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 // 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_DIYFP_H_
 #define RAPIDJSON_DIYFP_H_
  
 #include "../rapidjson.h"
 #include "clzll.h"
 #include <limits>
  
 #if defined(_MSC_VER) && defined(_M_AMD64) && !defined(__INTEL_COMPILER)
 #include <intrin.h>
 #if !defined(_ARM64EC_)
 #pragma intrinsic(_umul128)
 #else
 #pragma comment(lib, "softintrin")
 #endif
 #endif
  
 RAPIDJSON_NAMESPACE_BEGIN
 namespace internal {
  
 #ifdef __GNUC__
 RAPIDJSON_DIAG_PUSH
 RAPIDJSON_DIAG_OFF(effc++)
 #endif
  
 #ifdef __clang__
 RAPIDJSON_DIAG_PUSH
 RAPIDJSON_DIAG_OFF(padded)
 #endif
  
 struct DiyFp
 {
     DiyFp() : f(), e() {}
  
     DiyFp(uint64_t fp, int exp) : f(fp), e(exp) {}
  
     explicit DiyFp(double d)
     {
         union
         {
             double d;
             uint64_t u64;
         } u = {d};
  
         int biased_e         = static_cast<int>((u.u64 & kDpExponentMask) >> kDpSignificandSize);
         uint64_t significand = (u.u64 & kDpSignificandMask);
         if(biased_e != 0)
         {
             f = significand + kDpHiddenBit;
             e = biased_e - kDpExponentBias;
         }
         else
         {
             f = significand;
             e = kDpMinExponent + 1;
         }
     }
  
     DiyFp operator-(const DiyFp& rhs) const { return DiyFp(f - rhs.f, e); }
  
     DiyFp operator*(const DiyFp& rhs) const
     {
 #if defined(_MSC_VER) && defined(_M_AMD64)
         uint64_t h;
         uint64_t l = _umul128(f, rhs.f, &h);
         if(l & (uint64_t(1) << 63)) // rounding
             h++;
         return DiyFp(h, e + rhs.e + 64);
 #elif defined(__GNUC__) && (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && \
     defined(__x86_64__)
         __extension__ typedef unsigned __int128 uint128;
         uint128 p  = static_cast<uint128>(f) * static_cast<uint128>(rhs.f);
         uint64_t h = static_cast<uint64_t>(p >> 64);
         uint64_t l = static_cast<uint64_t>(p);
         if(l & (uint64_t(1) << 63)) // rounding
             h++;
         return DiyFp(h, e + rhs.e + 64);
 #else
         const uint64_t M32 = 0xFFFFFFFF;
         const uint64_t a   = f >> 32;
         const uint64_t b   = f & M32;
         const uint64_t c   = rhs.f >> 32;
         const uint64_t d   = rhs.f & M32;
         const uint64_t ac  = a * c;
         const uint64_t bc  = b * c;
         const uint64_t ad  = a * d;
         const uint64_t bd  = b * d;
         uint64_t tmp       = (bd >> 32) + (ad & M32) + (bc & M32);
         tmp += 1U << 31; 
         return DiyFp(ac + (ad >> 32) + (bc >> 32) + (tmp >> 32), e + rhs.e + 64);
 #endif
     }
  
     DiyFp Normalize() const
     {
         int s = static_cast<int>(clzll(f));
         return DiyFp(f << s, e - s);
     }
  
     DiyFp NormalizeBoundary() const
     {
         DiyFp res = *this;
         while(!(res.f & (kDpHiddenBit << 1)))
         {
             res.f <<= 1;
             res.e--;
         }
         res.f <<= (kDiySignificandSize - kDpSignificandSize - 2);
         res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 2);
         return res;
     }
  
     void NormalizedBoundaries(DiyFp* minus, DiyFp* plus) const
     {
         DiyFp pl = DiyFp((f << 1) + 1, e - 1).NormalizeBoundary();
         DiyFp mi = (f == kDpHiddenBit) ? DiyFp((f << 2) - 1, e - 2) : DiyFp((f << 1) - 1, e - 1);
         mi.f <<= mi.e - pl.e;
         mi.e   = pl.e;
         *plus  = pl;
         *minus = mi;
     }
  
