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Annotation of OpenXM_contrib/gmp/mpn/generic/jacbase.c, Revision 1.1.1.1

1.1       maekawa     1: /* mpn_jacobi_base -- limb/limb Jacobi symbol with restricted arguments.
                      2:
                      3:    THIS INTERFACE IS PRELIMINARY AND MIGHT DISAPPEAR OR BE SUBJECT TO
                      4:    INCOMPATIBLE CHANGES IN A FUTURE RELEASE OF GMP. */
                      5:
                      6: /*
                      7: Copyright (C) 1999, 2000 Free Software Foundation, Inc.
                      8:
                      9: This file is part of the GNU MP Library.
                     10:
                     11: The GNU MP Library is free software; you can redistribute it and/or modify
                     12: it under the terms of the GNU Lesser General Public License as published by
                     13: the Free Software Foundation; either version 2.1 of the License, or (at your
                     14: option) any later version.
                     15:
                     16: The GNU MP Library is distributed in the hope that it will be useful, but
                     17: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
                     18: or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
                     19: License for more details.
                     20:
                     21: You should have received a copy of the GNU Lesser General Public License
                     22: along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
                     23: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
                     24: MA 02111-1307, USA.  */
                     25:
                     26: #include "gmp.h"
                     27: #include "gmp-impl.h"
                     28: #include "longlong.h"
                     29:
                     30:
                     31: #if COUNT_TRAILING_ZEROS_TIME <= 7
                     32: /* If count_trailing_zeros is fast, use it.
                     33:    K7 at 7 cycles and P6 at 2 are good here.  K6 at 12-27 and P5 at 18-42
                     34:    are not.  The default 15 in longlong.h is meant to mean not good here.  */
                     35:
                     36: #define PROCESS_TWOS_ANY                                \
                     37:   {                                                     \
                     38:     mp_limb_t  twos;                                    \
                     39:     count_trailing_zeros (twos, a);                     \
                     40:     result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b);        \
                     41:     a >>= twos;                                         \
                     42:   }
                     43:
                     44: #define PROCESS_TWOS_EVEN  PROCESS_TWOS_ANY
                     45:
                     46: #else
                     47: /* Use a loop instead.  With "a" uniformly distributed there will usually be
                     48:    only a few trailing zeros.
                     49:
                     50:    Unfortunately the branch for the while loop here will be on a 50/50
                     51:    chance of a 1 or 0, which is bad for branch prediction.  */
                     52:
                     53: #define PROCESS_TWOS_EVEN               \
                     54:   {                                     \
                     55:     int  two;                           \
                     56:     two = JACOBI_TWO_U_BIT1 (b);        \
                     57:     do                                  \
                     58:       {                                 \
                     59:         a >>= 1;                        \
                     60:         result_bit1 ^= two;             \
                     61:         ASSERT (a != 0);                \
                     62:       }                                 \
                     63:     while ((a & 1) == 0);               \
                     64:   }
                     65:
                     66: #define PROCESS_TWOS_ANY        \
                     67:   if ((a & 1) == 0)             \
                     68:     PROCESS_TWOS_EVEN;
                     69:
                     70: #endif
                     71:
                     72:
                     73: /* Calculate the value of the Jacobi symbol (a/b) of two mp_limb_t's, but
                     74:    with a restricted range of inputs accepted, namely b>1, b odd, and a<=b.
                     75:
                     76:    The initial result_bit1 is taken as a parameter for the convenience of
                     77:    mpz_kronecker_zi_ui() et al.  The sign changes both here and in those
                     78:    routines accumulate nicely in bit 1, see the JACOBI macros.
                     79:
                     80:    The return value here is the normal +1, 0, or -1.  Note that +1 and -1
                     81:    have bit 1 in the "BIT1" sense, which could be useful if the caller is
                     82:    accumulating it into some extended calculation.
                     83:
                     84:    Duplicating the loop body to avoid the MP_LIMB_T_SWAP(a,b) would be
                     85:    possible, but a couple of tests suggest it's not a significant speedup,
                     86:    and may even be a slowdown, so what's here is good enough for now.
                     87:
                     88:    Future: The code doesn't demand a<=b actually, so maybe this could be
                     89:    relaxed.  All the places this is used currently call with a<=b though.  */
                     90:
                     91: int
                     92: #if __STDC__
                     93: mpn_jacobi_base (mp_limb_t a, mp_limb_t b, int result_bit1)
                     94: #else
                     95: mpn_jacobi_base (a, b, result_bit1)
                     96:      mp_limb_t a;
                     97:      mp_limb_t b;
                     98:      int       result_bit1;
                     99: #endif
                    100: {
                    101:   ASSERT (b & 1);  /* b odd */
                    102:   ASSERT (b != 1);
                    103:   ASSERT (a <= b);
                    104:
                    105:   if (a == 0)
                    106:     return 0;
                    107:
                    108:   PROCESS_TWOS_ANY;
                    109:   if (a == 1)
                    110:     goto done;
                    111:
                    112:   for (;;)
                    113:     {
                    114:       result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b);
                    115:       MP_LIMB_T_SWAP (a, b);
                    116:
                    117:       do
                    118:        {
                    119:           /* working on (a/b), a,b odd, a>=b */
                    120:           ASSERT (a & 1);
                    121:           ASSERT (b & 1);
                    122:           ASSERT (a >= b);
                    123:
                    124:          if ((a -= b) == 0)
                    125:            return 0;
                    126:
                    127:           PROCESS_TWOS_EVEN;
                    128:          if (a == 1)
                    129:            goto done;
                    130:        }
                    131:       while (a >= b);
                    132:     }
                    133:
                    134:  done:
                    135:   return JACOBI_BIT1_TO_PN (result_bit1);
                    136: }