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grisu2.c
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/*
* ********** REFERENCE **********
* URL: https://github.com/miloyip/dtoa-benchmark
* Section: src/grisu, src/milo
*/
#include <stdint.h>
#include <stdbool.h>
#include <string.h>
#include <stdlib.h>
/*
* Using table lookup methods to accelerate division, etc
*/
#ifndef GRISU2_USING_LUT_ACCELERATE
#define GRISU2_USING_LUT_ACCELERATE 1
#endif
#define DIY_SIGNIFICAND_SIZE 64 /* Symbol: 1 bit, Exponent, 11 bits, Mantissa, 52 bits */
#define DP_SIGNIFICAND_SIZE 52 /* Mantissa, 52 bits */
#define DP_EXPONENT_OFFSET 0x3FF /* Exponent offset is 0x3FF */
#define DP_EXPONENT_MASK 0x7FF0000000000000 /* Exponent Mask, 11 bits */
#define DP_SIGNIFICAND_MASK 0x000FFFFFFFFFFFFF /* Mantissa Mask, 52 bits */
#define DP_HIDDEN_BIT 0x0010000000000000 /* Integer bit for Mantissa */
#define D_1_LOG2_10 0.30102999566398114 /* 1/lg(10) */
typedef struct {
uint64_t f;
int32_t e;
} diy_fp_t;
#if 0
static void print_powers_ten_i(void)
{
/*
* min value of e is -1022 - 52 - 63 = -1137;
* max value of e is 1023 - 52 - 0 = 971;
* Range of (Exponent_Value - Exponent_Offset) is (-1022, 1023)
* Divisor of Mantissa is pow(2,52)
* Range of u64 right shift is (0, 63)
*/
int e = 0, k = 0, index = 0;
int min = -1137, max = 971, cnt = 0;
double dk = 0;
printf("static const uint8_t powers_ten_i[] = {");
for (e = min; e <= max; ++e) {
if (cnt++ % 20 == 0)
printf("\n ");
dk = (-61 - e) * D_1_LOG2_10 + 347;
k = (int)dk;
if (dk - k > 0.0)
++k;
index = (unsigned int)((k >> 3) + 1);
printf("%-2d", index);
if (e != max)
printf(", ");
}
printf("\n};\n\n");
}
static void print_number_lut(void)
{
int i = 0, index = 0, max = 0;
max = (100 >> 1) - 1;
printf("static const uint8_t num_10_lut[] = {");
for (i = 0; i <= max; ++i) {
if (i % 25 == 0)
printf("\n ");
index = i / 5;
printf("%d", index);
if (i != max)
printf(", ");
}
printf("\n};\n\n");
max = (1000 >> 2) - 1;
printf("static const uint8_t num_100_lut[] = {");
for (i = 0; i <= max; ++i) {
if (i % 25 == 0)
printf("\n ");
index = i / 25;
printf("%d", index);
if (i != max)
printf(", ");
}
printf("\n};\n\n");
max = (10000 >> 3) - 1;
printf("static const uint8_t num_1000_lut[] = {");
for (i = 0; i <= max; ++i) {
if (i % 25 == 0)
printf("\n ");
index = i / 125;
printf("%d", index);
if (i != max)
printf(", ");
}
printf("\n};\n\n");
}
#endif
#define get_10_multiple(v) (((v)<<1) + ((v)<<3))
#define get_100_multiple(v) (((v)<<2) + ((v)<<5) + ((v)<<6))
#define get_1000_multiple(v) (((v)<<3) + ((v)<<5) + ((v)<<6) + ((v)<<7) + ((v)<<8) + ((v)<<9))
#if GRISU2_USING_LUT_ACCELERATE
static const uint8_t num_10_lut[] = {
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4,
5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9
};
#define get_10_quotient(v) num_10_lut[(v)>>1]
static const uint8_t num_100_lut[] = {
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9
};
#define get_100_quotient(v) num_100_lut[(v)>>2]
static const uint8_t num_1000_lut[] = {
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9
};
#define get_1000_quotient(v) num_1000_lut[(v)>>3]
#else
#define get_10_quotient(v) ((v) / 10)
#define get_100_quotient(v) ((v) / 100)
#define get_1000_quotient(v) ((v) / 1000)
#endif
static inline diy_fp_t cached_power(int e, int* K)
{
// 10^-348, 10^-340, ..., 10^340
static const uint64_t powers_ten[] = {
0xfa8fd5a0081c0288, 0xbaaee17fa23ebf76, 0x8b16fb203055ac76, 0xcf42894a5dce35ea,
0x9a6bb0aa55653b2d, 0xe61acf033d1a45df, 0xab70fe17c79ac6ca, 0xff77b1fcbebcdc4f,
0xbe5691ef416bd60c, 0x8dd01fad907ffc3c, 0xd3515c2831559a83, 0x9d71ac8fada6c9b5,
0xea9c227723ee8bcb, 0xaecc49914078536d, 0x823c12795db6ce57, 0xc21094364dfb5637,
0x9096ea6f3848984f, 0xd77485cb25823ac7, 0xa086cfcd97bf97f4, 0xef340a98172aace5,
0xb23867fb2a35b28e, 0x84c8d4dfd2c63f3b, 0xc5dd44271ad3cdba, 0x936b9fcebb25c996,
0xdbac6c247d62a584, 0xa3ab66580d5fdaf6, 0xf3e2f893dec3f126, 0xb5b5ada8aaff80b8,
