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Diffstat (limited to 'gmp/mpz/kronsz.c')
| -rw-r--r-- | gmp/mpz/kronsz.c | 138 |
1 files changed, 138 insertions, 0 deletions
diff --git a/gmp/mpz/kronsz.c b/gmp/mpz/kronsz.c new file mode 100644 index 0000000000..12c8fbd0aa --- /dev/null +++ b/gmp/mpz/kronsz.c @@ -0,0 +1,138 @@ +/* mpz_si_kronecker -- long+mpz Kronecker/Jacobi symbol. + +Copyright 1999-2002 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 either: + + * 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. + +or + + * the GNU General Public License as published by the Free Software + Foundation; either version 2 of the License, or (at your option) any + later version. + +or both in parallel, as here. + +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 General Public License +for more details. + +You should have received copies of the GNU General Public License and the +GNU Lesser General Public License along with the GNU MP Library. If not, +see https://www.gnu.org/licenses/. */ + +#include "gmp.h" +#include "gmp-impl.h" +#include "longlong.h" + + +int +mpz_si_kronecker (long a, mpz_srcptr b) +{ + mp_srcptr b_ptr; + mp_limb_t b_low; + mp_size_t b_size; + mp_size_t b_abs_size; + mp_limb_t a_limb, b_rem; + unsigned twos; + int result_bit1; + +#if GMP_NUMB_BITS < BITS_PER_ULONG + if (a > GMP_NUMB_MAX || a < -GMP_NUMB_MAX) + { + mp_limb_t alimbs[2]; + mpz_t az; + ALLOC(az) = numberof (alimbs); + PTR(az) = alimbs; + mpz_set_si (az, a); + return mpz_kronecker (az, b); + } +#endif + + b_size = SIZ (b); + if (b_size == 0) + return JACOBI_S0 (a); /* (a/0) */ + + /* account for the effect of the sign of b, then ignore it */ + result_bit1 = JACOBI_BSGN_SS_BIT1 (a, b_size); + + b_ptr = PTR(b); + b_low = b_ptr[0]; + b_abs_size = ABS (b_size); + + if ((b_low & 1) != 0) + { + /* b odd */ + + result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low); + a_limb = (unsigned long) ABS(a); + + if ((a_limb & 1) == 0) + { + /* (0/b)=1 for b=+/-1, 0 otherwise */ + if (a_limb == 0) + return (b_abs_size == 1 && b_low == 1); + + /* a even, b odd */ + count_trailing_zeros (twos, a_limb); + a_limb >>= twos; + /* (a*2^n/b) = (a/b) * twos(n,a) */ + result_bit1 ^= JACOBI_TWOS_U_BIT1 (twos, b_low); + } + } + else + { + /* (even/even)=0, and (0/b)=0 for b!=+/-1 */ + if ((a & 1) == 0) + return 0; + + /* a odd, b even + + Establish shifted b_low with valid bit1 for ASGN and RECIP below. + Zero limbs stripped are accounted for, but zero bits on b_low are + not because they remain in {b_ptr,b_abs_size} for the + JACOBI_MOD_OR_MODEXACT_1_ODD. */ + + JACOBI_STRIP_LOW_ZEROS (result_bit1, a, b_ptr, b_abs_size, b_low); + if ((b_low & 1) == 0) + { + if (UNLIKELY (b_low == GMP_NUMB_HIGHBIT)) + { + /* need b_ptr[1] to get bit1 in b_low */ + if (b_abs_size == 1) + { + /* (a/0x80000000) = (a/2)^(BPML-1) */ + if ((GMP_NUMB_BITS % 2) == 0) + result_bit1 ^= JACOBI_TWO_U_BIT1 (a); + return JACOBI_BIT1_TO_PN (result_bit1); + } + + /* b_abs_size > 1 */ + b_low = b_ptr[1] << 1; + } + else + { + count_trailing_zeros (twos, b_low); + b_low >>= twos; + } + } + + result_bit1 ^= JACOBI_ASGN_SU_BIT1 (a, b_low); + a_limb = (unsigned long) ABS(a); + } + + if (a_limb == 1) + return JACOBI_BIT1_TO_PN (result_bit1); /* (1/b)=1 */ + + /* (a/b*2^n) = (b*2^n mod a / a) * recip(a,b) */ + JACOBI_MOD_OR_MODEXACT_1_ODD (result_bit1, b_rem, b_ptr, b_abs_size, a_limb); + result_bit1 ^= JACOBI_RECIP_UU_BIT1 (a_limb, b_low); + return mpn_jacobi_base (b_rem, a_limb, result_bit1); +} |