     double ToDouble() const
     {
         union
         {
             double d;
             uint64_t u64;
         } u;
         RAPIDJSON_ASSERT(f <= kDpHiddenBit + kDpSignificandMask);
         if(e < kDpDenormalExponent)
         {
             // Underflow.
             return 0.0;
         }
         if(e >= kDpMaxExponent)
         {
             // Overflow.
             return std::numeric_limits<double>::infinity();
         }
         const uint64_t be = (e == kDpDenormalExponent && (f & kDpHiddenBit) == 0)
                                 ? 0
                                 : static_cast<uint64_t>(e + kDpExponentBias);
         u.u64             = (f & kDpSignificandMask) | (be << kDpSignificandSize);
         return u.d;
     }
  
     static const int kDiySignificandSize     = 64;
     static const int kDpSignificandSize      = 52;
     static const int kDpExponentBias         = 0x3FF + kDpSignificandSize;
     static const int kDpMaxExponent          = 0x7FF - kDpExponentBias;
     static const int kDpMinExponent          = -kDpExponentBias;
     static const int kDpDenormalExponent     = -kDpExponentBias + 1;
     static const uint64_t kDpExponentMask    = RAPIDJSON_UINT64_C2(0x7FF00000, 0x00000000);
     static const uint64_t kDpSignificandMask = RAPIDJSON_UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
     static const uint64_t kDpHiddenBit       = RAPIDJSON_UINT64_C2(0x00100000, 0x00000000);
  
     uint64_t f;
     int e;
 };
  