0x87625f056c7c4a8b, 0xc9bcff6034c13053, 0x964e858c91ba2655, 0xdff9772470297ebd,
0xa6dfbd9fb8e5b88f, 0xf8a95fcf88747d94, 0xb94470938fa89bcf, 0x8a08f0f8bf0f156b,
0xcdb02555653131b6, 0x993fe2c6d07b7fac, 0xe45c10c42a2b3b06, 0xaa242499697392d3,
0xfd87b5f28300ca0e, 0xbce5086492111aeb, 0x8cbccc096f5088cc, 0xd1b71758e219652c,
0x9c40000000000000, 0xe8d4a51000000000, 0xad78ebc5ac620000, 0x813f3978f8940984,
0xc097ce7bc90715b3, 0x8f7e32ce7bea5c70, 0xd5d238a4abe98068, 0x9f4f2726179a2245,
0xed63a231d4c4fb27, 0xb0de65388cc8ada8, 0x83c7088e1aab65db, 0xc45d1df942711d9a,
0x924d692ca61be758, 0xda01ee641a708dea, 0xa26da3999aef774a, 0xf209787bb47d6b85,
0xb454e4a179dd1877, 0x865b86925b9bc5c2, 0xc83553c5c8965d3d, 0x952ab45cfa97a0b3,
0xde469fbd99a05fe3, 0xa59bc234db398c25, 0xf6c69a72a3989f5c, 0xb7dcbf5354e9bece,
0x88fcf317f22241e2, 0xcc20ce9bd35c78a5, 0x98165af37b2153df, 0xe2a0b5dc971f303a,
0xa8d9d1535ce3b396, 0xfb9b7cd9a4a7443c, 0xbb764c4ca7a44410, 0x8bab8eefb6409c1a,
0xd01fef10a657842c, 0x9b10a4e5e9913129, 0xe7109bfba19c0c9d, 0xac2820d9623bf429,
0x80444b5e7aa7cf85, 0xbf21e44003acdd2d, 0x8e679c2f5e44ff8f, 0xd433179d9c8cb841,
0x9e19db92b4e31ba9, 0xeb96bf6ebadf77d9, 0xaf87023b9bf0ee6b
};
static const int16_t powers_ten_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
};
#if GRISU2_USING_LUT_ACCELERATE
/* powers_ten_i is got from print_powers_ten_i */
static const uint8_t powers_ten_i[] = {
84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84, 84,
84, 84, 84, 84, 84, 84, 84, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83,
83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 82, 82, 82, 82, 82, 82, 82,
82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82, 82,
81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81,
81, 81, 81, 81, 81, 81, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80,
80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 80, 79, 79, 79, 79, 79, 79, 79,
79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79, 79,
78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78, 78,
78, 78, 78, 78, 78, 78, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77,
77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 76, 76, 76, 76, 76, 76, 76,
76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 76, 75,
75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75, 75,
75, 75, 75, 75, 75, 75, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74,
74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 74, 73, 73, 73, 73, 73, 73, 73,
73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 72,
72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72,
72, 72, 72, 72, 72, 72, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71,
71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 71, 70, 70, 70, 70, 70, 70, 70, 70,
70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 69,
69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69,
69, 69, 69, 69, 69, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68,
68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 67, 67, 67, 67, 67, 67, 67, 67,
67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 66,
66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66,
66, 66, 66, 66, 66, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65,
65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 64, 64, 64, 64, 64, 64, 64, 64,
64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 63, 63,
63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63,
63, 63, 63, 63, 63, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62,
62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 61, 61, 61, 61, 61, 61, 61, 61, 61,
61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 60, 60,
60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60, 60,
60, 60, 60, 60, 60, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59,
59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 58, 58, 58, 58, 58, 58, 58, 58, 58,
58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 57, 57,
