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dragonbox.c
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/*
* ********** REFERENCE **********
* URL: https://github.com/abolz/Drachennest
* Section: src/dragonbox.cc
*/
#include <stdint.h>
#include <stdbool.h>
#include <string.h>
#include <stdlib.h>
#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_MAX 0x7FF /* Max Exponent value */
#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 */
typedef struct {
uint64_t f;
int32_t e;
} diy_fp_t;
typedef struct {
uint64_t hi;
uint64_t lo;
} u64x2_t;
static const char ch_100_lut[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',
};
static const uint8_t tz_100_lut[100] = {
2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
};
#define FAST_DIV10(n) (ch_100_lut[(n) << 1] - '0') /* 0 <= n < 100 */
#define FAST_DIV100(n) (((n) * 5243) >> 19) /* 0 <= n < 10000 */
#define FAST_DIV10000(n) ((uint32_t)(((uint64_t)(n) * 109951163) >> 40)) /* 0 <= n < 100000000 */
static inline int32_t fill_t_4_digits(char *buffer, uint32_t digits, int32_t *ptz)
{
char *s = buffer;
uint32_t q = FAST_DIV100(digits);
uint32_t r = digits - q * 100;
memcpy(s, &ch_100_lut[q<<1], 2);
memcpy(s + 2, &ch_100_lut[r<<1], 2);
if (!r) {
*ptz = tz_100_lut[q] + 2;
} else {
*ptz = tz_100_lut[r];
}
return 4;
}
static inline int32_t fill_t_8_digits(char *buffer, uint32_t digits, int32_t *ptz)
{
char *s = buffer;
if (digits < 10000) {
memset(s, '0', 4);
fill_t_4_digits(s + 4, digits, ptz);
} else {
uint32_t q = FAST_DIV10000(digits);
uint32_t r = digits - q * 10000;
fill_t_4_digits(s, q, ptz);
if (!r) {
memset(s + 4, '0', 4);
*ptz += 4;
} else {
fill_t_4_digits(s + 4, r, ptz);
}
}
return 8;
}
static inline int32_t fill_t_16_digits(char *buffer, uint64_t digits, int32_t *ptz)
{
char *s = buffer;
if (digits < 100000000llu) {
memset(s, '0', 8);
fill_t_8_digits(s + 8, digits, ptz);
} else {
uint32_t q = (uint32_t)(digits / 100000000);
uint32_t r = (uint32_t)(digits - (uint64_t)q * 100000000);
fill_t_8_digits(s, q, ptz);
if (!r) {
memset(s + 8, '0', 8);
*ptz += 8;
} else {
fill_t_8_digits(s + 8, r, ptz);
}
}
return 16;
}
static inline int32_t fill_1_4_digits(char *buffer, uint32_t digits, int32_t *ptz)
{
char *s = buffer;
if (digits < 100) {
if (digits >= 10) {
*ptz = tz_100_lut[digits];
memcpy(s, &ch_100_lut[digits<<1], 2);
s += 2;
} else {
*ptz = 0;
*s++ = digits + '0';
}
} else {
uint32_t q = FAST_DIV100(digits);
uint32_t r = digits - q * 100;
if (q >= 10) {
*ptz = tz_100_lut[q];
memcpy(s, &ch_100_lut[q<<1], 2);
s += 2;
} else {
*ptz = 0;
*s++ = q + '0';
}
if (!r) {
*ptz += 2;
memset(s, '0', 2);
s += 2;
} else {
*ptz = tz_100_lut[r];
memcpy(s, &ch_100_lut[r<<1], 2);
s += 2;
}
}
return s - buffer;
}
