// SPDX-License-Identifier: MIT
// Copyright (C) 2014 Milo Yip
// https://github.com/miloyip/dtoa-benchmark
//
#pragma once
#include <cassert>
#include <cmath>
#include <limits>
#include <cstring>

//#if defined(_MSC_VER)
//#include "msinttypes/stdint.h"
//#include <intrin.h>
//#else
// cstdint should be available for VS2019 or later
#include <cstdint>
//#endif

// TINYUSDZ: TODO: Completely disable int128 feature for portablity?
#if defined(__GNUC__)
#if (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)) && \
    defined(__x86_64__)
namespace gcc_ints
{
    __extension__ typedef __int128 int128;
    __extension__ typedef unsigned __int128 uint128;
}  // namespace gcc_ints
#endif
#endif

#define UINT64_C2(h, l) ((static_cast<uint64_t>(h) << 32) | static_cast<uint64_t>(l))

class Double {
public:
    Double() {}
    Double(double d) : d_(d) {}
    Double(uint64_t u) : u_(u) {}

    double Value() const { return d_; }
    uint64_t Uint64Value() const { return u_; }

    double NextPositiveDouble() const {
        //RAPIDJSON_ASSERT(!Sign());
        return Double(u_ + 1).Value();
    }

    bool Sign() const { return (u_ & kSignMask) != 0; }
    uint64_t Significand() const { return u_ & kSignificandMask; }
    int Exponent() const { return static_cast<int>(((u_ & kExponentMask) >> kSignificandSize) - kExponentBias); }

    bool IsNan() const { return (u_ & kExponentMask) == kExponentMask && Significand() != 0; }
    bool IsInf() const { return (u_ & kExponentMask) == kExponentMask && Significand() == 0; }
    bool IsNanOrInf() const { return (u_ & kExponentMask) == kExponentMask; }
    bool IsNormal() const { return (u_ & kExponentMask) != 0 || Significand() == 0; }
    bool IsZero() const { return (u_ & (kExponentMask | kSignificandMask)) == 0; }

    uint64_t IntegerSignificand() const { return IsNormal() ? Significand() | kHiddenBit : Significand(); }
    int IntegerExponent() const { return (IsNormal() ? Exponent() : kDenormalExponent) - kSignificandSize; }
    uint64_t ToBias() const { return (u_ & kSignMask) ? ~u_ + 1 : u_ | kSignMask; }

    static int EffectiveSignificandSize(int order) {
        if (order >= -1021)
            return 53;
        else if (order <= -1074)
            return 0;
        else
            return order + 1074;
    }

private:
    static const int kSignificandSize = 52;
    static const int kExponentBias = 0x3FF;
    static const int kDenormalExponent = 1 - kExponentBias;
    static const uint64_t kSignMask = UINT64_C2(0x80000000, 0x00000000);
    static const uint64_t kExponentMask = UINT64_C2(0x7FF00000, 0x00000000);
    static const uint64_t kSignificandMask = UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
    static const uint64_t kHiddenBit = UINT64_C2(0x00100000, 0x00000000);

    union {
        double d_;
        uint64_t u_;
    };
};

struct DiyFp {
	DiyFp() {}

	DiyFp(uint64_t _f, int _e) : f(_f), e(_e) {}

	DiyFp(double d) {
		union {
			double d;
			uint64_t u64;
		} u = { d };

		int biased_e = (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 {
		assert(e == rhs.e);
		assert(f >= rhs.f);
		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__)
        gcc_ints::uint128 p = static_cast<gcc_ints::uint128>(f) * static_cast<gcc_ints::uint128>(rhs.f);
		uint64_t h = 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;  /// mult_round
		return DiyFp(ac + (ad >> 32) + (bc >> 32) + (tmp >> 32), e + rhs.e + 64);
#endif
	}

	DiyFp Normalize() const {
#if defined(_MSC_VER) && defined(_M_AMD64)
		unsigned long index;
		_BitScanReverse64(&index, f);
		return DiyFp(f << (63 - int(index)), e - (63 - int(index)));
#elif defined(__GNUC__)
		int s = __builtin_clzll(f);
		return DiyFp(f << s, e - s);
#else
		DiyFp res = *this;
		while (!(res.f & kDpHiddenBit)) {
			res.f <<= 1;
			res.e--;
		}
		res.f <<= (kDiySignificandSize - kDpSignificandSize - 1);
		res.e = res.e - (kDiySignificandSize - kDpSignificandSize - 1);
		return res;
#endif
	}

	DiyFp NormalizeBoundary() const {
#if defined(_MSC_VER) && defined(_M_AMD64)
		unsigned long index;
		_BitScanReverse64(&index, f);
		return DiyFp (f << (63 - int(index)), e - (63 - int(index)));
#else
		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;
#endif
	}

