X-Git-Url: https://oss.titaniummirror.com/gitweb?a=blobdiff_plain;f=gmp%2Fmpn%2Fgeneric%2Fperfsqr.c;fp=gmp%2Fmpn%2Fgeneric%2Fperfsqr.c;h=1995a944df9a5aff42fd4465718ae3f2586da9d6;hb=6fed43773c9b0ce596dca5686f37ac3fc0fa11c0;hp=0000000000000000000000000000000000000000;hpb=27b11d56b743098deb193d510b337ba22dc52e5c;p=msp430-gcc.git

diff --git a/gmp/mpn/generic/perfsqr.c b/gmp/mpn/generic/perfsqr.c
new file mode 100644
index 00000000..1995a944
--- /dev/null
+++ b/gmp/mpn/generic/perfsqr.c
@@ -0,0 +1,229 @@
+/* mpn_perfect_square_p(u,usize) -- Return non-zero if U is a perfect square,
+   zero otherwise.
+
+Copyright 1991, 1993, 1994, 1996, 1997, 2000, 2001, 2002, 2005 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 3 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.  If not, see http://www.gnu.org/licenses/.  */
+
+#include <stdio.h> /* for NULL */
+#include "gmp.h"
+#include "gmp-impl.h"
+#include "longlong.h"
+
+#include "perfsqr.h"
+
+
+/* change this to "#define TRACE(x) x" for diagnostics */
+#define TRACE(x)
+
+
+
+/* PERFSQR_MOD_* detects non-squares using residue tests.
+
+   A macro PERFSQR_MOD_TEST is setup by gen-psqr.c in perfsqr.h.  It takes
+   {up,usize} modulo a selected modulus to get a remainder r.  For 32-bit or
+   64-bit limbs this modulus will be 2^24-1 or 2^48-1 using PERFSQR_MOD_34,
+   or for other limb or nail sizes a PERFSQR_PP is chosen and PERFSQR_MOD_PP
+   used.  PERFSQR_PP_NORM and PERFSQR_PP_INVERTED are pre-calculated in this
+   case too.
+
+   PERFSQR_MOD_TEST then makes various calls to PERFSQR_MOD_1 or
+   PERFSQR_MOD_2 with divisors d which are factors of the modulus, and table
+   data indicating residues and non-residues modulo those divisors.  The
+   table data is in 1 or 2 limbs worth of bits respectively, per the size of
+   each d.
+
+   A "modexact" style remainder is taken to reduce r modulo d.
+   PERFSQR_MOD_IDX implements this, producing an index "idx" for use with
+   the table data.  Notice there's just one multiplication by a constant
+   "inv", for each d.
+
+   The modexact doesn't produce a true r%d remainder, instead idx satisfies
+   "-(idx<<PERFSQR_MOD_BITS) == r mod d".  Because d is odd, this factor
+   -2^PERFSQR_MOD_BITS is a one-to-one mapping between r and idx, and is
+   accounted for by having the table data suitably permuted.
+
+   The remainder r fits within PERFSQR_MOD_BITS which is less than a limb.
+   In fact the GMP_LIMB_BITS - PERFSQR_MOD_BITS spare bits are enough to fit
+   each divisor d meaning the modexact multiply can take place entirely
+   within one limb, giving the compiler the chance to optimize it, in a way
+   that say umul_ppmm would not give.
+
+   There's no need for the divisors d to be prime, in fact gen-psqr.c makes
+   a deliberate effort to combine factors so as to reduce the number of
+   separate tests done on r.  But such combining is limited to d <=
+   2*GMP_LIMB_BITS so that the table data fits in at most 2 limbs.
+
+   Alternatives:
+
+   It'd be possible to use bigger divisors d, and more than 2 limbs of table
+   data, but this doesn't look like it would be of much help to the prime
+   factors in the usual moduli 2^24-1 or 2^48-1.
+
+   The moduli 2^24-1 or 2^48-1 are nothing particularly special, they're
+   just easy to calculate (see mpn_mod_34lsub1) and have a nice set of prime
+   factors.  2^32-1 and 2^64-1 would be equally easy to calculate, but have
+   fewer prime factors.
+
+   The nails case usually ends up using mpn_mod_1, which is a lot slower
+   than mpn_mod_34lsub1.  Perhaps other such special moduli could be found
+   for the nails case.  Two-term things like 2^30-2^15-1 might be
+   candidates.  Or at worst some on-the-fly de-nailing would allow the plain
+   2^24-1 to be used.  Currently nails are too preliminary to be worried
+   about.
+
+*/
+
+#define PERFSQR_MOD_MASK       ((CNST_LIMB(1) << PERFSQR_MOD_BITS) - 1)
+
+#define MOD34_BITS  (GMP_NUMB_BITS / 4 * 3)
+#define MOD34_MASK  ((CNST_LIMB(1) << MOD34_BITS) - 1)
+
+#define PERFSQR_MOD_34(r, up, usize)				\
+  do {								\
+    (r) = mpn_mod_34lsub1 (up, usize);				\
+    (r) = ((r) & MOD34_MASK) + ((r) >> MOD34_BITS);		\
+  } while (0)
+
+/* FIXME: The %= here isn't good, and might destroy any savings from keeping
+   the PERFSQR_MOD_IDX stuff within a limb (rather than needing umul_ppmm).