static inline int32_t fill_1_8_digits(char *buffer, uint32_t digits, int32_t *ptz)
{
char *s = buffer;
if (digits < 10000) {
return fill_1_4_digits(s, digits, ptz);
} else {
uint32_t q = FAST_DIV10000(digits);
uint32_t r = digits - q * 10000;
s += fill_1_4_digits(s, q, ptz);
if (!r) {
*ptz += 4;
memset(s, '0', 4);
s += 4;
} else {
s += fill_t_4_digits(s, r, ptz);
}
}
return s - buffer;
}
static inline int32_t fill_1_16_digits(char *buffer, uint64_t digits, int32_t *ptz)
{
char *s = buffer;
if (digits < 100000000llu) {
return fill_1_8_digits(s, (uint32_t)digits, ptz);
} else {
uint32_t q = (uint32_t)(digits / 100000000);
uint32_t r = (uint32_t)(digits - (uint64_t)q * 100000000);
s += fill_1_8_digits(s, q, ptz);
if (!r) {
*ptz += 8;
memset(s, '0', 8);
s += 8;
} else {
s += fill_t_8_digits(s, r, ptz);
}
}
return s - buffer;
}
static inline u64x2_t compute_pow10_double(int32_t k)
{
#define MIN_K -292
#define MAX_K 326
static const u64x2_t pow10_lut[MAX_K - MIN_K + 1] = {
{0xFF77B1FCBEBCDC4F, 0x25E8E89C13BB0F7B},
{0x9FAACF3DF73609B1, 0x77B191618C54E9AD},
{0xC795830D75038C1D, 0xD59DF5B9EF6A2418},
{0xF97AE3D0D2446F25, 0x4B0573286B44AD1E},
{0x9BECCE62836AC577, 0x4EE367F9430AEC33},
{0xC2E801FB244576D5, 0x229C41F793CDA740},
{0xF3A20279ED56D48A, 0x6B43527578C11110},
{0x9845418C345644D6, 0x830A13896B78AAAA},
{0xBE5691EF416BD60C, 0x23CC986BC656D554},
{0xEDEC366B11C6CB8F, 0x2CBFBE86B7EC8AA9},
{0x94B3A202EB1C3F39, 0x7BF7D71432F3D6AA},
{0xB9E08A83A5E34F07, 0xDAF5CCD93FB0CC54},
{0xE858AD248F5C22C9, 0xD1B3400F8F9CFF69},
{0x91376C36D99995BE, 0x23100809B9C21FA2},
{0xB58547448FFFFB2D, 0xABD40A0C2832A78B},
{0xE2E69915B3FFF9F9, 0x16C90C8F323F516D},
{0x8DD01FAD907FFC3B, 0xAE3DA7D97F6792E4},
{0xB1442798F49FFB4A, 0x99CD11CFDF41779D},
{0xDD95317F31C7FA1D, 0x40405643D711D584},
{0x8A7D3EEF7F1CFC52, 0x482835EA666B2573},
{0xAD1C8EAB5EE43B66, 0xDA3243650005EED0},
{0xD863B256369D4A40, 0x90BED43E40076A83},
{0x873E4F75E2224E68, 0x5A7744A6E804A292},
{0xA90DE3535AAAE202, 0x711515D0A205CB37},
{0xD3515C2831559A83, 0x0D5A5B44CA873E04},
{0x8412D9991ED58091, 0xE858790AFE9486C3},
{0xA5178FFF668AE0B6, 0x626E974DBE39A873},
{0xCE5D73FF402D98E3, 0xFB0A3D212DC81290},
{0x80FA687F881C7F8E, 0x7CE66634BC9D0B9A},
{0xA139029F6A239F72, 0x1C1FFFC1EBC44E81},
{0xC987434744AC874E, 0xA327FFB266B56221},
{0xFBE9141915D7A922, 0x4BF1FF9F0062BAA9},
{0x9D71AC8FADA6C9B5, 0x6F773FC3603DB4AA},
{0xC4CE17B399107C22, 0xCB550FB4384D21D4},
{0xF6019DA07F549B2B, 0x7E2A53A146606A49},
{0x99C102844F94E0FB, 0x2EDA7444CBFC426E},
{0xC0314325637A1939, 0xFA911155FEFB5309},
{0xF03D93EEBC589F88, 0x793555AB7EBA27CB},
{0x96267C7535B763B5, 0x4BC1558B2F3458DF},
{0xBBB01B9283253CA2, 0x9EB1AAEDFB016F17},
{0xEA9C227723EE8BCB, 0x465E15A979C1CADD},
