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sbignum-tables.c
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sbignum-tables.c
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#include "sbignum-tables.h"
#include "sbignum.h"
/* maps a number to a char */
char *cset = "0123456789abcdefghijklmnopqrstuvwxyz";
/* maps a char to a number */
int8_t r_cset[256] = {
-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,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -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, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, -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, -1, -1, -1, -1, -1, -1, -1, -1,
};
/* bitstable[n] is the number of set bits
* in the number 'n' */
int8_t bitstable[256] = {
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8,
};
/* basetable[b] = number of digits needed to convert
* an mpz atom in base 'b' */
#if ATOMBYTES == 1
double basetable[37] = {
0, /* unused */
0, /* unused */
8.000000, /* (log of 2 in base 256) */
5.047438, /* (log of 3 in base 256) */
4.000000, /* (log of 4 in base 256) */
3.445412, /* (log of 5 in base 256) */
3.094822, /* (log of 6 in base 256) */
2.849657, /* (log of 7 in base 256) */
2.666667, /* (log of 8 in base 256) */
2.523719, /* (log of 9 in base 256) */
2.408240, /* (log of 10 in base 256) */
2.312519, /* (log of 11 in base 256) */
2.231544, /* (log of 12 in base 256) */
2.161905, /* (log of 13 in base 256) */
2.101196, /* (log of 14 in base 256) */
2.047664, /* (log of 15 in base 256) */
2.000000, /* (log of 16 in base 256) */
1.957204, /* (log of 17 in base 256) */
1.918500, /* (log of 18 in base 256) */
1.883271, /* (log of 19 in base 256) */
1.851026, /* (log of 20 in base 256) */
1.821362, /* (log of 21 in base 256) */
1.793951, /* (log of 22 in base 256) */
1.768518, /* (log of 23 in base 256) */
1.744834, /* (log of 24 in base 256) */
1.722706, /* (log of 25 in base 256) */
1.701968, /* (log of 26 in base 256) */
1.682479, /* (log of 27 in base 256) */
1.664117, /* (log of 28 in base 256) */
1.646775, /* (log of 29 in base 256) */
1.630360, /* (log of 30 in base 256) */
1.614793, /* (log of 31 in base 256) */
1.600000, /* (log of 32 in base 256) */
1.585919, /* (log of 33 in base 256) */
1.572493, /* (log of 34 in base 256) */
1.559672, /* (log of 35 in base 256) */
1.547411, /* (log of 36 in base 256) */
};
#endif
#if ATOMBYTES == 2
double basetable[37] = {
0, /* unused */
0, /* unused */
16.000000, /* (log of 2 in base 65536) */
10.094876, /* (log of 3 in base 65536) */
8.000000, /* (log of 4 in base 65536) */
6.890825, /* (log of 5 in base 65536) */
6.189645, /* (log of 6 in base 65536) */
5.699315, /* (log of 7 in base 65536) */
5.333333, /* (log of 8 in base 65536) */
5.047438, /* (log of 9 in base 65536) */
4.816480, /* (log of 10 in base 65536) */
4.625037, /* (log of 11 in base 65536) */
4.463087, /* (log of 12 in base 65536) */
4.323810, /* (log of 13 in base 65536) */
4.202393, /* (log of 14 in base 65536) */
4.095328, /* (log of 15 in base 65536) */
4.000000, /* (log of 16 in base 65536) */
3.914409, /* (log of 17 in base 65536) */
3.836999, /* (log of 18 in base 65536) */
3.766543, /* (log of 19 in base 65536) */
3.702051, /* (log of 20 in base 65536) */
3.642724, /* (log of 21 in base 65536) */
3.587901, /* (log of 22 in base 65536) */
3.537036, /* (log of 23 in base 65536) */
3.489669, /* (log of 24 in base 65536) */
3.445412, /* (log of 25 in base 65536) */
3.403937, /* (log of 26 in base 65536) */
3.364959, /* (log of 27 in base 65536) */
3.328234, /* (log of 28 in base 65536) */
3.293549, /* (log of 29 in base 65536) */
3.260721, /* (log of 30 in base 65536) */
3.229585, /* (log of 31 in base 65536) */
3.200000, /* (log of 32 in base 65536) */
3.171838, /* (log of 33 in base 65536) */
3.144986, /* (log of 34 in base 65536) */
3.119344, /* (log of 35 in base 65536) */