+   Maybe a new sort of mpn_preinv_mod_1 could accept an unnormalized divisor
+   and a shift count, like mpn_preinv_divrem_1.	 But mod_34lsub1 is our
+   normal case, so lets not worry too much about mod_1.	 */
+#define PERFSQR_MOD_PP(r, up, usize)				\
+  do {								\
+    if (USE_PREINV_MOD_1)					\
+      {								\
+	(r) = mpn_preinv_mod_1 (up, usize, PERFSQR_PP_NORM,	\
+				PERFSQR_PP_INVERTED);		\
+	(r) %= PERFSQR_PP;					\
+      }								\
+    else							\
+      {								\
+	(r) = mpn_mod_1 (up, usize, PERFSQR_PP);		\
+      }								\
+  } while (0)
+
+#define PERFSQR_MOD_IDX(idx, r, d, inv)				\
+  do {								\
+    mp_limb_t  q;						\
+    ASSERT ((r) <= PERFSQR_MOD_MASK);				\
+    ASSERT ((((inv) * (d)) & PERFSQR_MOD_MASK) == 1);		\
+    ASSERT (MP_LIMB_T_MAX / (d) >= PERFSQR_MOD_MASK);		\
+								\
+    q = ((r) * (inv)) & PERFSQR_MOD_MASK;			\
+    ASSERT (r == ((q * (d)) & PERFSQR_MOD_MASK));		\
+    (idx) = (q * (d)) >> PERFSQR_MOD_BITS;			\
+  } while (0)
+
+#define PERFSQR_MOD_1(r, d, inv, mask)				\
+  do {								\
+    unsigned   idx;						\
+    ASSERT ((d) <= GMP_LIMB_BITS);				\
+    PERFSQR_MOD_IDX(idx, r, d, inv);				\
+    TRACE (printf ("  PERFSQR_MOD_1 d=%u r=%lu idx=%u\n",	\
+		   d, r%d, idx));				\
+    if ((((mask) >> idx) & 1) == 0)				\
+      {								\
+	TRACE (printf ("  non-square\n"));			\
+	return 0;						\
+      }								\
+  } while (0)
+
+/* The expression "(int) idx - GMP_LIMB_BITS < 0" lets the compiler use the
+   sign bit from "idx-GMP_LIMB_BITS", which might help avoid a branch.	*/
+#define PERFSQR_MOD_2(r, d, inv, mhi, mlo)			\
+  do {								\
+    mp_limb_t  m;						\
+    unsigned   idx;						\
+    ASSERT ((d) <= 2*GMP_LIMB_BITS);				\
+								\
+    PERFSQR_MOD_IDX (idx, r, d, inv);				\
+    TRACE (printf ("  PERFSQR_MOD_2 d=%u r=%lu idx=%u\n",	\
+		   d, r%d, idx));				\
+    m = ((int) idx - GMP_LIMB_BITS < 0 ? (mlo) : (mhi));	\
+    idx %= GMP_LIMB_BITS;					\
+    if (((m >> idx) & 1) == 0)					\
+      {								\
+	TRACE (printf ("  non-square\n"));			\
+	return 0;						\
+      }								\
+  } while (0)
+
+
+int
+mpn_perfect_square_p (mp_srcptr up, mp_size_t usize)
+{
+  ASSERT (usize >= 1);
+
+  TRACE (gmp_printf ("mpn_perfect_square_p %Nd\n", up, usize));
+
+  /* The first test excludes 212/256 (82.8%) of the perfect square candidates
+     in O(1) time.  */
+  {
+    unsigned  idx = up[0] % 0x100;
+    if (((sq_res_0x100[idx / GMP_LIMB_BITS]
+	  >> (idx % GMP_LIMB_BITS)) & 1) == 0)
+      return 0;
+  }
+
+#if 0
+  /* Check that we have even multiplicity of 2, and then check that the rest is
+     a possible perfect square.  Leave disabled until we can determine this
+     really is an improvement.  It it is, it could completely replace the
+     simple probe above, since this should through out more non-squares, but at
+     the expense of somewhat more cycles.  */
+  {
+    mp_limb_t lo;
+    int cnt;
+    lo = up[0];
+    while (lo == 0)
+      up++, lo = up[0], usize--;
+    count_trailing_zeros (cnt, lo);
+    if ((cnt & 1) != 0)
+      return 0;			/* return of not even multiplicity of 2 */
+    lo >>= cnt;			/* shift down to align lowest non-zero bit */
+    lo >>= 1;			/* shift away lowest non-zero bit */
+    if ((lo & 3) != 0)
+      return 0;
+  }
+#endif
+
+
+  /* The second test uses mpn_mod_34lsub1 or mpn_mod_1 to detect non-squares
+     according to their residues modulo small primes (or powers of
+     primes).  See perfsqr.h.  */
+  PERFSQR_MOD_TEST (up, usize);
+
+
+  /* For the third and last test, we finally compute the square root,
+     to make sure we've really got a perfect square.  */
+  {
+    mp_ptr root_ptr;
+    int res;
+    TMP_DECL;
+
+    TMP_MARK;
+    root_ptr = (mp_ptr) TMP_ALLOC ((usize + 1) / 2 * BYTES_PER_MP_LIMB);
+
+    /* Iff mpn_sqrtrem returns zero, the square is perfect.  */
+    res = ! mpn_sqrtrem (root_ptr, NULL, up, usize);
+    TMP_FREE;
+
+    return res;
+  }
+}