57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57, 57,
57, 57, 57, 57, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56,
56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 55, 55, 55, 55, 55, 55, 55, 55, 55,
55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 54, 54, 54,
54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54, 54,
54, 54, 54, 54, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53,
53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 53, 52, 52, 52, 52, 52, 52, 52, 52, 52,
52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 51, 51, 51,
51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51,
51, 51, 51, 51, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50,
50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49,
49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 48, 48, 48,
48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48,
48, 48, 48, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 47,
47, 47, 47, 47, 47, 47, 47, 47, 47, 47, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46,
46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 45, 45, 45,
45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45, 45,
45, 45, 45, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44,
44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43,
43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 42, 42, 42, 42,
42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42,
42, 42, 42, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41,
41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40,
40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 39, 39, 39, 39,
39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39,
39, 39, 39, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38,
38, 38, 38, 38, 38, 38, 38, 38, 38, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 36, 36, 36, 36,
36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36,
36, 36, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35, 35,
35, 35, 35, 35, 35, 35, 35, 35, 35, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34,
34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 33, 33, 33, 33,
33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33,
33, 33, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32,
32, 32, 32, 32, 32, 32, 32, 32, 32, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31,
31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 30, 30, 30, 30, 30,
30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30,
30, 30, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29,
29, 29, 29, 29, 29, 29, 29, 29, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28,
28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 27, 27, 27, 27, 27,
27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27,
27, 27, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26,
26, 26, 26, 26, 26, 26, 26, 26, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25,
25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 24, 24, 24, 24, 24,
24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24,
24, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23,
23, 23, 23, 23, 23, 23, 23, 23, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22,
22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 21, 21, 21, 21, 21, 21,
21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21,
21, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20,
20, 20, 20, 20, 20, 20, 20, 20, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19,
19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 18, 18, 18, 18, 18, 18,
18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18,
18, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17,
17, 17, 17, 17, 17, 17, 17, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16,
16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 15, 15, 15, 15, 15, 15,
15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15,
