=================================================================== RCS file: /home/cvs/OpenXM_contrib/gmp/mpn/generic/Attic/mod_1.c,v retrieving revision 1.1.1.1 retrieving revision 1.1.1.3 diff -u -p -r1.1.1.1 -r1.1.1.3 --- OpenXM_contrib/gmp/mpn/generic/Attic/mod_1.c 2000/01/10 15:35:23 1.1.1.1 +++ OpenXM_contrib/gmp/mpn/generic/Attic/mod_1.c 2003/08/25 16:06:20 1.1.1.3 @@ -3,21 +3,21 @@ Return the single-limb remainder. There are no constraints on the value of the divisor. -Copyright (C) 1991, 1993, 1994, Free Software Foundation, Inc. +Copyright 1991, 1993, 1994, 1999, 2000, 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 the GNU Library General Public License as published by -the Free Software Foundation; either version 2 of the License, or (at your +it under the terms of the GNU Lesser General Public License as published by +the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. 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 Library General Public +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. -You should have received a copy of the GNU Library General Public License +You should have received a copy of the GNU Lesser General Public License along with the GNU MP Library; see the file COPYING.LIB. If not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ @@ -26,172 +26,149 @@ MA 02111-1307, USA. */ #include "gmp-impl.h" #include "longlong.h" -#ifndef UMUL_TIME -#define UMUL_TIME 1 -#endif -#ifndef UDIV_TIME -#define UDIV_TIME UMUL_TIME -#endif +/* 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. -/* FIXME: We should be using invert_limb (or invert_normalized_limb) - here (not udiv_qrnnd). */ + 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). */ -mp_limb_t -#if __STDC__ -mpn_mod_1 (mp_srcptr dividend_ptr, mp_size_t dividend_size, - mp_limb_t divisor_limb) -#else -mpn_mod_1 (dividend_ptr, dividend_size, divisor_limb) - mp_srcptr dividend_ptr; - mp_size_t dividend_size; - mp_limb_t divisor_limb; +#ifndef MOD_1_NORM_THRESHOLD +#define MOD_1_NORM_THRESHOLD 0 #endif -{ - mp_size_t i; - mp_limb_t n1, n0, r; - int dummy; +#ifndef MOD_1_UNNORM_THRESHOLD +#define MOD_1_UNNORM_THRESHOLD 0 +#endif - /* Botch: Should this be handled at all? Rely on callers? */ - if (dividend_size == 0) - return 0; - /* If multiplication is much faster than division, and the - dividend is large, pre-invert the divisor, and use - only multiplications in the inner loop. */ +/* The comments in mpn/generic/divrem_1.c apply here too. - /* This test should be read: - Does it ever help to use udiv_qrnnd_preinv? - && Does what we save compensate for the inversion overhead? */ - if (UDIV_TIME > (2 * UMUL_TIME + 6) - && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME) - { - int normalization_steps; + 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. */ - count_leading_zeros (normalization_steps, divisor_limb); - if (normalization_steps != 0) - { - mp_limb_t divisor_limb_inverted; +mp_limb_t +mpn_mod_1 (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; - divisor_limb <<= normalization_steps; + ASSERT (un >= 0); + ASSERT (d != 0); - /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The - result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the - most significant bit (with weight 2**N) implicit. */ + /* Botch: Should this be handled at all? Rely on callers? + But note un==0 is currently required by mpz/fdiv_r_ui.c and possibly + other places. */ + if (un == 0) + return 0; - /* Special case for DIVISOR_LIMB == 100...000. */ - if (divisor_limb << 1 == 0) - divisor_limb_inverted = ~(mp_limb_t) 0; - else - udiv_qrnnd (divisor_limb_inverted, dummy, - -divisor_limb, 0, divisor_limb); + d <<= GMP_NAIL_BITS; - n1 = dividend_ptr[dividend_size - 1]; - r = n1 >> (BITS_PER_MP_LIMB - normalization_steps); + if ((d & GMP_LIMB_HIGHBIT) != 0) + { + /* High limb is initial remainder, possibly with one subtract of + d to get r= d) + r -= d; + r >>= GMP_NAIL_BITS; + un--; + if (un == 0) + return r; - /* Possible optimization: - if (r == 0 - && divisor_limb > ((n1 << normalization_steps) - | (dividend_ptr[dividend_size - 2] >> ...))) - ...one division less... */ - - for (i = dividend_size - 2; i >= 0; i--) + if (BELOW_THRESHOLD (un, MOD_1_NORM_THRESHOLD)) + { + plain: + for (i = un - 1; i >= 0; i--) { - n0 = dividend_ptr[i]; - udiv_qrnnd_preinv (dummy, r, r, - ((n1 << normalization_steps) - | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))), - divisor_limb, divisor_limb_inverted); - n1 = n0; + n0 = up[i] << GMP_NAIL_BITS; + udiv_qrnnd (dummy, r, r, n0, d); + r >>= GMP_NAIL_BITS; } - udiv_qrnnd_preinv (dummy, r, r, - n1 << normalization_steps, - divisor_limb, divisor_limb_inverted); - return r >> normalization_steps; + return r; } else { - mp_limb_t divisor_limb_inverted; - - /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The - result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the - most significant bit (with weight 2**N) implicit. */ - - /* Special case for DIVISOR_LIMB == 100...000. */ - if (divisor_limb << 1 == 0) - divisor_limb_inverted = ~(mp_limb_t) 0; - else - udiv_qrnnd (divisor_limb_inverted, dummy, - -divisor_limb, 0, divisor_limb); - - i = dividend_size - 1; - r = dividend_ptr[i]; - - if (r >= divisor_limb) - r = 0; - else - i--; - - for (; i >= 0; i--) + mp_limb_t inv; + invert_limb (inv, d); + for (i = un - 1; i >= 0; i--) { - n0 = dividend_ptr[i]; - udiv_qrnnd_preinv (dummy, r, r, - n0, divisor_limb, divisor_limb_inverted); + n0 = up[i] << GMP_NAIL_BITS; + udiv_qrnnd_preinv (dummy, r, r, n0, d, inv); + r >>= GMP_NAIL_BITS; } return r; } } else { - if (UDIV_NEEDS_NORMALIZATION) + int norm; + + /* Skip a division if high < divisor. Having the test here before + normalizing will still skip as often as possible. */ + r = up[un - 1] << GMP_NAIL_BITS; + if (r < d) { - int normalization_steps; + r >>= GMP_NAIL_BITS; + un--; + if (un == 0) + return r; + } + else + r = 0; - count_leading_zeros (normalization_steps, divisor_limb); - if (normalization_steps != 0) - { - divisor_limb <<= normalization_steps; + /* 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)) + goto plain; - n1 = dividend_ptr[dividend_size - 1]; - r = n1 >> (BITS_PER_MP_LIMB - normalization_steps); + count_leading_zeros (norm, d); + d <<= norm; - /* Possible optimization: - if (r == 0 - && divisor_limb > ((n1 << normalization_steps) - | (dividend_ptr[dividend_size - 2] >> ...))) - ...one division less... */ + n1 = up[un - 1] << GMP_NAIL_BITS; + r = (r << norm) | (n1 >> (GMP_LIMB_BITS - norm)); - for (i = dividend_size - 2; i >= 0; i--) - { - n0 = dividend_ptr[i]; - udiv_qrnnd (dummy, r, r, - ((n1 << normalization_steps) - | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))), - divisor_limb); - n1 = n0; - } + if (UDIV_NEEDS_NORMALIZATION + && BELOW_THRESHOLD (un, MOD_1_UNNORM_THRESHOLD)) + { + for (i = un - 2; i >= 0; i--) + { + n0 = up[i] << GMP_NAIL_BITS; udiv_qrnnd (dummy, r, r, - n1 << normalization_steps, - divisor_limb); - return r >> normalization_steps; + (n1 << norm) | (n0 >> (GMP_NUMB_BITS - norm)), + d); + r >>= GMP_NAIL_BITS; + n1 = n0; } + udiv_qrnnd (dummy, r, r, n1 << norm, d); + r >>= GMP_NAIL_BITS; + return r >> norm; } - /* No normalization needed, either because udiv_qrnnd doesn't require - it, or because DIVISOR_LIMB is already normalized. */ - - i = dividend_size - 1; - r = dividend_ptr[i]; - - if (r >= divisor_limb) - r = 0; else - i--; - - for (; i >= 0; i--) { - n0 = dividend_ptr[i]; - udiv_qrnnd (dummy, r, r, n0, divisor_limb); + mp_limb_t inv; + invert_limb (inv, d); + + for (i = un - 2; i >= 0; i--) + { + n0 = up[i] << GMP_NAIL_BITS; + udiv_qrnnd_preinv (dummy, r, r, + (n1 << norm) | (n0 >> (GMP_NUMB_BITS - norm)), + d, inv); + r >>= GMP_NAIL_BITS; + n1 = n0; + } + udiv_qrnnd_preinv (dummy, r, r, n1 << norm, d, inv); + r >>= GMP_NAIL_BITS; + return r >> norm; } - return r; } }