diff options
Diffstat (limited to 'gmp-6.3.0/mpn/generic/mod_1.c')
| -rw-r--r-- | gmp-6.3.0/mpn/generic/mod_1.c | 278 |
1 files changed, 278 insertions, 0 deletions
diff --git a/gmp-6.3.0/mpn/generic/mod_1.c b/gmp-6.3.0/mpn/generic/mod_1.c new file mode 100644 index 0000000..f737bc2 --- /dev/null +++ b/gmp-6.3.0/mpn/generic/mod_1.c @@ -0,0 +1,278 @@ +/* mpn_mod_1(dividend_ptr, dividend_size, divisor_limb) -- + Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB. + Return the single-limb remainder. + There are no constraints on the value of the divisor. + +Copyright 1991, 1993, 1994, 1999, 2000, 2002, 2007-2009, 2012, 2020 +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-impl.h" +#include "longlong.h" + + +/* The size where udiv_qrnnd_preinv should be used rather than udiv_qrnnd, + meaning the quotient size where that should happen, the quotient size + being how many udiv divisions will be done. + + The default is to use preinv always, CPUs where this doesn't suit have + tuned thresholds. Note in particular that preinv should certainly be + used if that's the only division available (USE_PREINV_ALWAYS). */ + +#ifndef MOD_1_NORM_THRESHOLD +#define MOD_1_NORM_THRESHOLD 0 +#endif + +#ifndef MOD_1_UNNORM_THRESHOLD +#define MOD_1_UNNORM_THRESHOLD 0 +#endif + +#ifndef MOD_1U_TO_MOD_1_1_THRESHOLD +#define MOD_1U_TO_MOD_1_1_THRESHOLD MP_SIZE_T_MAX /* default is not to use mpn_mod_1s */ +#endif + +#ifndef MOD_1N_TO_MOD_1_1_THRESHOLD +#define MOD_1N_TO_MOD_1_1_THRESHOLD MP_SIZE_T_MAX /* default is not to use mpn_mod_1s */ +#endif + +#ifndef MOD_1_1_TO_MOD_1_2_THRESHOLD +#define MOD_1_1_TO_MOD_1_2_THRESHOLD 10 +#endif + +#ifndef MOD_1_2_TO_MOD_1_4_THRESHOLD +#define MOD_1_2_TO_MOD_1_4_THRESHOLD 20 +#endif + +#if TUNE_PROGRAM_BUILD && !HAVE_NATIVE_mpn_mod_1_1p +/* Duplicates declarations in tune/speed.h */ +mp_limb_t mpn_mod_1_1p_1 (mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [4]); +mp_limb_t mpn_mod_1_1p_2 (mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t [4]); + +void mpn_mod_1_1p_cps_1 (mp_limb_t [4], mp_limb_t); +void mpn_mod_1_1p_cps_2 (mp_limb_t [4], mp_limb_t); + +#undef mpn_mod_1_1p +#define mpn_mod_1_1p(ap, n, b, pre) \ + (mod_1_1p_method == 1 ? mpn_mod_1_1p_1 (ap, n, b, pre) \ + : (mod_1_1p_method == 2 ? mpn_mod_1_1p_2 (ap, n, b, pre) \ + : __gmpn_mod_1_1p (ap, n, b, pre))) + +#undef mpn_mod_1_1p_cps +#define mpn_mod_1_1p_cps(pre, b) \ + (mod_1_1p_method == 1 ? mpn_mod_1_1p_cps_1 (pre, b) \ + : (mod_1_1p_method == 2 ? mpn_mod_1_1p_cps_2 (pre, b) \ + : __gmpn_mod_1_1p_cps (pre, b))) +#endif /* TUNE_PROGRAM_BUILD && !HAVE_NATIVE_mpn_mod_1_1p */ + + +/* The comments in mpn/generic/divrem_1.c apply here too. + + As noted in the algorithms section of the manual, the shifts in the loop + for the unnorm case can be avoided by calculating r = a%(d*2^n), followed + by a final (r*2^n)%(d*2^n). In fact if it happens that a%(d*2^n) can + skip a division where (a*2^n)%(d*2^n) can't then there's the same number + of divide steps, though how often that happens depends on the assumed + distributions of dividend and divisor. In any case this idea is left to + CPU specific implementations to consider. */ + +static mp_limb_t +mpn_mod_1_unnorm (mp_srcptr up, mp_size_t un, mp_limb_t d) +{ + mp_size_t i; + mp_limb_t n1, n0, r; + mp_limb_t dummy; + int cnt; + + ASSERT (un > 0); + ASSERT (d != 0); + + /* Skip a division if high < divisor. Having the test here before + normalizing will still skip as often as possible. */ + r = up[un - 1]; + if (r < d) + { + if (--un == 0) + return r; + } + else + r = 0; + + d <<= GMP_NAIL_BITS; + + /* If udiv_qrnnd doesn't need a normalized divisor, can use the simple + code above. */ + if (! UDIV_NEEDS_NORMALIZATION + && BELOW_THRESHOLD (un, MOD_1_UNNORM_THRESHOLD)) + { + for (i = un - 1; i >= 0; i--) + { + n0 = up[i] << GMP_NAIL_BITS; + udiv_qrnnd (dummy, r, r, n0, d); + r >>= GMP_NAIL_BITS; + } + return r; + } + + count_leading_zeros (cnt, d); + d <<= cnt; + + n1 = up[un - 1] << GMP_NAIL_BITS; + r = (r << cnt) | (n1 >> (GMP_LIMB_BITS - cnt)); + + if (UDIV_NEEDS_NORMALIZATION + && BELOW_THRESHOLD (un, MOD_1_UNNORM_THRESHOLD)) + { + mp_limb_t nshift; + for (i = un - 2; i >= 0; i--) + { + n0 = up[i] << GMP_NAIL_BITS; + nshift = (n1 << cnt) | (n0 >> (GMP_NUMB_BITS - cnt)); + udiv_qrnnd (dummy, r, r, nshift, d); + r >>= GMP_NAIL_BITS; + n1 = n0; + } + udiv_qrnnd (dummy, r, r, n1 << cnt, d); + r >>= GMP_NAIL_BITS; + return r >> cnt; + } + else + { + mp_limb_t inv, nshift; + invert_limb (inv, d); + + for (i = un - 2; i >= 0; i--) + { + n0 = up[i] << GMP_NAIL_BITS; + nshift = (n1 << cnt) | (n0 >> (GMP_NUMB_BITS - cnt)); + udiv_rnnd_preinv (r, r, nshift, d, inv); + r >>= GMP_NAIL_BITS; + n1 = n0; + } + udiv_rnnd_preinv (r, r, n1 << cnt, d, inv); + r >>= GMP_NAIL_BITS; + return r >> cnt; + } +} + +static mp_limb_t +mpn_mod_1_norm (mp_srcptr up, mp_size_t un, mp_limb_t d) +{ + mp_size_t i; + mp_limb_t n0, r; + mp_limb_t dummy; + + ASSERT (un > 0); + + d <<= GMP_NAIL_BITS; + + ASSERT (d & GMP_LIMB_HIGHBIT); + + /* High limb is initial remainder, possibly with one subtract of + d to get r<d. */ + r = up[un - 1] << GMP_NAIL_BITS; + if (r >= d) + r -= d; + r >>= GMP_NAIL_BITS; + un--; + if (un == 0) + return r; + + if (BELOW_THRESHOLD (un, MOD_1_NORM_THRESHOLD)) + { + for (i = un - 1; i >= 0; i--) + { + n0 = up[i] << GMP_NAIL_BITS; + udiv_qrnnd (dummy, r, r, n0, d); + r >>= GMP_NAIL_BITS; + } + return r; + } + else + { + mp_limb_t inv; + invert_limb (inv, d); + for (i = un - 1; i >= 0; i--) + { + n0 = up[i] << GMP_NAIL_BITS; + udiv_rnnd_preinv (r, r, n0, d, inv); + r >>= GMP_NAIL_BITS; + } + return r; + } +} + +mp_limb_t +mpn_mod_1 (mp_srcptr ap, mp_size_t n, mp_limb_t b) +{ + ASSERT (n >= 0); + ASSERT (b != 0); + + /* Should this be handled at all? Rely on callers? Note un==0 is currently + required by mpz/fdiv_r_ui.c and possibly other places. */ + if (n == 0) + return 0; + + if (UNLIKELY ((b & GMP_NUMB_HIGHBIT) != 0)) + { + if (BELOW_THRESHOLD (n, MOD_1N_TO_MOD_1_1_THRESHOLD)) + { + return mpn_mod_1_norm (ap, n, b); + } + else + { + mp_limb_t pre[4]; + mpn_mod_1_1p_cps (pre, b); + return mpn_mod_1_1p (ap, n, b, pre); + } + } + else + { + if (BELOW_THRESHOLD (n, MOD_1U_TO_MOD_1_1_THRESHOLD)) + { + return mpn_mod_1_unnorm (ap, n, b); + } + else if (BELOW_THRESHOLD (n, MOD_1_1_TO_MOD_1_2_THRESHOLD)) + { + mp_limb_t pre[4]; + mpn_mod_1_1p_cps (pre, b); + return mpn_mod_1_1p (ap, n, b << pre[1], pre); + } + else if (BELOW_THRESHOLD (n, MOD_1_2_TO_MOD_1_4_THRESHOLD) || UNLIKELY (b > GMP_NUMB_MASK / 4)) + { + mp_limb_t pre[5]; + mpn_mod_1s_2p_cps (pre, b); + return mpn_mod_1s_2p (ap, n, b << pre[1], pre); + } + else + { + mp_limb_t pre[7]; + mpn_mod_1s_4p_cps (pre, b); + return mpn_mod_1s_4p (ap, n, b << pre[1], pre); + } + } +} |