14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14,
14, 14, 14, 14, 14, 14, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13,
13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11,
11, 11, 11, 11, 11, 11, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10,
10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6,
6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
5, 5, 5, 5, 5, 5, 5, 5, 5
};
const unsigned int index = powers_ten_i[e + 1137];
#else
const double dk = (-61 - e) * D_1_LOG2_10 + 347;
int k = (int)dk; /* dk must be positive, so can do ceiling in positive */
if (dk - k > 0.0)
++k;
const unsigned int index = (unsigned int)((k >> 3) + 1);
#endif
diy_fp_t res;
res.f = powers_ten[index];
res.e = powers_ten_e[index];
*K = -(-348 + (int)(index << 3)); /* decimal exponent no need lookup table */
return res;
}
static inline int get_u64_prefix0(uint64_t f)
{
#if defined(_MSC_VER) && defined(_M_AMD64)
unsigned long index;
_BitScanReverse64(&index, f);
return 63 - index;
#elif defined(__GNUC__) || defined(__clang__)
return __builtin_clzll(f);
#else
int index = DP_SIGNIFICAND_SIZE + 1; /* max value of diy_fp_t.f is smaller than pow(2, 54) */
while (!(f & ((uint64_t)1 << index)))
--index;
return (63 - index);
#endif
}
static diy_fp_t diy_fp_multiply(diy_fp_t x, diy_fp_t y)
{
#if defined(_MSC_VER) && defined(_M_AMD64)
uint64_t h;
const uint64_t l = _umul128(x.f, y.f, &h);
if (l & ((uint64_t)1 << 63)) /* rounding */
++h;
#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) || __clang_major__ >= 9) && (__WORDSIZE == 64)
__extension__ typedef unsigned __int128 uint128;
const uint128 p = (uint128)x.f * (uint128)y.f;
uint64_t h = (uint64_t)(p >> 64);
if ((uint64_t)p & ((uint64_t)1 << 63)) /* rounding */
++h;
#else
const uint64_t M32 = 0XFFFFFFFF;
const uint64_t a = x.f >> 32;
const uint64_t b = x.f & M32;
const uint64_t c = y.f >> 32;
const uint64_t d = y.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 */
const uint64_t h = ac + (ad >> 32) + (bc >> 32) + (tmp >> 32);
#endif
diy_fp_t r;
r.f = h;
r.e = x.e + y.e + 64;
return r;
}
static inline void grisu_round(char* buffer, int len,
uint64_t delta, uint64_t rest, uint64_t ten_kappa, uint64_t W_pv)
{
uint64_t t = rest + ten_kappa;
while (rest < W_pv && delta >= t && (W_pv - rest > t - W_pv || t < W_pv)) {
--buffer[len - 1];
rest += ten_kappa;
t += ten_kappa;
}
}
static inline void digit_gen(diy_fp_t Wv, diy_fp_t Wp, uint64_t delta, char* buffer, int* len, int* K)
{
static const uint32_t divs[] = {1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000};
uint32_t p1;
uint64_t p2, p3;
int d, kappa;
diy_fp_t one, W_pv;
one.f = ((uint64_t)1) << -Wp.e;
one.e = Wp.e;
W_pv.f = Wp.f - Wv.f;
W_pv.e = Wp.e;
p1 = Wp.f >> -one.e; /* Mp_cut */
p2 = Wp.f & (one.f - 1);
/* count decimal digit 32bit */
if (p1 >= 100000) {
if (p1 < 1000000) kappa = 6;
else if (p1 < 10000000) kappa = 7;
else if (p1 < 100000000) kappa = 8;
else if (p1 < 1000000000) kappa = 9;
else kappa = 10;
} else {
if (p1 >= 10000) kappa = 5;
else if (p1 >= 1000) kappa = 4;
else if (p1 >= 100) kappa = 3;
else if (p1 >= 10) kappa = 2;
else kappa = 1;
}
*len = 0;
while (kappa > 0) {
switch (kappa) {
case 10: d = p1 / 1000000000 ; p1 -= d * 1000000000 ; break;
case 9: d = p1 / 100000000 ; p1 -= d * 100000000 ; break;
case 8: d = p1 / 10000000 ; p1 -= d * 10000000 ; break;
case 7: d = p1 / 1000000 ; p1 -= d * 1000000 ; break;
case 6: d = p1 / 100000 ; p1 -= d * 100000 ; break;
case 5: d = p1 / 10000 ; p1 -= d * 10000 ; break;
case 4: d = get_1000_quotient(p1); p1 -= get_1000_multiple(d); break;
case 3: d = get_100_quotient(p1) ; p1 -= get_100_multiple(d) ; break;
case 2: d = get_10_quotient(p1) ; p1 -= get_10_multiple(d) ; 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
break;
}
buffer[(*len)++] = '0' + d; /* Mp_inv1 */
--kappa;
p3 = (((uint64_t)p1) << -one.e) + p2;
if (p3 <= delta) { /* Mp_delta */
*K += kappa;
grisu_round(buffer, *len, delta, p3, ((uint64_t)divs[kappa]) << -one.e, W_pv.f);
