dtoa.h Source File

dtoa.h Source File#

Composable Kernel: dtoa.h Source File
// Tencent is pleased to support the open source community by making RapidJSON available.
//
// Copyright (C) 2015 THL A29 Limited, a Tencent company, and Milo Yip.
//
// Licensed under the MIT License (the "License"); you may not use this file except
// in compliance with the License. You may obtain a copy of the License at
//
// http://opensource.org/licenses/MIT
//
// Unless required by applicable law or agreed to in writing, software distributed
// under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
// CONDITIONS OF ANY KIND, either express or implied. See the License for the
// specific language governing permissions and limitations under the License.
 
// This is a C++ header-only implementation of Grisu2 algorithm from the publication:
// Loitsch, Florian. "Printing floating-point numbers quickly and accurately with
// integers." ACM Sigplan Notices 45.6 (2010): 233-243.
 
#ifndef RAPIDJSON_DTOA_
#define RAPIDJSON_DTOA_
 
#include "itoa.h" // GetDigitsLut()
#include "diyfp.h"
#include "ieee754.h"
 
RAPIDJSON_NAMESPACE_BEGIN
namespace internal {
 
#ifdef __GNUC__
RAPIDJSON_DIAG_PUSH
RAPIDJSON_DIAG_OFF(effc++)
RAPIDJSON_DIAG_OFF(array - bounds) // some gcc versions generate wrong warnings
                                   // https://gcc.gnu.org/bugzilla/show_bug.cgi?id=59124
#endif
 
inline void
GrisuRound(char* buffer, int len, uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t wp_w)
{
    while(rest < wp_w && delta - rest >= ten_kappa &&
          (rest + ten_kappa < wp_w || 
           wp_w - rest > rest + ten_kappa - wp_w))
    {
        buffer[len - 1]--;
        rest += ten_kappa;
    }
}
 
inline int CountDecimalDigit32(uint32_t n)
{
    // Simple pure C++ implementation was faster than __builtin_clz version in this situation.
    if(n < 10)
        return 1;
    if(n < 100)
        return 2;
    if(n < 1000)
        return 3;
    if(n < 10000)
        return 4;
    if(n < 100000)
        return 5;
    if(n < 1000000)
        return 6;
    if(n < 10000000)
        return 7;
    if(n < 100000000)
        return 8;
    // Will not reach 10 digits in DigitGen()
    // if (n < 1000000000) return 9;
    // return 10;
    return 9;
}
 
inline void
DigitGen(const DiyFp& W, const DiyFp& Mp, uint64_t delta, char* buffer, int* len, int* K)
{
    static const uint64_t kPow10[] = {1ULL,
                                      10ULL,
                                      100ULL,
                                      1000ULL,
                                      10000ULL,
                                      100000ULL,
                                      1000000ULL,
                                      10000000ULL,
                                      100000000ULL,
                                      1000000000ULL,
                                      10000000000ULL,
                                      100000000000ULL,
                                      1000000000000ULL,
                                      10000000000000ULL,
                                      100000000000000ULL,
                                      1000000000000000ULL,
                                      10000000000000000ULL,
                                      100000000000000000ULL,
                                      1000000000000000000ULL,
                                      10000000000000000000ULL};
    const DiyFp one(uint64_t(1) << -Mp.e, Mp.e);
    const DiyFp wp_w = Mp - W;
    uint32_t p1      = static_cast<uint32_t>(Mp.f >> -one.e);
    uint64_t p2      = Mp.f & (one.f - 1);
    int kappa        = CountDecimalDigit32(p1); // kappa in [0, 9]
    *len             = 0;
 
    while(kappa > 0)
    {
        uint32_t d = 0;
        switch(kappa)
        {
        case 9:
            d = p1 / 100000000;
            p1 %= 100000000;
            break;
        case 8:
            d = p1 / 10000000;
            p1 %= 10000000;
            break;
        case 7:
            d = p1 / 1000000;
            p1 %= 1000000;
            break;
        case 6:
            d = p1 / 100000;
            p1 %= 100000;
            break;
        case 5:
            d = p1 / 10000;
            p1 %= 10000;
            break;
        case 4:
            d = p1 / 1000;
            p1 %= 1000;
            break;
        case 3:
            d = p1 / 100;
            p1 %= 100;
            break;
        case 2:
            d = p1 / 10;
            p1 %= 10;
            break;
        case 1:
            d  = p1;
            p1 = 0;
            break;
        default:;
        }
        if(d || *len)
            buffer[(*len)++] = static_cast<char>('0' + static_cast<char>(d));
        kappa--;
        uint64_t tmp = (static_cast<uint64_t>(p1) << -one.e) + p2;
        if(tmp <= delta)
        {
            *K += kappa;
            GrisuRound(buffer, *len, delta, tmp, kPow10[kappa] << -one.e, wp_w.f);
            return;
        }
    }
 