	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;
	}

	static const int kDiySignificandSize = 64;
	static const int kDpSignificandSize = 52;
	static const int kDpExponentBias = 0x3FF + kDpSignificandSize;
	static const int kDpMinExponent = -kDpExponentBias;
	static const uint64_t kDpExponentMask = UINT64_C2(0x7FF00000, 0x00000000);
	static const uint64_t kDpSignificandMask = UINT64_C2(0x000FFFFF, 0xFFFFFFFF);
	static const uint64_t kDpHiddenBit = UINT64_C2(0x00100000, 0x00000000);

	uint64_t f;
	int e;
};

inline DiyFp GetCachedPower(int e, int* K) {
	// 10^-348, 10^-340, ..., 10^340
	static const uint64_t kCachedPowers_F[] = {
		UINT64_C2(0xfa8fd5a0, 0x081c0288), UINT64_C2(0xbaaee17f, 0xa23ebf76),
		UINT64_C2(0x8b16fb20, 0x3055ac76), UINT64_C2(0xcf42894a, 0x5dce35ea),
		UINT64_C2(0x9a6bb0aa, 0x55653b2d), UINT64_C2(0xe61acf03, 0x3d1a45df),
		UINT64_C2(0xab70fe17, 0xc79ac6ca), UINT64_C2(0xff77b1fc, 0xbebcdc4f),
		UINT64_C2(0xbe5691ef, 0x416bd60c), UINT64_C2(0x8dd01fad, 0x907ffc3c),
		UINT64_C2(0xd3515c28, 0x31559a83), UINT64_C2(0x9d71ac8f, 0xada6c9b5),
		UINT64_C2(0xea9c2277, 0x23ee8bcb), UINT64_C2(0xaecc4991, 0x4078536d),
		UINT64_C2(0x823c1279, 0x5db6ce57), UINT64_C2(0xc2109436, 0x4dfb5637),
		UINT64_C2(0x9096ea6f, 0x3848984f), UINT64_C2(0xd77485cb, 0x25823ac7),
		UINT64_C2(0xa086cfcd, 0x97bf97f4), UINT64_C2(0xef340a98, 0x172aace5),
		UINT64_C2(0xb23867fb, 0x2a35b28e), UINT64_C2(0x84c8d4df, 0xd2c63f3b),
		UINT64_C2(0xc5dd4427, 0x1ad3cdba), UINT64_C2(0x936b9fce, 0xbb25c996),
		UINT64_C2(0xdbac6c24, 0x7d62a584), UINT64_C2(0xa3ab6658, 0x0d5fdaf6),
		UINT64_C2(0xf3e2f893, 0xdec3f126), UINT64_C2(0xb5b5ada8, 0xaaff80b8),
		UINT64_C2(0x87625f05, 0x6c7c4a8b), UINT64_C2(0xc9bcff60, 0x34c13053),
		UINT64_C2(0x964e858c, 0x91ba2655), UINT64_C2(0xdff97724, 0x70297ebd),
		UINT64_C2(0xa6dfbd9f, 0xb8e5b88f), UINT64_C2(0xf8a95fcf, 0x88747d94),
		UINT64_C2(0xb9447093, 0x8fa89bcf), UINT64_C2(0x8a08f0f8, 0xbf0f156b),
		UINT64_C2(0xcdb02555, 0x653131b6), UINT64_C2(0x993fe2c6, 0xd07b7fac),
		UINT64_C2(0xe45c10c4, 0x2a2b3b06), UINT64_C2(0xaa242499, 0x697392d3),
		UINT64_C2(0xfd87b5f2, 0x8300ca0e), UINT64_C2(0xbce50864, 0x92111aeb),
		UINT64_C2(0x8cbccc09, 0x6f5088cc), UINT64_C2(0xd1b71758, 0xe219652c),
		UINT64_C2(0x9c400000, 0x00000000), UINT64_C2(0xe8d4a510, 0x00000000),
		UINT64_C2(0xad78ebc5, 0xac620000), UINT64_C2(0x813f3978, 0xf8940984),
		UINT64_C2(0xc097ce7b, 0xc90715b3), UINT64_C2(0x8f7e32ce, 0x7bea5c70),
		UINT64_C2(0xd5d238a4, 0xabe98068), UINT64_C2(0x9f4f2726, 0x179a2245),
		UINT64_C2(0xed63a231, 0xd4c4fb27), UINT64_C2(0xb0de6538, 0x8cc8ada8),
		UINT64_C2(0x83c7088e, 0x1aab65db), UINT64_C2(0xc45d1df9, 0x42711d9a),
		UINT64_C2(0x924d692c, 0xa61be758), UINT64_C2(0xda01ee64, 0x1a708dea),
		UINT64_C2(0xa26da399, 0x9aef774a), UINT64_C2(0xf209787b, 0xb47d6b85),
		UINT64_C2(0xb454e4a1, 0x79dd1877), UINT64_C2(0x865b8692, 0x5b9bc5c2),
		UINT64_C2(0xc83553c5, 0xc8965d3d), UINT64_C2(0x952ab45c, 0xfa97a0b3),
		UINT64_C2(0xde469fbd, 0x99a05fe3), UINT64_C2(0xa59bc234, 0xdb398c25),
		UINT64_C2(0xf6c69a72, 0xa3989f5c), UINT64_C2(0xb7dcbf53, 0x54e9bece),
		UINT64_C2(0x88fcf317, 0xf22241e2), UINT64_C2(0xcc20ce9b, 0xd35c78a5),
		UINT64_C2(0x98165af3, 0x7b2153df), UINT64_C2(0xe2a0b5dc, 0x971f303a),
		UINT64_C2(0xa8d9d153, 0x5ce3b396), UINT64_C2(0xfb9b7cd9, 0xa4a7443c),
		UINT64_C2(0xbb764c4c, 0xa7a44410), UINT64_C2(0x8bab8eef, 0xb6409c1a),
		UINT64_C2(0xd01fef10, 0xa657842c), UINT64_C2(0x9b10a4e5, 0xe9913129),
		UINT64_C2(0xe7109bfb, 0xa19c0c9d), UINT64_C2(0xac2820d9, 0x623bf429),
		UINT64_C2(0x80444b5e, 0x7aa7cf85), UINT64_C2(0xbf21e440, 0x03acdd2d),
		UINT64_C2(0x8e679c2f, 0x5e44ff8f), UINT64_C2(0xd433179d, 0x9c8cb841),
		UINT64_C2(0x9e19db92, 0xb4e31ba9), UINT64_C2(0xeb96bf6e, 0xbadf77d9),
		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
	};