 inline DiyFp GetCachedPowerByIndex(size_t index)
 {
     // 10^-348, 10^-340, ..., 10^340
     static const uint64_t kCachedPowers_F[] = {
         RAPIDJSON_UINT64_C2(0xfa8fd5a0, 0x081c0288), RAPIDJSON_UINT64_C2(0xbaaee17f, 0xa23ebf76),
         RAPIDJSON_UINT64_C2(0x8b16fb20, 0x3055ac76), RAPIDJSON_UINT64_C2(0xcf42894a, 0x5dce35ea),
         RAPIDJSON_UINT64_C2(0x9a6bb0aa, 0x55653b2d), RAPIDJSON_UINT64_C2(0xe61acf03, 0x3d1a45df),
         RAPIDJSON_UINT64_C2(0xab70fe17, 0xc79ac6ca), RAPIDJSON_UINT64_C2(0xff77b1fc, 0xbebcdc4f),
         RAPIDJSON_UINT64_C2(0xbe5691ef, 0x416bd60c), RAPIDJSON_UINT64_C2(0x8dd01fad, 0x907ffc3c),
         RAPIDJSON_UINT64_C2(0xd3515c28, 0x31559a83), RAPIDJSON_UINT64_C2(0x9d71ac8f, 0xada6c9b5),
         RAPIDJSON_UINT64_C2(0xea9c2277, 0x23ee8bcb), RAPIDJSON_UINT64_C2(0xaecc4991, 0x4078536d),
         RAPIDJSON_UINT64_C2(0x823c1279, 0x5db6ce57), RAPIDJSON_UINT64_C2(0xc2109436, 0x4dfb5637),
         RAPIDJSON_UINT64_C2(0x9096ea6f, 0x3848984f), RAPIDJSON_UINT64_C2(0xd77485cb, 0x25823ac7),
         RAPIDJSON_UINT64_C2(0xa086cfcd, 0x97bf97f4), RAPIDJSON_UINT64_C2(0xef340a98, 0x172aace5),
         RAPIDJSON_UINT64_C2(0xb23867fb, 0x2a35b28e), RAPIDJSON_UINT64_C2(0x84c8d4df, 0xd2c63f3b),
         RAPIDJSON_UINT64_C2(0xc5dd4427, 0x1ad3cdba), RAPIDJSON_UINT64_C2(0x936b9fce, 0xbb25c996),
         RAPIDJSON_UINT64_C2(0xdbac6c24, 0x7d62a584), RAPIDJSON_UINT64_C2(0xa3ab6658, 0x0d5fdaf6),
         RAPIDJSON_UINT64_C2(0xf3e2f893, 0xdec3f126), RAPIDJSON_UINT64_C2(0xb5b5ada8, 0xaaff80b8),
         RAPIDJSON_UINT64_C2(0x87625f05, 0x6c7c4a8b), RAPIDJSON_UINT64_C2(0xc9bcff60, 0x34c13053),
         RAPIDJSON_UINT64_C2(0x964e858c, 0x91ba2655), RAPIDJSON_UINT64_C2(0xdff97724, 0x70297ebd),
         RAPIDJSON_UINT64_C2(0xa6dfbd9f, 0xb8e5b88f), RAPIDJSON_UINT64_C2(0xf8a95fcf, 0x88747d94),
         RAPIDJSON_UINT64_C2(0xb9447093, 0x8fa89bcf), RAPIDJSON_UINT64_C2(0x8a08f0f8, 0xbf0f156b),
         RAPIDJSON_UINT64_C2(0xcdb02555, 0x653131b6), RAPIDJSON_UINT64_C2(0x993fe2c6, 0xd07b7fac),
         RAPIDJSON_UINT64_C2(0xe45c10c4, 0x2a2b3b06), RAPIDJSON_UINT64_C2(0xaa242499, 0x697392d3),
         RAPIDJSON_UINT64_C2(0xfd87b5f2, 0x8300ca0e), RAPIDJSON_UINT64_C2(0xbce50864, 0x92111aeb),
         RAPIDJSON_UINT64_C2(0x8cbccc09, 0x6f5088cc), RAPIDJSON_UINT64_C2(0xd1b71758, 0xe219652c),
         RAPIDJSON_UINT64_C2(0x9c400000, 0x00000000), RAPIDJSON_UINT64_C2(0xe8d4a510, 0x00000000),
         RAPIDJSON_UINT64_C2(0xad78ebc5, 0xac620000), RAPIDJSON_UINT64_C2(0x813f3978, 0xf8940984),
         RAPIDJSON_UINT64_C2(0xc097ce7b, 0xc90715b3), RAPIDJSON_UINT64_C2(0x8f7e32ce, 0x7bea5c70),
         RAPIDJSON_UINT64_C2(0xd5d238a4, 0xabe98068), RAPIDJSON_UINT64_C2(0x9f4f2726, 0x179a2245),
         RAPIDJSON_UINT64_C2(0xed63a231, 0xd4c4fb27), RAPIDJSON_UINT64_C2(0xb0de6538, 0x8cc8ada8),
         RAPIDJSON_UINT64_C2(0x83c7088e, 0x1aab65db), RAPIDJSON_UINT64_C2(0xc45d1df9, 0x42711d9a),
         RAPIDJSON_UINT64_C2(0x924d692c, 0xa61be758), RAPIDJSON_UINT64_C2(0xda01ee64, 0x1a708dea),
         RAPIDJSON_UINT64_C2(0xa26da399, 0x9aef774a), RAPIDJSON_UINT64_C2(0xf209787b, 0xb47d6b85),
         RAPIDJSON_UINT64_C2(0xb454e4a1, 0x79dd1877), RAPIDJSON_UINT64_C2(0x865b8692, 0x5b9bc5c2),
         RAPIDJSON_UINT64_C2(0xc83553c5, 0xc8965d3d), RAPIDJSON_UINT64_C2(0x952ab45c, 0xfa97a0b3),
         RAPIDJSON_UINT64_C2(0xde469fbd, 0x99a05fe3), RAPIDJSON_UINT64_C2(0xa59bc234, 0xdb398c25),
         RAPIDJSON_UINT64_C2(0xf6c69a72, 0xa3989f5c), RAPIDJSON_UINT64_C2(0xb7dcbf53, 0x54e9bece),
         RAPIDJSON_UINT64_C2(0x88fcf317, 0xf22241e2), RAPIDJSON_UINT64_C2(0xcc20ce9b, 0xd35c78a5),
         RAPIDJSON_UINT64_C2(0x98165af3, 0x7b2153df), RAPIDJSON_UINT64_C2(0xe2a0b5dc, 0x971f303a),
         RAPIDJSON_UINT64_C2(0xa8d9d153, 0x5ce3b396), RAPIDJSON_UINT64_C2(0xfb9b7cd9, 0xa4a7443c),
         RAPIDJSON_UINT64_C2(0xbb764c4c, 0xa7a44410), RAPIDJSON_UINT64_C2(0x8bab8eef, 0xb6409c1a),
         RAPIDJSON_UINT64_C2(0xd01fef10, 0xa657842c), RAPIDJSON_UINT64_C2(0x9b10a4e5, 0xe9913129),
         RAPIDJSON_UINT64_C2(0xe7109bfb, 0xa19c0c9d), RAPIDJSON_UINT64_C2(0xac2820d9, 0x623bf429),
         RAPIDJSON_UINT64_C2(0x80444b5e, 0x7aa7cf85), RAPIDJSON_UINT64_C2(0xbf21e440, 0x03acdd2d),
         RAPIDJSON_UINT64_C2(0x8e679c2f, 0x5e44ff8f), RAPIDJSON_UINT64_C2(0xd433179d, 0x9c8cb841),
         RAPIDJSON_UINT64_C2(0x9e19db92, 0xb4e31ba9), RAPIDJSON_UINT64_C2(0xeb96bf6e, 0xbadf77d9),
         RAPIDJSON_UINT64_C2(0xaf87023b, 0x9bf0ee6b)};
     static const int16_t kCachedPowers_E[] = {
         -1220, -1193, -1166, -1140, -1113, -1087, -1060, -1034, -1007, -980, -954, -927, -901,
         -874,  -847,  -821,  -794,  -768,  -741,  -715,  -688,  -661,  -635, -608, -582, -555,
         -529,  -502,  -475,  -449,  -422,  -396,  -369,  -343,  -316,  -289, -263, -236, -210,
         -183,  -157,  -130,  -103,  -77,   -50,   -24,   3,     30,    56,   83,   109,  136,
         162,   189,   216,   242,   269,   295,   322,   348,   375,   402,  428,  455,  481,
         508,   534,   561,   588,   614,   641,   667,   694,   720,   747,  774,  800,  827,
         853,   880,   907,   933,   960,   986,   1013,  1039,  1066};
     RAPIDJSON_ASSERT(index < 87);
     return DiyFp(kCachedPowers_F[index], kCachedPowers_E[index]);
 }
  
