emyg_dtoa.c

/* emyg_dtoa.c 
** Copyright (C) 2015 Doug Currie
** based on dtoa_milo.h
** Copyright (C) 2014 Milo Yip
** 
** Permission is hereby granted, free of charge, to any person obtaining a copy
** of this software and associated documentation files (the "Software"), to deal
** in the Software without restriction, including without limitation the rights
** to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
** copies of the Software, and to permit persons to whom the Software is
** furnished to do so, subject to the following conditions:
** 
** The above copyright notice and this permission notice shall be included in
** all copies or substantial portions of the Software.
** 
** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
** IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
** FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
** AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
** LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
** OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
** THE SOFTWARE.
*/

/* This code is a mostly mechanical translation of Milo Yip's C++ version of 
** Grisu2 to C.  For algorithm information, see Loitsch, Florian. "Printing 
** floating-point numbers quickly and accurately with integers." ACM Sigplan 
** Notices 45.6 (2010): 233-243.
*/

#include <assert.h>
#include <math.h>

#if defined(_MSC_VER)
#include "msinttypes/stdint.h"
#include <intrin.h>
#else
#include <stdint.h>
#endif

#include <string.h>

#include "emyg_dtoa.h"

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

typedef struct DiyFp_s {
	uint64_t f;
	int e;
} DiyFp;

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);

static inline DiyFp DiyFp_from_parts (uint64_t f, int e) {
	DiyFp fp;
	fp.f = f;
	fp.e = e;
	return fp;
}

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

	int biased_e = (u.u64 & kDpExponentMask) >> kDpSignificandSize;
	uint64_t significand = (u.u64 & kDpSignificandMask);
	if (biased_e != 0) {
		res.f = significand + kDpHiddenBit;
		res.e = biased_e - kDpExponentBias;
	} 
	else {
		res.f = significand;
		res.e = kDpMinExponent + 1;
	}
	return res;
}

static inline DiyFp DiyFp_subtract (const DiyFp lhs, const DiyFp rhs) {
	assert(lhs.e == rhs.e);
	assert(lhs.f >= rhs.f);
	return DiyFp_from_parts(lhs.f - rhs.f, lhs.e);
}

static inline DiyFp DiyFp_multiply (const DiyFp lhs, const DiyFp rhs) {
#if defined(_MSC_VER) && defined(_M_AMD64)
	uint64_t h;
	uint64_t l = _umul128(lhs.f, rhs.f, &h);
	if (l & (uint64_t(1) << 63)) // rounding
		h++;
	return DiyFp_fro_parts(h, e + rhs.e + 64);
#elif ((__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) || __clang_major__ >= 9) && defined(__x86_64__))
	unsigned __int128 p = (unsigned __int128 )(lhs.f) * (unsigned __int128 )(rhs.f);
	uint64_t h = p >> 64;
	uint64_t l = (uint64_t )(p);
	if (l & ((uint64_t )1u << 63)) // rounding
		h++;
	return DiyFp_from_parts(h, lhs.e + rhs.e + 64);
#else
	const uint64_t M32 = 0xFFFFFFFF;
	const uint64_t a = lhs.f >> 32;
	const uint64_t b = lhs.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_from_parts(ac + (ad >> 32) + (bc >> 32) + (tmp >> 32), lhs.e + rhs.e + 64);
#endif
}

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

static inline DiyFp NormalizeBoundary (const DiyFp lhs) {
#if defined(_MSC_VER) && defined(_M_AMD64)
	unsigned long index;
	_BitScanReverse64(&index, lhs.f);
	return DiyFp_from_parts(lhs.f << (63 - index), lhs.e - (63 - index));
#else
	DiyFp res = lhs;
	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
}

static inline void NormalizedBoundaries (DiyFp lhs, DiyFp* minus, DiyFp* plus) {
	DiyFp pl = NormalizeBoundary(DiyFp_from_parts((lhs.f << 1) + 1, lhs.e - 1));
	DiyFp mi = (lhs.f == kDpHiddenBit) 
				? DiyFp_from_parts((lhs.f << 2) - 1, lhs.e - 2) 
				: DiyFp_from_parts((lhs.f << 1) - 1, lhs.e - 1);
	mi.f <<= mi.e - pl.e;
	mi.e = pl.e;
	*plus = pl;
	*minus = mi;
}

static 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 = (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 = (int )(dk);
	if (k != dk)
		k++;

	unsigned index = (unsigned )((k >> 3) + 1);
	*K = -(-348 + (int )(index << 3));	// decimal exponent no need lookup table