3.094822, /* (log of 36 in base 65536) */
};
#endif
#if ATOMBYTES == 4
double basetable[37] = {
0, /* unused */
0, /* unused */
32.000000, /* (log of 2 in base 4294967296) */
20.189752, /* (log of 3 in base 4294967296) */
16.000000, /* (log of 4 in base 4294967296) */
13.781650, /* (log of 5 in base 4294967296) */
12.379290, /* (log of 6 in base 4294967296) */
11.398630, /* (log of 7 in base 4294967296) */
10.666667, /* (log of 8 in base 4294967296) */
10.094876, /* (log of 9 in base 4294967296) */
9.632960, /* (log of 10 in base 4294967296) */
9.250074, /* (log of 11 in base 4294967296) */
8.926174, /* (log of 12 in base 4294967296) */
8.647621, /* (log of 13 in base 4294967296) */
8.404785, /* (log of 14 in base 4294967296) */
8.190657, /* (log of 15 in base 4294967296) */
8.000000, /* (log of 16 in base 4294967296) */
7.828817, /* (log of 17 in base 4294967296) */
7.673999, /* (log of 18 in base 4294967296) */
7.533085, /* (log of 19 in base 4294967296) */
7.404103, /* (log of 20 in base 4294967296) */
7.285448, /* (log of 21 in base 4294967296) */
7.175802, /* (log of 22 in base 4294967296) */
7.074071, /* (log of 23 in base 4294967296) */
6.979337, /* (log of 24 in base 4294967296) */
6.890825, /* (log of 25 in base 4294967296) */
6.807874, /* (log of 26 in base 4294967296) */
6.729917, /* (log of 27 in base 4294967296) */
6.656467, /* (log of 28 in base 4294967296) */
6.587099, /* (log of 29 in base 4294967296) */
6.521442, /* (log of 30 in base 4294967296) */
6.459171, /* (log of 31 in base 4294967296) */
6.400000, /* (log of 32 in base 4294967296) */
6.343676, /* (log of 33 in base 4294967296) */
6.289972, /* (log of 34 in base 4294967296) */
6.238689, /* (log of 35 in base 4294967296) */
6.189645, /* (log of 36 in base 4294967296) */
};
#endif
/* basepowtable[b] = the first column is the biggest power of 'b'
* that fits in mpz_atom_t, the second column is the exponent
* 'e' so that b^e = the value of the first column */
#if ATOMBYTES == 1
struct sbn_basepow basepowtable[37] = {
{0,0}, /* unused */
{0,0}, /* unused */
{128U, 7U}, /* floor(log of 2 in base 255) */
{243U, 5U}, /* floor(log of 3 in base 255) */
{64U, 3U}, /* floor(log of 4 in base 255) */
{125U, 3U}, /* floor(log of 5 in base 255) */
{216U, 3U}, /* floor(log of 6 in base 255) */
{49U, 2U}, /* floor(log of 7 in base 255) */
{64U, 2U}, /* floor(log of 8 in base 255) */
{81U, 2U}, /* floor(log of 9 in base 255) */
{100U, 2U}, /* floor(log of 10 in base 255) */
{121U, 2U}, /* floor(log of 11 in base 255) */
{144U, 2U}, /* floor(log of 12 in base 255) */
{169U, 2U}, /* floor(log of 13 in base 255) */
{196U, 2U}, /* floor(log of 14 in base 255) */
{225U, 2U}, /* floor(log of 15 in base 255) */
{16U, 1U}, /* floor(log of 16 in base 255) */
{17U, 1U}, /* floor(log of 17 in base 255) */
{18U, 1U}, /* floor(log of 18 in base 255) */
{19U, 1U}, /* floor(log of 19 in base 255) */
{20U, 1U}, /* floor(log of 20 in base 255) */
{21U, 1U}, /* floor(log of 21 in base 255) */
{22U, 1U}, /* floor(log of 22 in base 255) */
{23U, 1U}, /* floor(log of 23 in base 255) */
{24U, 1U}, /* floor(log of 24 in base 255) */
{25U, 1U}, /* floor(log of 25 in base 255) */
{26U, 1U}, /* floor(log of 26 in base 255) */
{27U, 1U}, /* floor(log of 27 in base 255) */
{28U, 1U}, /* floor(log of 28 in base 255) */
{29U, 1U}, /* floor(log of 29 in base 255) */
{30U, 1U}, /* floor(log of 30 in base 255) */
{31U, 1U}, /* floor(log of 31 in base 255) */
{32U, 1U}, /* floor(log of 32 in base 255) */
{33U, 1U}, /* floor(log of 33 in base 255) */
{34U, 1U}, /* floor(log of 34 in base 255) */
{35U, 1U}, /* floor(log of 35 in base 255) */
{36U, 1U}, /* floor(log of 36 in base 255) */
};
#endif
#if ATOMBYTES == 2
struct sbn_basepow basepowtable[37] = {
{0,0}, /* unused */
{0,0}, /* unused */
{32768U, 15U}, /* floor(log of 2 in base 65535) */
{59049U, 10U}, /* floor(log of 3 in base 65535) */
