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author | Simon Marlow <simonmar@microsoft.com> | 2006-04-07 02:05:11 +0000 |
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committer | Simon Marlow <simonmar@microsoft.com> | 2006-04-07 02:05:11 +0000 |
commit | 0065d5ab628975892cea1ec7303f968c3338cbe1 (patch) | |
tree | 8e2afe0ab48ee33cf95009809d67c9649573ef92 /rts/gmp/mpz/perfpow.c | |
parent | 28a464a75e14cece5db40f2765a29348273ff2d2 (diff) | |
download | haskell-0065d5ab628975892cea1ec7303f968c3338cbe1.tar.gz |
Reorganisation of the source tree
Most of the other users of the fptools build system have migrated to
Cabal, and with the move to darcs we can now flatten the source tree
without losing history, so here goes.
The main change is that the ghc/ subdir is gone, and most of what it
contained is now at the top level. The build system now makes no
pretense at being multi-project, it is just the GHC build system.
No doubt this will break many things, and there will be a period of
instability while we fix the dependencies. A straightforward build
should work, but I haven't yet fixed binary/source distributions.
Changes to the Building Guide will follow, too.
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; +} |