{0x92A1958A7675175F, 0x0BFACD89EC191ECA},
{0xB749FAED14125D36, 0xCEF980EC671F667C},
{0xE51C79A85916F484, 0x82B7E12780E7401B},
{0x8F31CC0937AE58D2, 0xD1B2ECB8B0908811},
{0xB2FE3F0B8599EF07, 0x861FA7E6DCB4AA16},
{0xDFBDCECE67006AC9, 0x67A791E093E1D49B},
{0x8BD6A141006042BD, 0xE0C8BB2C5C6D24E1},
{0xAECC49914078536D, 0x58FAE9F773886E19},
{0xDA7F5BF590966848, 0xAF39A475506A899F},
{0x888F99797A5E012D, 0x6D8406C952429604},
{0xAAB37FD7D8F58178, 0xC8E5087BA6D33B84},
{0xD5605FCDCF32E1D6, 0xFB1E4A9A90880A65},
{0x855C3BE0A17FCD26, 0x5CF2EEA09A550680},
{0xA6B34AD8C9DFC06F, 0xF42FAA48C0EA481F},
{0xD0601D8EFC57B08B, 0xF13B94DAF124DA27},
{0x823C12795DB6CE57, 0x76C53D08D6B70859},
{0xA2CB1717B52481ED, 0x54768C4B0C64CA6F},
{0xCB7DDCDDA26DA268, 0xA9942F5DCF7DFD0A},
{0xFE5D54150B090B02, 0xD3F93B35435D7C4D},
{0x9EFA548D26E5A6E1, 0xC47BC5014A1A6DB0},
{0xC6B8E9B0709F109A, 0x359AB6419CA1091C},
{0xF867241C8CC6D4C0, 0xC30163D203C94B63},
{0x9B407691D7FC44F8, 0x79E0DE63425DCF1E},
{0xC21094364DFB5636, 0x985915FC12F542E5},
{0xF294B943E17A2BC4, 0x3E6F5B7B17B2939E},
{0x979CF3CA6CEC5B5A, 0xA705992CEECF9C43},
{0xBD8430BD08277231, 0x50C6FF782A838354},
{0xECE53CEC4A314EBD, 0xA4F8BF5635246429},
{0x940F4613AE5ED136, 0x871B7795E136BE9A},
{0xB913179899F68584, 0x28E2557B59846E40},
{0xE757DD7EC07426E5, 0x331AEADA2FE589D0},
{0x9096EA6F3848984F, 0x3FF0D2C85DEF7622},
{0xB4BCA50B065ABE63, 0x0FED077A756B53AA},
{0xE1EBCE4DC7F16DFB, 0xD3E8495912C62895},
{0x8D3360F09CF6E4BD, 0x64712DD7ABBBD95D},
{0xB080392CC4349DEC, 0xBD8D794D96AACFB4},
{0xDCA04777F541C567, 0xECF0D7A0FC5583A1},
{0x89E42CAAF9491B60, 0xF41686C49DB57245},
{0xAC5D37D5B79B6239, 0x311C2875C522CED6},
{0xD77485CB25823AC7, 0x7D633293366B828C},
{0x86A8D39EF77164BC, 0xAE5DFF9C02033198},
{0xA8530886B54DBDEB, 0xD9F57F830283FDFD},
{0xD267CAA862A12D66, 0xD072DF63C324FD7C},
{0x8380DEA93DA4BC60, 0x4247CB9E59F71E6E},
{0xA46116538D0DEB78, 0x52D9BE85F074E609},
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{0xEA1575143CF97226, 0xF52D09D71A3293BD},
{0x924D692CA61BE758, 0x593C2626705F9C56},
{0xB6E0C377CFA2E12E, 0x6F8B2FB00C77836C},
{0xE498F455C38B997A, 0x0B6DFB9C0F956447},
{0x8EDF98B59A373FEC, 0x4724BD4189BD5EAC},
{0xB2977EE300C50FE7, 0x58EDEC91EC2CB657},
{0xDF3D5E9BC0F653E1, 0x2F2967B66737E3ED},
{0x8B865B215899F46C, 0xBD79E0D20082EE74},
{0xAE67F1E9AEC07187, 0xECD8590680A3AA11},
{0xDA01EE641A708DE9, 0xE80E6F4820CC9495},
{0x884134FE908658B2, 0x3109058D147FDCDD},
{0xAA51823E34A7EEDE, 0xBD4B46F0599FD415},
{0xD4E5E2CDC1D1EA96, 0x6C9E18AC7007C91A},
{0x850FADC09923329E, 0x03E2CF6BC604DDB0},
{0xA6539930BF6BFF45, 0x84DB8346B786151C},
{0xCFE87F7CEF46FF16, 0xE612641865679A63},
{0x81F14FAE158C5F6E, 0x4FCB7E8F3F60C07E},
{0xA26DA3999AEF7749, 0xE3BE5E330F38F09D},
{0xCB090C8001AB551C, 0x5CADF5BFD3072CC5},