return;
}
}
while (1) {
p2 = (p2 << 1) + (p2 << 3);
delta = (delta << 1) + (delta << 3);
d = p2 >> -one.e;
buffer[(*len)++] = '0' + d;
--kappa;
p2 &= one.f - 1;
if (p2 < delta) {
*K += kappa;
grisu_round(buffer, *len, delta, p2, one.f, W_pv.f * divs[-kappa]);
return;
}
}
}
static inline void grisu2(double value, char* buffer, int* length, int* K)
{
diy_fp_t v, w_v, w_m, w_p, c_mk, Wv, Wm, Wp;
int z_v, z_p;
/* convert double to diy_fp */
union {double d; uint64_t n;} u = {.d = value};
int biased_e = (u.n & DP_EXPONENT_MASK) >> DP_SIGNIFICAND_SIZE; /* Exponent */
uint64_t significand = u.n & DP_SIGNIFICAND_MASK; /* Mantissa */
if (biased_e != 0) { /* normalized double */
v.f = significand + DP_HIDDEN_BIT; /* Normalized double has a extra integer bit for Mantissa */
v.e = biased_e - DP_EXPONENT_OFFSET - DP_SIGNIFICAND_SIZE; /* Exponent offset: -1023, divisor of Mantissa: pow(2,52) */
} else { /* no-normalized double */
v.f = significand; /* Non-normalized double doesn't have a extra integer bit for Mantissa */
v.e = 1 - DP_EXPONENT_OFFSET - DP_SIGNIFICAND_SIZE; /* Fixed Exponent: -1022, divisor of Mantissa: pow(2,52) */
}
/* normalize v and boundaries */
z_v = get_u64_prefix0(v.f);
w_v.f = v.f << z_v;
w_v.e = v.e - z_v;
w_p.f = (v.f << 1) + 1;
w_p.e = v.e - 1;
z_p = get_u64_prefix0(w_p.f);
w_p.f <<= z_p;
w_p.e -= z_p;
if (v.f == DP_HIDDEN_BIT) {
w_m.f = (v.f << 2) - 1;
w_m.e = v.e - 2;
} else {
w_m.f = (v.f << 1) - 1;
w_m.e = v.e - 1;
}
w_m.f <<= w_m.e - w_p.e;
w_m.e = w_p.e;
c_mk = cached_power(w_p.e, K);
Wv = diy_fp_multiply(w_v, c_mk);
Wp = diy_fp_multiply(w_p, c_mk);
Wm = diy_fp_multiply(w_m, c_mk);
++Wm.f;
--Wp.f;
digit_gen(Wv, Wp, Wp.f - Wm.f, buffer, length, K);
}
static inline int fill_exponent(int K, char *buffer)
{
int32_t i = 0, k = 0;
if (K < 0) {
buffer[i++] = '-';
K = -K;
} else {
buffer[i++] = '+';
}
if (K < 10) {
buffer[i++] = '0' + K;
buffer[i] = '\0';
return i;
}
if (K >= 100) {
k = get_100_quotient(K);
K -= get_100_multiple(k);
buffer[i++] = '0' + k;
}
k = get_10_quotient(K);
K -= get_10_multiple(k);
buffer[i++] = '0' + k;
buffer[i++] = '0' + K;
buffer[i] = '\0';
return i;
}
static inline int prettify_string(char* buffer, int length, int K)
{
/*
* v = buffer * 10^k
* kk is such that 10^(kk-1) <= v < 10^kk
* this way kk gives the position of the comma.
*/
const int kk = length + K;
int offset;
if (kk <= 21) {
if (length <= kk) {
/*
* 1234e7 -> 12340000000
* the first digits are already in. Add some 0s and call it a day.
* the 21 is a personal choice. Only 16 digits could possibly be relevant.
* Basically we want to print 12340000000 rather than 1234.0e7 or 1.234e10
*/
memset(&buffer[length], '0', K);
buffer[kk] = '.';
buffer[kk + 1] = '0';
buffer[kk + 2] = '\0';
return (kk + 2);
}
if (kk > 0) {
/*
* 1234e-2 -> 12.34
* comma number. Just insert a '.' at the correct location.
*/
memmove(&buffer[kk + 1], &buffer[kk], length - kk);
buffer[kk] = '.';
buffer[length + 1] = '\0';
return length + 1;
}
if (kk > -6) {
/*
* 1234e-6 -> 0.001234
* something like 0.000abcde.
* add '0.' and some '0's
*/
offset = 2 - kk;
memmove(&buffer[offset], &buffer[0], length);
buffer[0] = '0';
buffer[1] = '.';
memset(&buffer[2], '0', offset - 2);
buffer[length + offset] = '\0';
return length + offset;
}
}
if (length == 1) {
/*
* 1e30
* just add 'e...'
* fill_positive_fixnum will terminate the string
*/
buffer[1] = 'e';
return (2 + fill_exponent(kk - 1, &buffer[2]));
}
/*
* 1234e30 -> 1.234e33
* leave the first digit. then add a '.' and at the end 'e...'
* fill_fixnum will terminate the string.
*/
memmove(&buffer[2], &buffer[1], length - 1);
buffer[1] = '.';
buffer[length + 1] = 'e';
return (length + 2 + fill_exponent(kk - 1, &buffer[length + 2]));
}
int grisu2_dtoa(double num, char *buffer)
{
int length, K, pre = 0;
if (num == 0) {
memcpy(buffer, "0.0", 4);
return 3;
}
if (num < 0) {
*buffer++ = '-';
num = -num;
pre = 1;
}
grisu2(num, buffer, &length, &K);
return (pre + prettify_string(buffer, length, K));
}