{16384U, 7U}, /* floor(log of 4 in base 65535) */
{15625U, 6U}, /* floor(log of 5 in base 65535) */
{46656U, 6U}, /* floor(log of 6 in base 65535) */
{16807U, 5U}, /* floor(log of 7 in base 65535) */
{32768U, 5U}, /* floor(log of 8 in base 65535) */
{59049U, 5U}, /* floor(log of 9 in base 65535) */
{10000U, 4U}, /* floor(log of 10 in base 65535) */
{14641U, 4U}, /* floor(log of 11 in base 65535) */
{20736U, 4U}, /* floor(log of 12 in base 65535) */
{28561U, 4U}, /* floor(log of 13 in base 65535) */
{38416U, 4U}, /* floor(log of 14 in base 65535) */
{50625U, 4U}, /* floor(log of 15 in base 65535) */
{4096U, 3U}, /* floor(log of 16 in base 65535) */
{4913U, 3U}, /* floor(log of 17 in base 65535) */
{5832U, 3U}, /* floor(log of 18 in base 65535) */
{6859U, 3U}, /* floor(log of 19 in base 65535) */
{8000U, 3U}, /* floor(log of 20 in base 65535) */
{9261U, 3U}, /* floor(log of 21 in base 65535) */
{10648U, 3U}, /* floor(log of 22 in base 65535) */
{12167U, 3U}, /* floor(log of 23 in base 65535) */
{13824U, 3U}, /* floor(log of 24 in base 65535) */
{15625U, 3U}, /* floor(log of 25 in base 65535) */
{17576U, 3U}, /* floor(log of 26 in base 65535) */
{19683U, 3U}, /* floor(log of 27 in base 65535) */
{21952U, 3U}, /* floor(log of 28 in base 65535) */
{24389U, 3U}, /* floor(log of 29 in base 65535) */
{27000U, 3U}, /* floor(log of 30 in base 65535) */
{29791U, 3U}, /* floor(log of 31 in base 65535) */
{32768U, 3U}, /* floor(log of 32 in base 65535) */
{35937U, 3U}, /* floor(log of 33 in base 65535) */
{39304U, 3U}, /* floor(log of 34 in base 65535) */
{42875U, 3U}, /* floor(log of 35 in base 65535) */
{46656U, 3U}, /* floor(log of 36 in base 65535) */
};
#endif
#if ATOMBYTES == 4
struct sbn_basepow basepowtable[37] = {
{0,0}, /* unused */
{0,0}, /* unused */
{2147483648U, 31U}, /* floor(log of 2 in base 4294967295) */
{3486784401U, 20U}, /* floor(log of 3 in base 4294967295) */
{1073741824U, 15U}, /* floor(log of 4 in base 4294967295) */
{1220703125U, 13U}, /* floor(log of 5 in base 4294967295) */
{2176782336U, 12U}, /* floor(log of 6 in base 4294967295) */
{1977326743U, 11U}, /* floor(log of 7 in base 4294967295) */
{1073741824U, 10U}, /* floor(log of 8 in base 4294967295) */
{3486784401U, 10U}, /* floor(log of 9 in base 4294967295) */
{1000000000U, 9U}, /* floor(log of 10 in base 4294967295) */
{2357947691U, 9U}, /* floor(log of 11 in base 4294967295) */
{429981696U, 8U}, /* floor(log of 12 in base 4294967295) */
{815730721U, 8U}, /* floor(log of 13 in base 4294967295) */
{1475789056U, 8U}, /* floor(log of 14 in base 4294967295) */
{2562890625U, 8U}, /* floor(log of 15 in base 4294967295) */
{268435456U, 7U}, /* floor(log of 16 in base 4294967295) */
{410338673U, 7U}, /* floor(log of 17 in base 4294967295) */
{612220032U, 7U}, /* floor(log of 18 in base 4294967295) */
{893871739U, 7U}, /* floor(log of 19 in base 4294967295) */
{1280000000U, 7U}, /* floor(log of 20 in base 4294967295) */
{1801088541U, 7U}, /* floor(log of 21 in base 4294967295) */
{2494357888U, 7U}, /* floor(log of 22 in base 4294967295) */
{3404825447U, 7U}, /* floor(log of 23 in base 4294967295) */
{191102976U, 6U}, /* floor(log of 24 in base 4294967295) */
{244140625U, 6U}, /* floor(log of 25 in base 4294967295) */
{308915776U, 6U}, /* floor(log of 26 in base 4294967295) */
{387420489U, 6U}, /* floor(log of 27 in base 4294967295) */
{481890304U, 6U}, /* floor(log of 28 in base 4294967295) */
{594823321U, 6U}, /* floor(log of 29 in base 4294967295) */
{729000000U, 6U}, /* floor(log of 30 in base 4294967295) */
{887503681U, 6U}, /* floor(log of 31 in base 4294967295) */
{1073741824U, 6U}, /* floor(log of 32 in base 4294967295) */
{1291467969U, 6U}, /* floor(log of 33 in base 4294967295) */
{1544804416U, 6U}, /* floor(log of 34 in base 4294967295) */
{1838265625U, 6U}, /* floor(log of 35 in base 4294967295) */
{2176782336U, 6U}, /* floor(log of 36 in base 4294967295) */
};
#endif