{0xFDCB4FA002162A63, 0x73D9732FC7C8F7F6},
{0x9E9F11C4014DDA7E, 0x2867E7FDDCDD9AFA},
{0xC646D63501A1511D, 0xB281E1FD541501B8},
{0xF7D88BC24209A565, 0x1F225A7CA91A4226},
{0x9AE757596946075F, 0x3375788DE9B06958},
{0xC1A12D2FC3978937, 0x0052D6B1641C83AE},
{0xF209787BB47D6B84, 0xC0678C5DBD23A49A},
{0x9745EB4D50CE6332, 0xF840B7BA963646E0},
{0xBD176620A501FBFF, 0xB650E5A93BC3D898},
{0xEC5D3FA8CE427AFF, 0xA3E51F138AB4CEBE},
{0x93BA47C980E98CDF, 0xC66F336C36B10137},
{0xB8A8D9BBE123F017, 0xB80B0047445D4184},
{0xE6D3102AD96CEC1D, 0xA60DC059157491E5},
{0x9043EA1AC7E41392, 0x87C89837AD68DB2F},
{0xB454E4A179DD1877, 0x29BABE4598C311FB},
{0xE16A1DC9D8545E94, 0xF4296DD6FEF3D67A},
{0x8CE2529E2734BB1D, 0x1899E4A65F58660C},
{0xB01AE745B101E9E4, 0x5EC05DCFF72E7F8F},
{0xDC21A1171D42645D, 0x76707543F4FA1F73},
{0x899504AE72497EBA, 0x6A06494A791C53A8},
{0xABFA45DA0EDBDE69, 0x0487DB9D17636892},
{0xD6F8D7509292D603, 0x45A9D2845D3C42B6},
{0x865B86925B9BC5C2, 0x0B8A2392BA45A9B2},
{0xA7F26836F282B732, 0x8E6CAC7768D7141E},
{0xD1EF0244AF2364FF, 0x3207D795430CD926},
{0x8335616AED761F1F, 0x7F44E6BD49E807B8},
{0xA402B9C5A8D3A6E7, 0x5F16206C9C6209A6},
{0xCD036837130890A1, 0x36DBA887C37A8C0F},
{0x802221226BE55A64, 0xC2494954DA2C9789},
{0xA02AA96B06DEB0FD, 0xF2DB9BAA10B7BD6C},
{0xC83553C5C8965D3D, 0x6F92829494E5ACC7},
{0xFA42A8B73ABBF48C, 0xCB772339BA1F17F9},
{0x9C69A97284B578D7, 0xFF2A760414536EFB},
{0xC38413CF25E2D70D, 0xFEF5138519684ABA},
{0xF46518C2EF5B8CD1, 0x7EB258665FC25D69},
{0x98BF2F79D5993802, 0xEF2F773FFBD97A61},
{0xBEEEFB584AFF8603, 0xAAFB550FFACFD8FA},
{0xEEAABA2E5DBF6784, 0x95BA2A53F983CF38},
{0x952AB45CFA97A0B2, 0xDD945A747BF26183},
{0xBA756174393D88DF, 0x94F971119AEEF9E4},
{0xE912B9D1478CEB17, 0x7A37CD5601AAB85D},
{0x91ABB422CCB812EE, 0xAC62E055C10AB33A},
{0xB616A12B7FE617AA, 0x577B986B314D6009},
{0xE39C49765FDF9D94, 0xED5A7E85FDA0B80B},
{0x8E41ADE9FBEBC27D, 0x14588F13BE847307},
{0xB1D219647AE6B31C, 0x596EB2D8AE258FC8},
{0xDE469FBD99A05FE3, 0x6FCA5F8ED9AEF3BB},
{0x8AEC23D680043BEE, 0x25DE7BB9480D5854},
{0xADA72CCC20054AE9, 0xAF561AA79A10AE6A},
{0xD910F7FF28069DA4, 0x1B2BA1518094DA04},
{0x87AA9AFF79042286, 0x90FB44D2F05D0842},
{0xA99541BF57452B28, 0x353A1607AC744A53},
{0xD3FA922F2D1675F2, 0x42889B8997915CE8},
{0x847C9B5D7C2E09B7, 0x69956135FEBADA11},
{0xA59BC234DB398C25, 0x43FAB9837E699095},
{0xCF02B2C21207EF2E, 0x94F967E45E03F4BB},
{0x8161AFB94B44F57D, 0x1D1BE0EEBAC278F5},
{0xA1BA1BA79E1632DC, 0x6462D92A69731732},
{0xCA28A291859BBF93, 0x7D7B8F7503CFDCFE},
{0xFCB2CB35E702AF78, 0x5CDA735244C3D43E},
{0x9DEFBF01B061ADAB, 0x3A0888136AFA64A7},
{0xC56BAEC21C7A1916, 0x088AAA1845B8FDD0},
{0xF6C69A72A3989F5B, 0x8AAD549E57273D45},
{0x9A3C2087A63F6399, 0x36AC54E2F678864B},
{0xC0CB28A98FCF3C7F, 0x84576A1BB416A7DD},
