Annotation of OpenXM_contrib/gmp/mpn/generic/jacbase.c, Revision 1.1.1.2
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
1.1.1.2 ! ohara 4: INCOMPATIBLE CHANGES IN A FUTURE RELEASE OF GMP.
1.1 maekawa 5:
1.1.1.2 ! ohara 6: Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
1.1 maekawa 7:
8: This file is part of the GNU MP Library.
9:
10: The GNU MP Library is free software; you can redistribute it and/or modify
11: it under the terms of the GNU Lesser General Public License as published by
12: the Free Software Foundation; either version 2.1 of the License, or (at your
13: option) any later version.
14:
15: The GNU MP Library is distributed in the hope that it will be useful, but
16: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
17: or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
18: License for more details.
19:
20: You should have received a copy of the GNU Lesser General Public License
21: along with the GNU MP Library; see the file COPYING.LIB. If not, write to
22: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
1.1.1.2 ! ohara 23: MA 02111-1307, USA. */
1.1 maekawa 24:
25: #include "gmp.h"
26: #include "gmp-impl.h"
27: #include "longlong.h"
28:
29:
1.1.1.2 ! ohara 30: /* Use the simple loop by default. The generic count_trailing_zeros is not
! 31: very fast, and the extra trickery of method 3 has proven to be less use
! 32: than might have been though. */
! 33: #ifndef JACOBI_BASE_METHOD
! 34: #define JACOBI_BASE_METHOD 2
! 35: #endif
! 36:
1.1 maekawa 37:
1.1.1.2 ! ohara 38: /* Use count_trailing_zeros. */
! 39: #if JACOBI_BASE_METHOD == 1
1.1 maekawa 40: #define PROCESS_TWOS_ANY \
41: { \
42: mp_limb_t twos; \
43: count_trailing_zeros (twos, a); \
44: result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b); \
45: a >>= twos; \
46: }
47: #define PROCESS_TWOS_EVEN PROCESS_TWOS_ANY
1.1.1.2 ! ohara 48: #endif
1.1 maekawa 49:
1.1.1.2 ! ohara 50: /* Use a simple loop. A disadvantage of this is that there's a branch on a
! 51: 50/50 chance of a 0 or 1 low bit. */
! 52: #if JACOBI_BASE_METHOD == 2
1.1 maekawa 53: #define PROCESS_TWOS_EVEN \
54: { \
55: int two; \
56: two = JACOBI_TWO_U_BIT1 (b); \
57: do \
58: { \
1.1.1.2 ! ohara 59: a >>= 1; \
! 60: result_bit1 ^= two; \
! 61: ASSERT (a != 0); \
1.1 maekawa 62: } \
63: while ((a & 1) == 0); \
64: }
65: #define PROCESS_TWOS_ANY \
66: if ((a & 1) == 0) \
67: PROCESS_TWOS_EVEN;
1.1.1.2 ! ohara 68: #endif
1.1 maekawa 69:
1.1.1.2 ! ohara 70: /* Process one bit arithmetically, then a simple loop. This cuts the loop
! 71: condition down to a 25/75 chance, which should branch predict better.
! 72: The CPU will need a reasonable variable left shift. */
! 73: #if JACOBI_BASE_METHOD == 3
! 74: #define PROCESS_TWOS_EVEN \
! 75: { \
! 76: int two, mask, shift; \
! 77: \
! 78: two = JACOBI_TWO_U_BIT1 (b); \
! 79: mask = (~a & 2); \
! 80: a >>= 1; \
! 81: \
! 82: shift = (~a & 1); \
! 83: a >>= shift; \
! 84: result_bit1 ^= two ^ (two & mask); \
! 85: \
! 86: while ((a & 1) == 0) \
! 87: { \
! 88: a >>= 1; \
! 89: result_bit1 ^= two; \
! 90: ASSERT (a != 0); \
! 91: } \
! 92: }
! 93: #define PROCESS_TWOS_ANY \
! 94: { \
! 95: int two, mask, shift; \
! 96: \
! 97: two = JACOBI_TWO_U_BIT1 (b); \
! 98: shift = (~a & 1); \
! 99: a >>= shift; \
! 100: \
! 101: mask = shift << 1; \
! 102: result_bit1 ^= (two & mask); \
! 103: \
! 104: while ((a & 1) == 0) \
! 105: { \
! 106: a >>= 1; \
! 107: result_bit1 ^= two; \
! 108: ASSERT (a != 0); \
! 109: } \
! 110: }
1.1 maekawa 111: #endif
112:
113:
114: /* Calculate the value of the Jacobi symbol (a/b) of two mp_limb_t's, but
115: with a restricted range of inputs accepted, namely b>1, b odd, and a<=b.
116:
117: The initial result_bit1 is taken as a parameter for the convenience of
1.1.1.2 ! ohara 118: mpz_kronecker_ui() et al. The sign changes both here and in those
1.1 maekawa 119: routines accumulate nicely in bit 1, see the JACOBI macros.
120:
121: The return value here is the normal +1, 0, or -1. Note that +1 and -1
122: have bit 1 in the "BIT1" sense, which could be useful if the caller is
123: accumulating it into some extended calculation.
124:
125: Duplicating the loop body to avoid the MP_LIMB_T_SWAP(a,b) would be
126: possible, but a couple of tests suggest it's not a significant speedup,
127: and may even be a slowdown, so what's here is good enough for now.
128:
129: Future: The code doesn't demand a<=b actually, so maybe this could be
130: relaxed. All the places this is used currently call with a<=b though. */
131:
132: int
133: mpn_jacobi_base (mp_limb_t a, mp_limb_t b, int result_bit1)
134: {
135: ASSERT (b & 1); /* b odd */
136: ASSERT (b != 1);
137: ASSERT (a <= b);
138:
139: if (a == 0)
140: return 0;
141:
142: PROCESS_TWOS_ANY;
143: if (a == 1)
144: goto done;
145:
146: for (;;)
147: {
148: result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a, b);
149: MP_LIMB_T_SWAP (a, b);
150:
151: do
152: {
1.1.1.2 ! ohara 153: /* working on (a/b), a,b odd, a>=b */
! 154: ASSERT (a & 1);
! 155: ASSERT (b & 1);
! 156: ASSERT (a >= b);
1.1 maekawa 157:
158: if ((a -= b) == 0)
159: return 0;
160:
1.1.1.2 ! ohara 161: PROCESS_TWOS_EVEN;
1.1 maekawa 162: if (a == 1)
163: goto done;
164: }
165: while (a >= b);
166: }
167:
168: done:
169: return JACOBI_BIT1_TO_PN (result_bit1);
170: }
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