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is_perfect_power implementation #137
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,154 @@ | ||
| /*============================================================================= | ||
| This file is part of FLINT. | ||
| FLINT is free software; you can redistribute it and/or modify | ||
| it under the terms of the GNU General Public License as published by | ||
| the Free Software Foundation; either version 2 of the License, or | ||
| (at your option) any later version. | ||
| FLINT is distributed in the hope that it will be useful, | ||
| but WITHOUT ANY WARRANTY; without even the implied warranty of | ||
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | ||
| GNU General Public License for more details. | ||
| You should have received a copy of the GNU General Public License | ||
| along with FLINT; if not, write to the Free Software | ||
| Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA | ||
| =============================================================================*/ | ||
| /****************************************************************************** | ||
| Copyright (C) 2015 Nitin Kumar | ||
| ******************************************************************************/ | ||
|
|
||
| #include <stdlib.h> | ||
| #include <flint.h> | ||
| #include <ulong_extras.h> | ||
|
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|
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| /* | ||
| check for the bit size of mp_limb_t, which is equal to FLINT_BITS, | ||
| q[i] - 1 congruent class modulo q[i] (about q[i] line no. 105) | ||
| are stored as follows: | ||
| qclass[i][j]th word contain FLINT_BITS Number of bit and | ||
| kth bit (from LSB To MSB) represents the, | ||
| (say y = FLINT_BITS * max(j - 1, 0) + k), y mod q[i] congruent | ||
| class of q[i] and it is set to 1 if y satisfy the property mentioned | ||
| in the line no. 106 otherwise it is set to 0. | ||
| for total q[i] congruent class modulo q[i], | ||
| q[i] / FLINT_BITS + (q[i] % FLINT_BITS) ? 0 : 1; | ||
| word are used, i.e. the size of qclass[i]th row. | ||
| */ | ||
|
|
||
| #if FLINT_BITS == 32 | ||
| mp_limb_t qclass[18][25] = {{ 0x3 }, { 0x43 }, { 0x403 }, { 0x10021003 } | ||
| , { 0x400003 },{ 0x40800002 , 0x100001 }, | ||
| { 0x2 , 0x300c000 , 0x0 , 0x41 }, | ||
| { 0x82 , 0x20080 , 0x40000 , 0x2000 , | ||
| 0x1004000 , 0x41000001 }, | ||
| { 0x2 , 0x4001 }, { 0x2 , 0x4000001 }, | ||
| { 0x42 , 0x100010 , UWORD(0x80000000) , 0x0 | ||
| , 0x0 , 0x0 , 0x1000000 , 0x0 , 0x80008 , | ||
| 0x420001 }, { 0x2 , 0x1000 , 0x0 , 0x200 , | ||
| 0x100001 }, { 0x2 , 0x0 , 0x40001 }, | ||
| { 0x2 , 0x0 , 0x20010000 , 0x0 , 0x0 , | ||
| 0x1001 }, { 0x2 , 0x3000 , 0x0 , 0x0 , 0x0 , | ||
| 0x0 , 0x0 , 0xc000 , 0x4000001 }, | ||
| { 0x2 , 0x0 , 0x0 , 0x401 }, { 0x2 , 0x0 , | ||
| 0x8000001 , 0x0 , 0x0 , 0x8000000 , 0x0 , | ||
| 0x18 , 0x0 , 0x0 , 0x0 , 0x0 , 0x0 , 0x0 , | ||
| 0x0 , 0x6 , 0x400 , 0x0 , 0x0 , 0x420 , 0x0 | ||
| , 0x0 , 0x11 }, { 0x2 , 0x0 , 0x180000 , | ||
| 0x0 , 0x0 , 0x0 , 0x0 , 0x0 , 0x18000000 , | ||
| 0x0 , 0x0 , 0x4001 } | ||
| }; | ||
| #else | ||
| mp_limb_t qclass[18][15] = { { 0x3 }, { 0x43 }, { 0x403 }, | ||
| { 0x10021003 } , { 0x400003 }, | ||
| { UWORD(0x10000040800003) }, | ||
| { UWORD(0x300c00000000002) , | ||
| UWORD(0x4000000001) }, | ||
| { UWORD(0x2008000000082) , | ||
| UWORD(0x200000040000) , | ||
| UWORD(0x4100000001004001) }, | ||
| { UWORD(0x400000000003) }, | ||
| { UWORD(0x400000000000003) }, | ||
| { UWORD(0x10001000000042) | ||
| , UWORD(0x80000000) , 0x0 , 0x1000000 , | ||
| UWORD(0x42000000080009) }, | ||
| { UWORD(0x100000000002) , | ||
| UWORD(0x20000000000) , 0x100001 },{ 0x2 , | ||
| 0x40001 }, { 0x2 , 0x20010000 , | ||
| UWORD(0x100000000001) }, { | ||
| UWORD(0x300000000002) , 0x0 , | ||
| 0x0 , UWORD(0xc00000000000) , 0x4000001 }, | ||
| { 0x2 , UWORD(0x40000000001) }, { 0x2 , | ||
| UWORD(0x108000000) , | ||
| UWORD(0x800000000000000) , | ||
| UWORD(0x1800000000) , 0x0 , 0x0 , 0x0 , | ||
| UWORD(0x600000000) , 0x400 , | ||
| UWORD(0x42000000000) , | ||
| 0x0 , 0x11 }, { 0x2 , 0x180000 , 0x0 , | ||
| 0x0 , 0x18000000 , UWORD(0x400000000001) } | ||
| }; | ||
| #endif | ||
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| int n_is_perfect_power(mp_limb_t * r, mp_limb_t x) | ||
| { | ||
| /* | ||
| p[i], is prime less than 64. | ||
| q[i], is prime such that q[i] mod p[i] = 1. | ||
| if x = y ^ p[i] , for some y than, | ||
| x ^ ((q[i] - 1) / p[i]) mod q[i] <= 1. | ||
| see this following link for info: | ||
| ("http://citeseerx.ist.psu.edu/viewdoc/ | ||
| download?doi=10.1.1.108.458&rep=rep1&type=pdf") | ||
| z[i] = maximum k such that i = j ^ k for some positive integer j. | ||
| v[i] = minimum j such that i = j ^ k for some positive integer k. | ||
| */ | ||
|
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||
| int p[] = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, | ||