{0xF0FDF2D3F3C30B9F, 0x656D44A2A11C51D5},
{0x969EB7C47859E743, 0x9F644AE5A4B1B325},
{0xBC4665B596706114, 0x873D5D9F0DDE1FEE},
{0xEB57FF22FC0C7959, 0xA90CB506D155A7EA},
{0x9316FF75DD87CBD8, 0x09A7F12442D588F2},
{0xB7DCBF5354E9BECE, 0x0C11ED6D538AEB2F},
{0xE5D3EF282A242E81, 0x8F1668C8A86DA5FA},
{0x8FA475791A569D10, 0xF96E017D694487BC},
{0xB38D92D760EC4455, 0x37C981DCC395A9AC},
{0xE070F78D3927556A, 0x85BBE253F47B1417},
{0x8C469AB843B89562, 0x93956D7478CCEC8E},
{0xAF58416654A6BABB, 0x387AC8D1970027B2},
{0xDB2E51BFE9D0696A, 0x06997B05FCC0319E},
{0x88FCF317F22241E2, 0x441FECE3BDF81F03},
{0xAB3C2FDDEEAAD25A, 0xD527E81CAD7626C3},
{0xD60B3BD56A5586F1, 0x8A71E223D8D3B074},
{0x85C7056562757456, 0xF6872D5667844E49},
{0xA738C6BEBB12D16C, 0xB428F8AC016561DB},
{0xD106F86E69D785C7, 0xE13336D701BEBA52},
{0x82A45B450226B39C, 0xECC0024661173473},
{0xA34D721642B06084, 0x27F002D7F95D0190},
{0xCC20CE9BD35C78A5, 0x31EC038DF7B441F4},
{0xFF290242C83396CE, 0x7E67047175A15271},
{0x9F79A169BD203E41, 0x0F0062C6E984D386},
{0xC75809C42C684DD1, 0x52C07B78A3E60868},
{0xF92E0C3537826145, 0xA7709A56CCDF8A82},
{0x9BBCC7A142B17CCB, 0x88A66076400BB691},
{0xC2ABF989935DDBFE, 0x6ACFF893D00EA435},
{0xF356F7EBF83552FE, 0x0583F6B8C4124D43},
{0x98165AF37B2153DE, 0xC3727A337A8B704A},
{0xBE1BF1B059E9A8D6, 0x744F18C0592E4C5C},
{0xEDA2EE1C7064130C, 0x1162DEF06F79DF73},
{0x9485D4D1C63E8BE7, 0x8ADDCB5645AC2BA8},
{0xB9A74A0637CE2EE1, 0x6D953E2BD7173692},
{0xE8111C87C5C1BA99, 0xC8FA8DB6CCDD0437},
{0x910AB1D4DB9914A0, 0x1D9C9892400A22A2},
{0xB54D5E4A127F59C8, 0x2503BEB6D00CAB4B},
{0xE2A0B5DC971F303A, 0x2E44AE64840FD61D},
{0x8DA471A9DE737E24, 0x5CEAECFED289E5D2},
{0xB10D8E1456105DAD, 0x7425A83E872C5F47},
{0xDD50F1996B947518, 0xD12F124E28F77719},
{0x8A5296FFE33CC92F, 0x82BD6B70D99AAA6F},
{0xACE73CBFDC0BFB7B, 0x636CC64D1001550B},
{0xD8210BEFD30EFA5A, 0x3C47F7E05401AA4E},
{0x8714A775E3E95C78, 0x65ACFAEC34810A71},
{0xA8D9D1535CE3B396, 0x7F1839A741A14D0D},
{0xD31045A8341CA07C, 0x1EDE48111209A050},
{0x83EA2B892091E44D, 0x934AED0AAB460432},
{0xA4E4B66B68B65D60, 0xF81DA84D5617853F},
{0xCE1DE40642E3F4B9, 0x36251260AB9D668E},
{0x80D2AE83E9CE78F3, 0xC1D72B7C6B426019},
{0xA1075A24E4421730, 0xB24CF65B8612F81F},
{0xC94930AE1D529CFC, 0xDEE033F26797B627},
{0xFB9B7CD9A4A7443C, 0x169840EF017DA3B1},
{0x9D412E0806E88AA5, 0x8E1F289560EE864E},
{0xC491798A08A2AD4E, 0xF1A6F2BAB92A27E2},
{0xF5B5D7EC8ACB58A2, 0xAE10AF696774B1DB},
{0x9991A6F3D6BF1765, 0xACCA6DA1E0A8EF29},
{0xBFF610B0CC6EDD3F, 0x17FD090A58D32AF3},
{0xEFF394DCFF8A948E, 0xDDFC4B4CEF07F5B0},
{0x95F83D0A1FB69CD9, 0x4ABDAF101564F98E},
{0xBB764C4CA7A4440F, 0x9D6D1AD41ABE37F1},
{0xEA53DF5FD18D5513, 0x84C86189216DC5ED},
{0x92746B9BE2F8552C, 0x32FD3CF5B4E49BB4},