	//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

	assert(index < sizeof(kCachedPowers_F) / sizeof(kCachedPowers_F[0]));
	return DiyFp(kCachedPowers_F[index], kCachedPowers_E[index]);
}

inline const char* GetDigitsLut() {
	static const char cDigitsLut[200] = {
		'0', '0', '0', '1', '0', '2', '0', '3', '0', '4', '0', '5', '0', '6', '0', '7', '0', '8', '0', '9',
		'1', '0', '1', '1', '1', '2', '1', '3', '1', '4', '1', '5', '1', '6', '1', '7', '1', '8', '1', '9',
		'2', '0', '2', '1', '2', '2', '2', '3', '2', '4', '2', '5', '2', '6', '2', '7', '2', '8', '2', '9',
		'3', '0', '3', '1', '3', '2', '3', '3', '3', '4', '3', '5', '3', '6', '3', '7', '3', '8', '3', '9',
		'4', '0', '4', '1', '4', '2', '4', '3', '4', '4', '4', '5', '4', '6', '4', '7', '4', '8', '4', '9',
		'5', '0', '5', '1', '5', '2', '5', '3', '5', '4', '5', '5', '5', '6', '5', '7', '5', '8', '5', '9',
		'6', '0', '6', '1', '6', '2', '6', '3', '6', '4', '6', '5', '6', '6', '6', '7', '6', '8', '6', '9',
		'7', '0', '7', '1', '7', '2', '7', '3', '7', '4', '7', '5', '7', '6', '7', '7', '7', '8', '7', '9',
		'8', '0', '8', '1', '8', '2', '8', '3', '8', '4', '8', '5', '8', '6', '8', '7', '8', '8', '8', '9',
		'9', '0', '9', '1', '9', '2', '9', '3', '9', '4', '9', '5', '9', '6', '9', '7', '9', '8', '9', '9'
	};
	return cDigitsLut;
}

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 ||  /// closer
            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_milo(double value, char* buffer) {

  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];
#if 0
  } else if (d.IsInf()) {
      if (d.Sign())
          *buffer++ = '-';     
      buffer[0] = 'i';
      buffer[1] = 'n';
      buffer[2] = 'f';
      return &buffer[3];
  } else if (d.IsNan()) {
      if (d.Sign())
          *buffer++ = '-';  
      buffer[0] = 'n';
      buffer[1] = 'a';
      buffer[2] = 'n';
      return &buffer[3];
#endif
  } else {
      if (value < 0) {
          *buffer++ = '-';
          value = -value;
      }
      int length, K;
      Grisu2(value, buffer, &length, &K);
      
      int maxDecimalPlaces = 324;
      return Prettify(buffer, length, K, maxDecimalPlaces);
  }

}
