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source:
trunk/third/gmp/mpz/kronsz.c
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18191

Revision 18191, 3.7 KB checked in by ghudson, 22 years ago (diff) |
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1 | /* mpz_si_kronecker -- long+mpz Kronecker/Jacobi symbol. |

2 | |

3 | Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc. |

4 | |

5 | This file is part of the GNU MP Library. |

6 | |

7 | The GNU MP Library is free software; you can redistribute it and/or modify |

8 | it under the terms of the GNU Lesser General Public License as published by |

9 | the Free Software Foundation; either version 2.1 of the License, or (at your |

10 | option) any later version. |

11 | |

12 | The GNU MP Library is distributed in the hope that it will be useful, but |

13 | WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |

14 | or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public |

15 | License for more details. |

16 | |

17 | You should have received a copy of the GNU Lesser General Public License |

18 | along with the GNU MP Library; see the file COPYING.LIB. If not, write to |

19 | the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |

20 | MA 02111-1307, USA. */ |

21 | |

22 | #include "gmp.h" |

23 | #include "gmp-impl.h" |

24 | #include "longlong.h" |

25 | |

26 | |

27 | /* This implementation depends on BITS_PER_MP_LIMB being even, so that |

28 | (a/2)^BITS_PER_MP_LIMB = 1 and so there's no need to pay attention to how |

29 | many low zero limbs are stripped. */ |

30 | #if BITS_PER_MP_LIMB % 2 != 0 |

31 | Error, error, unsupported BITS_PER_MP_LIMB |

32 | #endif |

33 | |

34 | |

35 | int |

36 | mpz_si_kronecker (long a, mpz_srcptr b) |

37 | { |

38 | mp_srcptr b_ptr = PTR(b); |

39 | mp_limb_t b_low = b_ptr[0]; |

40 | mp_size_t b_size = SIZ (b); |

41 | mp_size_t b_abs_size = ABS (b_size); |

42 | mp_limb_t a_limb, b_rem; |

43 | unsigned twos; |

44 | int result_bit1; |

45 | |

46 | #if GMP_NUMB_BITS < BITS_PER_ULONG |

47 | if (a > GMP_NUMB_MAX || a < -GMP_NUMB_MAX) |

48 | { |

49 | mp_limb_t alimbs[2]; |

50 | mpz_t az; |

51 | ALLOC(az) = numberof (alimbs); |

52 | PTR(az) = alimbs; |

53 | mpz_set_si (az, a); |

54 | return mpz_kronecker (az, b); |

55 | } |

56 | #endif |

57 | |

58 | if (b_abs_size == 0) |

59 | return JACOBI_S0 (a); /* (a/0) */ |

60 | |

61 | /* account for the effect of the sign of b, then ignore it */ |

62 | result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size); |

63 | |

64 | if ((b_low & 1) != 0) |

65 | { |

66 | /* b odd */ |

67 | |

68 | result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low); |

69 | a_limb = (unsigned long) ABS(a); |

70 | |

71 | if ((a_limb & 1) == 0) |

72 | { |

73 | /* (0/b)=1 for b=+/-1, 0 otherwise */ |

74 | if (a_limb == 0) |

75 | return (b_abs_size == 1 && b_low == 1); |

76 | |

77 | /* a even, b odd */ |

78 | count_trailing_zeros (twos, a_limb); |

79 | a_limb >>= twos; |

80 | /* (a*2^n/b) = (a/b) * twos(n,a) */ |

81 | result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low); |

82 | } |

83 | } |

84 | else |

85 | { |

86 | /* (even/even)=0, and (0/b)=0 for b!=+/-1 */ |

87 | if ((a & 1) == 0) |

88 | return 0; |

89 | |

90 | /* a odd, b even */ |

91 | |

92 | /* establish shifted b_low with valid bit1 for use with ASGN and RECIP */ |

93 | MPN_STRIP_LOW_ZEROS_NOT_ZERO (b_ptr, b_abs_size, b_low); |

94 | if ((b_low & 1) == 0) |

95 | { |

96 | if (b_low == GMP_NUMB_HIGHBIT) |

97 | { |

98 | if (b_abs_size == 1) |

99 | { |

100 | /* (a/0x80000000) = (a/2)^(BPML-1) */ |

101 | result_bit1 ^= JACOBI_TWOS_U_BIT1 (GMP_NUMB_BITS - 1, a); |

102 | return JACOBI_BIT1_TO_PN (result_bit1); |

103 | } |

104 | |

105 | /* b_abs_size > 1 */ |

106 | b_low = b_ptr[1] << 1; |

107 | } |

108 | else |

109 | { |

110 | count_trailing_zeros (twos, b_low); |

111 | b_low >>= twos; |

112 | } |

113 | } |

114 | |

115 | result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low); |

116 | a_limb = (unsigned long) ABS(a); |

117 | } |

118 | |

119 | if (a_limb == 1) |

120 | return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */ |

121 | |

122 | /* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */ |

123 | JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a_limb); |

124 | result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a_limb, b_low); |

125 | return mpn_jacobi_base (b_rem, a_limb, result_bit1); |

126 | } |

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