{0xB7118682DBB66A77, 0x3FBC8C33221DC2A1},
{0xE4D5E82392A40515, 0x0FABAF3FEAA5334A},
{0x8F05B1163BA6832D, 0x29CB4D87F2A7400E},
{0xB2C71D5BCA9023F8, 0x743E20E9EF511012},
{0xDF78E4B2BD342CF6, 0x914DA9246B255416},
{0x8BAB8EEFB6409C1A, 0x1AD089B6C2F7548E},
{0xAE9672ABA3D0C320, 0xA184AC2473B529B1},
{0xDA3C0F568CC4F3E8, 0xC9E5D72D90A2741E},
{0x8865899617FB1871, 0x7E2FA67C7A658892},
{0xAA7EEBFB9DF9DE8D, 0xDDBB901B98FEEAB7},
{0xD51EA6FA85785631, 0x552A74227F3EA565},
{0x8533285C936B35DE, 0xD53A88958F87275F},
{0xA67FF273B8460356, 0x8A892ABAF368F137},
{0xD01FEF10A657842C, 0x2D2B7569B0432D85},
{0x8213F56A67F6B29B, 0x9C3B29620E29FC73},
{0xA298F2C501F45F42, 0x8349F3BA91B47B8F},
{0xCB3F2F7642717713, 0x241C70A936219A73},
{0xFE0EFB53D30DD4D7, 0xED238CD383AA0110},
{0x9EC95D1463E8A506, 0xF4363804324A40AA},
{0xC67BB4597CE2CE48, 0xB143C6053EDCD0D5},
{0xF81AA16FDC1B81DA, 0xDD94B7868E94050A},
{0x9B10A4E5E9913128, 0xCA7CF2B4191C8326},
{0xC1D4CE1F63F57D72, 0xFD1C2F611F63A3F0},
{0xF24A01A73CF2DCCF, 0xBC633B39673C8CEC},
{0x976E41088617CA01, 0xD5BE0503E085D813},
{0xBD49D14AA79DBC82, 0x4B2D8644D8A74E18},
{0xEC9C459D51852BA2, 0xDDF8E7D60ED1219E},
{0x93E1AB8252F33B45, 0xCABB90E5C942B503},
{0xB8DA1662E7B00A17, 0x3D6A751F3B936243},
{0xE7109BFBA19C0C9D, 0x0CC512670A783AD4},
{0x906A617D450187E2, 0x27FB2B80668B24C5},
{0xB484F9DC9641E9DA, 0xB1F9F660802DEDF6},
{0xE1A63853BBD26451, 0x5E7873F8A0396973},
{0x8D07E33455637EB2, 0xDB0B487B6423E1E8},
{0xB049DC016ABC5E5F, 0x91CE1A9A3D2CDA62},
{0xDC5C5301C56B75F7, 0x7641A140CC7810FB},
{0x89B9B3E11B6329BA, 0xA9E904C87FCB0A9D},
{0xAC2820D9623BF429, 0x546345FA9FBDCD44},
{0xD732290FBACAF133, 0xA97C177947AD4095},
{0x867F59A9D4BED6C0, 0x49ED8EABCCCC485D},
{0xA81F301449EE8C70, 0x5C68F256BFFF5A74},
{0xD226FC195C6A2F8C, 0x73832EEC6FFF3111},
{0x83585D8FD9C25DB7, 0xC831FD53C5FF7EAB},
{0xA42E74F3D032F525, 0xBA3E7CA8B77F5E55},
{0xCD3A1230C43FB26F, 0x28CE1BD2E55F35EB},
{0x80444B5E7AA7CF85, 0x7980D163CF5B81B3},
{0xA0555E361951C366, 0xD7E105BCC332621F},
{0xC86AB5C39FA63440, 0x8DD9472BF3FEFAA7},
{0xFA856334878FC150, 0xB14F98F6F0FEB951},
{0x9C935E00D4B9D8D2, 0x6ED1BF9A569F33D3},
{0xC3B8358109E84F07, 0x0A862F80EC4700C8},
{0xF4A642E14C6262C8, 0xCD27BB612758C0FA},
{0x98E7E9CCCFBD7DBD, 0x8038D51CB897789C},
{0xBF21E44003ACDD2C, 0xE0470A63E6BD56C3},
{0xEEEA5D5004981478, 0x1858CCFCE06CAC74},
{0x95527A5202DF0CCB, 0x0F37801E0C43EBC8},
{0xBAA718E68396CFFD, 0xD30560258F54E6BA},
{0xE950DF20247C83FD, 0x47C6B82EF32A2069},
{0x91D28B7416CDD27E, 0x4CDC331D57FA5441},
{0xB6472E511C81471D, 0xE0133FE4ADF8E952},
{0xE3D8F9E563A198E5, 0x58180FDDD97723A6},
{0x8E679C2F5E44FF8F, 0x570F09EAA7EA7648},
{0xB201833B35D63F73, 0x2CD2CC6551E513DA},
{0xDE81E40A034BCF4F, 0xF8077F7EA65E58D1},
{0x8B112E86420F6191, 0xFB04AFAF27FAF782},
