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