 inline DiyFp GetCachedPower(int e, int* K)
 {
  
     // int k = static_cast<int>(ceil((-61 - e) * 0.30102999566398114)) + 374;
     double dk =
         (-61 - e) * 0.30102999566398114 + 347; // dk must be positive, so can do ceiling in positive
     int k = static_cast<int>(dk);
     if(dk - k > 0.0)
         k++;
  
     unsigned index = static_cast<unsigned>((k >> 3) + 1);
     *K = -(-348 + static_cast<int>(index << 3)); // decimal exponent no need lookup table
  
     return GetCachedPowerByIndex(index);
 }
  
 inline DiyFp GetCachedPower10(int exp, int* outExp)
 {
     RAPIDJSON_ASSERT(exp >= -348);
     unsigned index = static_cast<unsigned>(exp + 348) / 8u;
     *outExp        = -348 + static_cast<int>(index) * 8;
     return GetCachedPowerByIndex(index);
 }
  
 #ifdef __GNUC__
 RAPIDJSON_DIAG_POP
 #endif
  
 #ifdef __clang__
 RAPIDJSON_DIAG_POP
 RAPIDJSON_DIAG_OFF(padded)
 #endif
  
 } // namespace internal
 RAPIDJSON_NAMESPACE_END
  
 #endif // RAPIDJSON_DIYFP_H_