{0xADD57A27D29339F6, 0x79C5DB9AF1F9B563},
{0xD94AD8B1C7380874, 0x18375281AE7822BC},
{0x87CEC76F1C830548, 0x8F2293910D0B15B5},
{0xA9C2794AE3A3C69A, 0xB2EB3875504DDB22},
{0xD433179D9C8CB841, 0x5FA60692A46151EB},
{0x849FEEC281D7F328, 0xDBC7C41BA6BCD333},
{0xA5C7EA73224DEFF3, 0x12B9B522906C0800},
{0xCF39E50FEAE16BEF, 0xD768226B34870A00},
{0x81842F29F2CCE375, 0xE6A1158300D46640},
{0xA1E53AF46F801C53, 0x60495AE3C1097FD0},
{0xCA5E89B18B602368, 0x385BB19CB14BDFC4},
{0xFCF62C1DEE382C42, 0x46729E03DD9ED7B5},
{0x9E19DB92B4E31BA9, 0x6C07A2C26A8346D1},
{0xC5A05277621BE293, 0xC7098B7305241885},
{0xF70867153AA2DB38, 0xB8CBEE4FC66D1EA7},
};
return pow10_lut[k - MIN_K];
}
static inline bool multiple_of_pow2(uint64_t value, int32_t e2)
{
/* Return whether value is divisible by 2^e2 */
return (value & (((uint64_t)1 << e2) - 1)) == 0 && e2 < 64;
}
static inline bool multiple_of_pow5(uint64_t value, int32_t e5)
{
struct mul_cmp {
uint64_t mul;
uint64_t cmp;
};
/* Return whether value is divisible by 5^e5 */
static struct mul_cmp mod5_lut[] = {
{0x0000000000000001u, 0xFFFFFFFFFFFFFFFFu}, // 5^0
{0xCCCCCCCCCCCCCCCDu, 0x3333333333333333u}, // 5^1
{0x8F5C28F5C28F5C29u, 0x0A3D70A3D70A3D70u}, // 5^2
{0x1CAC083126E978D5u, 0x020C49BA5E353F7Cu}, // 5^3
{0xD288CE703AFB7E91u, 0x0068DB8BAC710CB2u}, // 5^4
{0x5D4E8FB00BCBE61Du, 0x0014F8B588E368F0u}, // 5^5
{0x790FB65668C26139u, 0x000431BDE82D7B63u}, // 5^6
{0xE5032477AE8D46A5u, 0x0000D6BF94D5E57Au}, // 5^7
{0xC767074B22E90E21u, 0x00002AF31DC46118u}, // 5^8
{0x8E47CE423A2E9C6Du, 0x0000089705F4136Bu}, // 5^9
{0x4FA7F60D3ED61F49u, 0x000001B7CDFD9D7Bu}, // 5^10
{0x0FEE64690C913975u, 0x00000057F5FF85E5u}, // 5^11
{0x3662E0E1CF503EB1u, 0x000000119799812Du}, // 5^12
{0xA47A2CF9F6433FBDu, 0x0000000384B84D09u}, // 5^13
{0x54186F653140A659u, 0x00000000B424DC35u}, // 5^14
{0x7738164770402145u, 0x0000000024075F3Du}, // 5^15
{0xE4A4D1417CD9A041u, 0x000000000734ACA5u}, // 5^16
{0xC75429D9E5C5200Du, 0x000000000170EF54u}, // 5^17
{0xC1773B91FAC10669u, 0x000000000049C977u}, // 5^18
{0x26B172506559CE15u, 0x00000000000EC1E4u}, // 5^19
{0xD489E3A9ADDEC2D1u, 0x000000000002F394u}, // 5^20
{0x90E860BB892C8D5Du, 0x000000000000971Du}, // 5^21
{0x502E79BF1B6F4F79u, 0x0000000000001E39u}, // 5^22
{0xDCD618596BE30FE5u, 0x000000000000060Bu}, // 5^23
{0x2C2AD1AB7BFA3661u, 0x0000000000000135u}, // 5^24
};
/* The range of e5 is [0, 24] */
const struct mul_cmp m5 = mod5_lut[e5];
return value * m5.mul <= m5.cmp;
}
static inline bool is_integral_end_point(uint64_t two_f, int32_t e2, int32_t minus_k)
{
if (e2 < -2)
return false;
if (e2 <= 9)
return true;
if (e2 <= 86)
return multiple_of_pow5(two_f, minus_k);
return false;
}
static inline bool is_integral_mid_point(uint64_t two_f, int32_t e2, int32_t minus_k)