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

static 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;
	}
}

static inline unsigned 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;
	if (n < 1000000000) return 9;
	return 10;
}

static inline void DigitGen(const DiyFp W, const DiyFp Mp, uint64_t delta, char* buffer, int* len, int* K) {
	static const uint32_t kPow10[] = { 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000 };
	const DiyFp one = DiyFp_from_parts((uint64_t )(1) << -Mp.e, Mp.e);
	const DiyFp wp_w = DiyFp_subtract(Mp, W);
	uint32_t p1 = (uint32_t )(Mp.f >> -one.e);
	uint64_t p2 = Mp.f & (one.f - 1);
	int kappa = (int )(CountDecimalDigit32(p1));
	*len = 0;

	while (kappa > 0) {
		uint32_t d;
		switch (kappa) {
			case 10: d = p1 / 1000000000; p1 %= 1000000000; break;
			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 defined(_MSC_VER)
				__assume(0);
#elif __GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 5)
				__builtin_unreachable();
#else
				d = 0;
#endif
		}
		if (d || *len)
			buffer[(*len)++] = '0' + (char )(d);
		kappa--;
		uint64_t tmp = ((uint64_t )(p1) << -one.e) + p2;
		if (tmp <= delta) {
			*K += kappa;
			GrisuRound(buffer, *len, delta, tmp, (uint64_t )(kPow10[kappa]) << -one.e, wp_w.f);
			return;
		}
	}

	// kappa = 0
	for (;;) {
		p2 *= 10;
		delta *= 10;
		char d = (char )(p2 >> -one.e);
		if (d || *len)
			buffer[(*len)++] = '0' + d;
		p2 &= one.f - 1;
		kappa--;
		if (p2 < delta) {
			*K += kappa;
			GrisuRound(buffer, *len, delta, p2, one.f, wp_w.f * kPow10[-kappa]);
			return;
		}
	}
}

static inline void Grisu2(double value, char* buffer, int* length, int* K) {
	const DiyFp v = DiyFp_from_double(value);
	DiyFp w_m, w_p;
	NormalizedBoundaries(v, &w_m, &w_p);

	const DiyFp c_mk = GetCachedPower(w_p.e, K);
	const DiyFp W = DiyFp_multiply(Normalize(v), c_mk);
	DiyFp Wp = DiyFp_multiply(w_p, c_mk);
	DiyFp Wm = DiyFp_multiply(w_m, c_mk);
	Wm.f++;
	Wp.f--;
	DigitGen(W, Wp, Wp.f - Wm.f, buffer, length, K);
}

static 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;
}

static inline void WriteExponent(int K, char* buffer) {
	if (K < 0) {
		*buffer++ = '-';
		K = -K;
	}

	if (K >= 100) {
		*buffer++ = '0' + (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++ = '0' + (char )(K);

	*buffer = '\0';
}

static inline void Prettify(char* buffer, int length, int k) {
	const int kk = length + k;	// 10^(kk-1) <= v < 10^kk

	if (length <= kk && kk <= 21) {
		// 1234e7 -> 12340000000
		for (int i = length; i < kk; i++)
			buffer[i] = '0';
		buffer[kk] = '.';
		buffer[kk + 1] = '0';
		buffer[kk + 2] = '\0';
	}
	else if (0 < kk && kk <= 21) {
		// 1234e-2 -> 12.34
		memmove(&buffer[kk + 1], &buffer[kk], length - kk);
		buffer[kk] = '.';
		buffer[length + 1] = '\0';
	}
	else if (-6 < kk && kk <= 0) {
		// 1234e-6 -> 0.001234
		const int offset = 2 - kk;
		memmove(&buffer[offset], &buffer[0], length);
		buffer[0] = '0';
		buffer[1] = '.';
		for (int i = 2; i < offset; i++)
			buffer[i] = '0';
		buffer[length + offset] = '\0';
	}
	else if (length == 1) {
		// 1e30
		buffer[1] = 'e';
		WriteExponent(kk - 1, &buffer[2]);
	}
	else {
		// 1234e30 -> 1.234e33
		memmove(&buffer[2], &buffer[1], length - 1);
		buffer[1] = '.';
		buffer[length + 1] = 'e';
		WriteExponent(kk - 1, &buffer[0 + length + 2]);
	}
}

void emyg_dtoa (double value, char* buffer) {
	// Not handling NaN and inf
	assert(!isnan(value));
	assert(!isinf(value));

	if (value == 0) {
		buffer[0] = '0';
		buffer[1] = '.';
		buffer[2] = '0';
		buffer[3] = '\0';
	}
	else {
		if (value < 0) {
			*buffer++ = '-';
			value = -value;
		}
		int length, K;
		Grisu2(value, buffer, &length, &K);
		Prettify(buffer, length, K);
	}
}