint64_t(1) << 52)) ? 0 : 1;
        d = to_double(mantissa, real_exponent, negative);
        return true;
    }
    if ((lower <= 1) && (power >= -4) && (power <= 23) && ((mantissa & 3) == 1)) {
        if ((mantissa << (upperbit + 64 - 53 - 2)) == upper) {
            mantissa &= ~1;
        }
    }
    mantissa += mantissa & 1;
    mantissa >>= 1;
    if (mantissa >= (1ULL << 53)) {
        mantissa = (1ULL << 52);
        real_exponent++;
    }
    mantissa &= ~(1ULL << 52);
    if (real_exponent > 2046) {
        return false;
    }
    d = to_double(mantissa, real_exponent, negative);
    return true;
}

// Parses a single digit character and updates the integer value.
template<typename K>
bool parse_digit(const K c, uint64_t& i) {
    auto digit = int_convert::toDigit<K, 10>(c);
    if (digit > 9) {
        return false;
    }
    i = 10 * i + digit;
    return true;
}

} // namespace

template<typename K>
SIMSTR_API std::optional<double> impl_to_double(const K* start, const K* end) {
    auto get_value = [&](const K* pointer) -> K {
        if (pointer == end) {
            return '\0';
        }
        return *pointer;
    };
    const K* srcinit = start;
    bool negative = (get_value(start) == '-');
    start += (uint8_t)negative;
    if (end - start == 3) {
        if (!negative && (start[0] | 0x20) == K('n')) {
            if ((start[1] | 0x20) == K('a') && (start[2] | 0x20) == K('n')) {
                return std::nan("0");
            }
        } else if ((start[0] | 0x20) == K('i') && (start[1] | 0x20) == K('n') && (start[2] | 0x20) == K('f')) {
            return negative ? -std::numeric_limits<double>::infinity() : std::numeric_limits<double>::infinity();
        }
    }
    uint64_t digits = 0;
    const K* p = start;
    p += parse_digit(get_value(p), digits);
    bool leading_zero = (digits == 0);
    while (parse_digit(get_value(p), digits)) {
        p++;
    }
    if (p == start) {
        return {};
    }
    if ((leading_zero && p != start + 1)) {
        return {};
    }
    int64_t exponent = 0;
    int max_digits = 19;
    bool overflow;
    if (get_value(p) == '.') {
        p++;
        const K* start_decimal_digits = p;
        if (!parse_digit(get_value(p), digits)) {
            return {};
        } // no decimal digits
        p++;
        while (parse_digit(get_value(p), digits)) {
            p++;
        }
        exponent = -(p - start_decimal_digits);
        overflow = p - start - 1 > max_digits;
        if (overflow && leading_zero) {
            const K* start_digits = start + 2;
            while (get_value(start_digits) == '0') {
                start_digits++;
            }
            overflow = p - start_digits > max_digits;
        }
    } else {
        overflow = p - start > max_digits;
    }
    if (overflow) {
        return {};
    }
    if ((get_value(p) | 0x20)  == K('e')) {
        p++;
        bool exp_neg = get_value(p) == '-';
        p += exp_neg || get_value(p) == '+';
        uint64_t exp = 0;
        const K* start_exp_digits = p;
        while (parse_digit(get_value(p), exp)) {
            p++;
        }
        if (p - start_exp_digits == 0 || p - start_exp_digits > max_digits) {
            return {};
        }
        exponent += exp_neg ? 0 - exp : exp;
    }

    if (exponent < smallest_power || exponent > largest_power || p != end) {
        return {};
    }
    double d;
    if (!compute_float_64(exponent, digits, negative, d)) {
        return {};
    }
    return d;
}

template std::optional<double> impl_to_double<u8s>(const u8s* start, const u8s* end);
template std::optional<double> impl_to_double<u16s>(const u16s* start, const u16s* end);
template std::optional<double> impl_to_double<u32s>(const u32s* start, const u32s* end);
template std::optional<double> impl_to_double<uws>(const uws* start, const uws* end);

} // namespace simstr