{
if (e2 < -4)
return multiple_of_pow2(two_f, minus_k - e2 + 1);
if (e2 <= 9)
return true;
if (e2 <= 86)
return multiple_of_pow5(two_f, minus_k);
return false;
}
static inline int32_t floor_log2_pow10(int32_t e)
{
/* The range of e is [-1233, 1233] */
return ((e * 1741647) >> 19);
}
static inline int32_t floor_log10_pow2(int32_t e)
{
/* The range of e is [-1500, 1500] */
return ((e * 1262611) >> 22);
}
static inline int32_t floor_log10_threequarters_pow2(int32_t e)
{
/* The range of e is [-1500, 1500] */
return ((e * 1262611 - 524031) >> 22);
}
static inline u64x2_t mul128_calc(uint64_t x, uint64_t y)
{
u64x2_t r;
#if defined(_MSC_VER) && defined(_M_AMD64)
r.lo = _umul128(x, y, &r.hi);
#elif (__GNUC__ > 4 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6) || __clang_major__ >= 9) && (__WORDSIZE == 64)
__extension__ typedef unsigned __int128 uint128;
const uint128 p = (uint128)x * (uint128)y;
r.hi = (uint64_t)(p >> 64);
r.lo = (uint64_t)p;
#else
const uint64_t M32 = 0XFFFFFFFF;
const uint64_t a = x >> 32;
const uint64_t b = x & M32;
const uint64_t c = y >> 32;
const uint64_t d = y & 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;
const uint64_t mid1 = ad + (bd >> 32);
const uint64_t mid2 = bc + (mid1 & M32);
r.hi = ac + (mid1 >> 32) + (mid2 >> 32);
r.lo = (bd & M32) | (mid2 & M32) << 32;
#endif
return r;
}
static inline uint64_t mul128_shift(uint64_t x, u64x2_t y)
{
/* Return (x * y) / 2^128 */
u64x2_t p1 = mul128_calc(x, y.hi);
u64x2_t p0 = mul128_calc(x, y.lo);
p1.lo += p0.hi;
p1.hi += p1.lo < p0.hi;
return p1.hi;
}
static inline bool compute_parity(uint64_t two_f, u64x2_t pow10, int32_t minus_1)
{
/* The range of minus_1 is [1, 63] */
const uint64_t mid = two_f * pow10.hi + mul128_calc(two_f, pow10.lo).hi;
return (mid & ((uint64_t)1 << (64 - minus_1))) != 0;
}
static inline uint32_t compute_delta(u64x2_t pow10, int32_t minus_1)
{
/* The range of minus_1 is [0, 63] */
return (uint32_t)(pow10.hi >> (63 - minus_1));
}
static inline void dragonbox_convert_asymmetric(diy_fp_t *v)
{
int32_t e = v->e;
const int32_t minus_k = floor_log10_threequarters_pow2(e);
const int32_t minus_1 = e + floor_log2_pow10(-minus_k);
const u64x2_t pow10 = compute_pow10_double(-minus_k);
uint64_t lower = (pow10.hi - (pow10.hi >> (DP_SIGNIFICAND_SIZE + 2))) >> (63 - DP_SIGNIFICAND_SIZE - minus_1);
uint64_t upper = (pow10.hi + (pow10.hi >> (DP_SIGNIFICAND_SIZE + 1))) >> (63 - DP_SIGNIFICAND_SIZE - minus_1);
/*
* If we don't accept the left endpoint (but we do!)
* or if the left endpoint is not an integer, increase it
*/
lower += !(2 <= e && e <= 3);
/* Try bigger divisor */
uint64_t q = upper / 10;
if ((q << 1) + (q << 3) >= lower) {
v->f = q;
v->e = minus_k + 1;