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Diffstat (limited to 'rts/gmp/mpz/perfpow.c')
| -rw-r--r-- | rts/gmp/mpz/perfpow.c | 272 |
1 files changed, 272 insertions, 0 deletions
diff --git a/rts/gmp/mpz/perfpow.c b/rts/gmp/mpz/perfpow.c new file mode 100644 index 0000000000..e71670a0be --- /dev/null +++ b/rts/gmp/mpz/perfpow.c @@ -0,0 +1,272 @@ +/* mpz_perfect_power_p(arg) -- Return non-zero if ARG is a perfect power, + zero otherwise. + +Copyright (C) 1998, 1999, 2000 Free Software Foundation, Inc. + +This file is part of the GNU MP Library. + +The GNU MP Library is free software; you can redistribute it and/or modify +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation; either version 2.1 of the License, or (at your +option) any later version. + +The GNU MP Library 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 Lesser General Public +License for more details. + +You should have received a copy of the GNU Lesser General Public License +along with the GNU MP Library; see the file COPYING.LIB. If not, write to +the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, +MA 02111-1307, USA. */ + +/* + We are to determine if c is a perfect power, c = a ^ b. + Assume c is divisible by 2^n and that codd = c/2^n is odd. + Assume a is divisible by 2^m and that aodd = a/2^m is odd. + It is always true that m divides n. + + * If n is prime, either 1) a is 2*aodd and b = n + or 2) a = c and b = 1. + So for n prime, we readily have a solution. + * If n is factorable into the non-trivial factors p1,p2,... + Since m divides n, m has a subset of n's factors and b = n / m. + + BUG: Should handle negative numbers, since they can be odd perfect powers. +*/ + +/* This is a naive approach to recognizing perfect powers. + Many things can be improved. In particular, we should use p-adic + arithmetic for computing possible roots. */ + +#include <stdio.h> /* for NULL */ +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" + +static unsigned long int gcd _PROTO ((unsigned long int a, unsigned long int b)); +static int isprime _PROTO ((unsigned long int t)); + +static const unsigned short primes[] = +{ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, + 59, 61, 67, 71, 73, 79, 83, 89, 97,101,103,107,109,113,127,131, + 137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223, + 227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311, + 313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409, + 419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503, + 509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613, + 617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719, + 727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827, + 829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941, + 947,953,967,971,977,983,991,997,0 +}; +#define SMALLEST_OMITTED_PRIME 1009 + + +int +#if __STDC__ +mpz_perfect_power_p (mpz_srcptr u) +#else +mpz_perfect_power_p (u) + mpz_srcptr u; +#endif +{ + unsigned long int prime; + unsigned long int n, n2; + int i; + unsigned long int rem; + mpz_t u2, q; + int exact; + mp_size_t uns; + TMP_DECL (marker); + + if (mpz_cmp_ui (u, 1) <= 0) + return 0; + + n2 = mpz_scan1 (u, 0); + if (n2 == 1) + return 0; + + TMP_MARK (marker); + + uns = ABSIZ (u) - n2 / BITS_PER_MP_LIMB; + MPZ_TMP_INIT (q, uns); + MPZ_TMP_INIT (u2, uns); + + mpz_tdiv_q_2exp (u2, u, n2); + + if (isprime (n2)) + goto n2prime; + + for (i = 1; primes[i] != 0; i++) + { + prime = primes[i]; + rem = mpz_tdiv_ui (u2, prime); + if (rem == 0) /* divisable? */ + { + rem = mpz_tdiv_q_ui (q, u2, prime * prime); + if (rem != 0) + { + TMP_FREE (marker); + return 0; + } + mpz_swap (q, u2); + for (n = 2;;) + { + rem = mpz_tdiv_q_ui (q, u2, prime); + if (rem != 0) + break; + mpz_swap (q, u2); + n++; + } + + n2 = gcd (n2, n); + if (n2 == 1) + { + TMP_FREE (marker); + return 0; + } + + /* As soon as n2 becomes a prime number, stop factoring. + Either we have u=x^n2 or u is not a perfect power. */ + if (isprime (n2)) + goto n2prime; + } + } + + if (mpz_cmp_ui (u2, 1) == 0) + { + TMP_FREE (marker); + return 1; + } + + if (n2 == 0) + { + unsigned long int nth; + /* We did not find any factors above. We have to consider all values + of n. */ + for (nth = 2;; nth++) + { + if (! isprime (nth)) + continue; +#if 0 + exact = mpz_padic_root (q, u2, nth, PTH); + if (exact) +#endif + exact = mpz_root (q, u2, nth); + if (exact) + { + TMP_FREE (marker); + return 1; + } + if (mpz_cmp_ui (q, SMALLEST_OMITTED_PRIME) < 0) + { + TMP_FREE (marker); + return 0; + } + } + } + else + { + unsigned long int nth; + /* We found some factors above. We just need to consider values of n + that divides n2. */ + for (nth = 2; nth <= n2; nth++) + { + if (! isprime (nth)) + continue; + if (n2 % nth != 0) + continue; +#if 0 + exact = mpz_padic_root (q, u2, nth, PTH); + if (exact) +#endif + exact = mpz_root (q, u2, nth); + if (exact) + { + TMP_FREE (marker); + return 1; + } + if (mpz_cmp_ui (q, SMALLEST_OMITTED_PRIME) < 0) + { + TMP_FREE (marker); + return 0; + } + } + + TMP_FREE (marker); + return 0; + } + +n2prime: + exact = mpz_root (NULL, u2, n2); + TMP_FREE (marker); + return exact; +} + +static unsigned long int +#if __STDC__ +gcd (unsigned long int a, unsigned long int b) +#else +gcd (a, b) + unsigned long int a, b; +#endif +{ + int an2, bn2, n2; + + if (a == 0) + return b; + if (b == 0) + return a; + + count_trailing_zeros (an2, a); + a >>= an2; + + count_trailing_zeros (bn2, b); + b >>= bn2; + + n2 = MIN (an2, bn2); + + while (a != b) + { + if (a > b) + { + a -= b; + do + a >>= 1; + while ((a & 1) == 0); + } + else /* b > a. */ + { + b -= a; + do + b >>= 1; + while ((b & 1) == 0); + } + } + + return a << n2; +} + +static int +#if __STDC__ +isprime (unsigned long int t) +#else +isprime (t) + unsigned long int t; +#endif +{ + unsigned long int q, r, d; + + if (t < 3 || (t & 1) == 0) + return t == 2; + + for (d = 3, r = 1; r != 0; d += 2) + { + q = t / d; + r = t - q * d; + if (q < d) + return 1; + } + return 0; +} |