    // kappa = 0
    for(;;)
    {
        p2 *= 10;
        delta *= 10;
        char d = static_cast<char>(p2 >> -one.e);
        if(d || *len)
            buffer[(*len)++] = static_cast<char>('0' + d);
        p2 &= one.f - 1;
        kappa--;
        if(p2 < delta)
        {
            *K += kappa;
            int index = -kappa;
            GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * (index < 20 ? kPow10[index] : 0));
            return;
        }
    }
}
 
inline void Grisu2(double value, char* buffer, int* length, int* K)
{
    const DiyFp v(value);
    DiyFp w_m, w_p;
    v.NormalizedBoundaries(&w_m, &w_p);
 
    const DiyFp c_mk = GetCachedPower(w_p.e, K);
    const DiyFp W    = v.Normalize() * c_mk;
    DiyFp Wp         = w_p * c_mk;
    DiyFp Wm         = w_m * c_mk;
    Wm.f++;
    Wp.f--;
    DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K);
}
 
inline char* WriteExponent(int K, char* buffer)
{
    if(K < 0)
    {
        *buffer++ = '-';
        K         = -K;
    }
 
    if(K >= 100)
    {
        *buffer++ = static_cast<char>('0' + static_cast<char>(K / 100));
        K %= 100;
        const char* d = GetDigitsLut() + K * 2;
        *buffer++     = d[0];
        *buffer++     = d[1];
    }
    else if(K >= 10)
    {
        const char* d = GetDigitsLut() + K * 2;
        *buffer++     = d[0];
        *buffer++     = d[1];
    }
    else
        *buffer++ = static_cast<char>('0' + static_cast<char>(K));
 
    return buffer;
}
 
inline char* Prettify(char* buffer, int length, int k, int maxDecimalPlaces)
{
    const int kk = length + k; // 10^(kk-1) <= v < 10^kk
 
    if(0 <= k && kk <= 21)
    {
        // 1234e7 -> 12340000000
        for(int i = length; i < kk; i++)
            buffer[i] = '0';
        buffer[kk]     = '.';
        buffer[kk + 1] = '0';
        return &buffer[kk + 2];
    }
    else if(0 < kk && kk <= 21)
    {
        // 1234e-2 -> 12.34
        std::memmove(&buffer[kk + 1], &buffer[kk], static_cast<size_t>(length - kk));
        buffer[kk] = '.';
        if(0 > k + maxDecimalPlaces)
        {
            // When maxDecimalPlaces = 2, 1.2345 -> 1.23, 1.102 -> 1.1
            // Remove extra trailing zeros (at least one) after truncation.
            for(int i = kk + maxDecimalPlaces; i > kk + 1; i--)
                if(buffer[i] != '0')
                    return &buffer[i + 1];
            return &buffer[kk + 2]; // Reserve one zero
        }
        else
            return &buffer[length + 1];
    }
    else if(-6 < kk && kk <= 0)
    {
        // 1234e-6 -> 0.001234
        const int offset = 2 - kk;
        std::memmove(&buffer[offset], &buffer[0], static_cast<size_t>(length));
        buffer[0] = '0';
        buffer[1] = '.';
        for(int i = 2; i < offset; i++)
            buffer[i] = '0';
        if(length - kk > maxDecimalPlaces)
        {
            // When maxDecimalPlaces = 2, 0.123 -> 0.12, 0.102 -> 0.1
            // Remove extra trailing zeros (at least one) after truncation.
            for(int i = maxDecimalPlaces + 1; i > 2; i--)
                if(buffer[i] != '0')
                    return &buffer[i + 1];
            return &buffer[3]; // Reserve one zero
        }
        else
            return &buffer[length + offset];
    }
    else if(kk < -maxDecimalPlaces)
    {
        // Truncate to zero
        buffer[0] = '0';
        buffer[1] = '.';
        buffer[2] = '0';
        return &buffer[3];
    }
    else if(length == 1)
    {
        // 1e30
        buffer[1] = 'e';
        return WriteExponent(kk - 1, &buffer[2]);
    }
    else
    {
        // 1234e30 -> 1.234e33
        std::memmove(&buffer[2], &buffer[1], static_cast<size_t>(length - 1));
        buffer[1]          = '.';
        buffer[length + 1] = 'e';
        return WriteExponent(kk - 1, &buffer[0 + length + 2]);
    }
}
 
inline char* dtoa(double value, char* buffer, int maxDecimalPlaces = 324)
{
    RAPIDJSON_ASSERT(maxDecimalPlaces >= 1);
    Double d(value);
    if(d.IsZero())
    {
        if(d.Sign())
            *buffer++ = '-'; // -0.0, Issue #289
        buffer[0] = '0';
        buffer[1] = '.';
        buffer[2] = '0';
        return &buffer[3];
    }
    else
    {
        if(value < 0)
        {
            *buffer++ = '-';
            value     = -value;
        }
        int length, K;
        Grisu2(value, buffer, &length, &K);
        return Prettify(buffer, length, K, maxDecimalPlaces);
    }
}
 
#ifdef __GNUC__
RAPIDJSON_DIAG_POP
#endif
 
} // namespace internal
RAPIDJSON_NAMESPACE_END
 
#endif // RAPIDJSON_DTOA_