| 31, 37, 41, 43, 47, 53, 59, 61}; | ||
| int q[] = {3, 7, 11, 29, 23, 53, 103, 191, 47, 59, | ||
| 311, 149, 83, 173, 283, 107, 709, 367}; | ||
| int z[] = {1, 1, 1, 1, 2, 1, 1, 1, 3, 2, | ||
| 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1}; | ||
| int v[] = {0, 1, 2, 3, 2, 5, 6, 7, 2, 3, | ||
| 10, 11, 12, 13, 14, 15, 2, 17, 18, 19, 20}; | ||
|
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| int i, power = 1, pos, k; | ||
| mp_limb_t prev; | ||
|
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| for (i = 0; i < 18; i++) | ||
| { | ||
| if (x <= 20) | ||
| { | ||
| power *= z[x]; | ||
| x = v[x]; | ||
| break; | ||
| } | ||
|
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||
| /* k is congruent class of x mod q[i] */ | ||
| k = x % q[i]; | ||
| /* pos is the position of above class, in the table*/ | ||
| pos = k / FLINT_BITS + (k % FLINT_BITS) ? 0 : 1; | ||
|
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| if (pos == 0) pos = 1; /* in case q[i] divides x */ | ||
| /* check if bit corresponding to above position is set */ | ||
| if ((qclass[i][pos - 1] & (1 << (k % FLINT_BITS)))) | ||
| { | ||
| prev = x; | ||
| x = n_rootrem(r, x, p[i]); /* test if x is p[i]th power */ | ||
| if (*r == 0) | ||
| { | ||
| while (*r == 0) /* test also for subsequent power of p[i] */ | ||
| { | ||
| power = power * p[i]; | ||
| prev = x; | ||
| x = n_rootrem(r, x, p[i]); | ||
| } | ||
| x = prev; | ||
| } | ||
| else x = prev; | ||
| } | ||
| } | ||
|
|
||
| *r = x; /* store root in r */ | ||
| return (power == 1 ? 0 : power); /* return power */ | ||
| } | ||
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,77 @@ | ||
| /*============================================================================= | ||
| This file is part of FLINT. | ||
| FLINT is free software; you can redistribute it and/or modify | ||
| it under the terms of the GNU General Public License as published by | ||
| the Free Software Foundation; either version 2 of the License, or | ||
| (at your option) any later version. | ||
| FLINT is distributed in the hope that it will be useful, | ||
| but WITHOUT ANY WARRANTY; without even the implied warranty of | ||
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | ||
| GNU General Public License for more details. | ||
| You should have received a copy of the GNU General Public License | ||
| along with FLINT; if not, write to the Free Software | ||
| Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA | ||
| =============================================================================*/ | ||
| /****************************************************************************** | ||
| Copyright (C) 2015 Nitin Kumar | ||
| ******************************************************************************/ | ||
|
|
||
| #include <stdio.h> | ||
| #include <stdlib.h> | ||
| #include <flint.h> | ||
| #include <ulong_extras.h> | ||
|
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| int main() | ||
| { | ||
| int i, result, j, k; | ||
| mp_limb_t d, r, t; | ||
| FLINT_TEST_INIT(state); | ||
|
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| flint_printf("n_is_perfect_power...."); | ||
| fflush(stdout); | ||
|
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| /* check for random number */ | ||
| for (i = 0; i < 100000; i++) | ||
| { | ||
| d = n_randlimb(state); | ||
| result = n_is_perfect_power(&r, d); | ||
| if (result && n_pow(r, result) != d) | ||
| { | ||
| flint_printf("FAIL:\n"); | ||
| flint_printf("%wu ** %wu != %wu\n", r, result, d); | ||
| abort(); | ||
| } | ||
| } | ||
|
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| /* check for possible power of random numbers, which are not | ||
| perfect powers. | ||
| */ | ||
|
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| for (j = 0; j < 100000; j++) | ||
| { | ||
| d = n_randtest_not_zero(state); | ||
|
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| if (d == 1) continue; | ||
|
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| while (d < UWORD_MAX && n_is_perfect_power(&r, d) != 0) d += 1; | ||
|
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| i = FLINT_BIT_COUNT(d); | ||
|
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| for (k = 2; k <= FLINT_BITS / i; k++) | ||
| { | ||
| t = n_pow(d, k); | ||
| result = n_is_perfect_power(&r, t); | ||
| if (result != k) | ||
| { | ||
| flint_printf("FAIL:\n"); | ||
| flint_printf("%wu ** %wu != %wu ( = %wu ** %wu)\n", r, result, t, d, k); | ||
| abort(); | ||
| } | ||
| } | ||
| } | ||
|
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| FLINT_TEST_CLEANUP(state); | ||
|
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| flint_printf("PASS\n"); | ||
| return 0; | ||
| } |
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AKA
Eric Bach, Jonathan Sorenson,
Sieve algorithms for perfect power testing,
Algorithmica 9 (1993), 313–328. MR 94d:11103