Annotation of OpenXM_contrib/gmp/mpn/generic/mod_1.c, Revision 1.1
1.1 ! maekawa 1: /* mpn_mod_1(dividend_ptr, dividend_size, divisor_limb) --
! 2: Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
! 3: Return the single-limb remainder.
! 4: There are no constraints on the value of the divisor.
! 5:
! 6: Copyright (C) 1991, 1993, 1994, Free Software Foundation, Inc.
! 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 Library General Public License as published by
! 12: the Free Software Foundation; either version 2 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 Library General Public
! 18: License for more details.
! 19:
! 20: You should have received a copy of the GNU Library 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,
! 23: MA 02111-1307, USA. */
! 24:
! 25: #include "gmp.h"
! 26: #include "gmp-impl.h"
! 27: #include "longlong.h"
! 28:
! 29: #ifndef UMUL_TIME
! 30: #define UMUL_TIME 1
! 31: #endif
! 32:
! 33: #ifndef UDIV_TIME
! 34: #define UDIV_TIME UMUL_TIME
! 35: #endif
! 36:
! 37: /* FIXME: We should be using invert_limb (or invert_normalized_limb)
! 38: here (not udiv_qrnnd). */
! 39:
! 40: mp_limb_t
! 41: #if __STDC__
! 42: mpn_mod_1 (mp_srcptr dividend_ptr, mp_size_t dividend_size,
! 43: mp_limb_t divisor_limb)
! 44: #else
! 45: mpn_mod_1 (dividend_ptr, dividend_size, divisor_limb)
! 46: mp_srcptr dividend_ptr;
! 47: mp_size_t dividend_size;
! 48: mp_limb_t divisor_limb;
! 49: #endif
! 50: {
! 51: mp_size_t i;
! 52: mp_limb_t n1, n0, r;
! 53: int dummy;
! 54:
! 55: /* Botch: Should this be handled at all? Rely on callers? */
! 56: if (dividend_size == 0)
! 57: return 0;
! 58:
! 59: /* If multiplication is much faster than division, and the
! 60: dividend is large, pre-invert the divisor, and use
! 61: only multiplications in the inner loop. */
! 62:
! 63: /* This test should be read:
! 64: Does it ever help to use udiv_qrnnd_preinv?
! 65: && Does what we save compensate for the inversion overhead? */
! 66: if (UDIV_TIME > (2 * UMUL_TIME + 6)
! 67: && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME)
! 68: {
! 69: int normalization_steps;
! 70:
! 71: count_leading_zeros (normalization_steps, divisor_limb);
! 72: if (normalization_steps != 0)
! 73: {
! 74: mp_limb_t divisor_limb_inverted;
! 75:
! 76: divisor_limb <<= normalization_steps;
! 77:
! 78: /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
! 79: result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
! 80: most significant bit (with weight 2**N) implicit. */
! 81:
! 82: /* Special case for DIVISOR_LIMB == 100...000. */
! 83: if (divisor_limb << 1 == 0)
! 84: divisor_limb_inverted = ~(mp_limb_t) 0;
! 85: else
! 86: udiv_qrnnd (divisor_limb_inverted, dummy,
! 87: -divisor_limb, 0, divisor_limb);
! 88:
! 89: n1 = dividend_ptr[dividend_size - 1];
! 90: r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
! 91:
! 92: /* Possible optimization:
! 93: if (r == 0
! 94: && divisor_limb > ((n1 << normalization_steps)
! 95: | (dividend_ptr[dividend_size - 2] >> ...)))
! 96: ...one division less... */
! 97:
! 98: for (i = dividend_size - 2; i >= 0; i--)
! 99: {
! 100: n0 = dividend_ptr[i];
! 101: udiv_qrnnd_preinv (dummy, r, r,
! 102: ((n1 << normalization_steps)
! 103: | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
! 104: divisor_limb, divisor_limb_inverted);
! 105: n1 = n0;
! 106: }
! 107: udiv_qrnnd_preinv (dummy, r, r,
! 108: n1 << normalization_steps,
! 109: divisor_limb, divisor_limb_inverted);
! 110: return r >> normalization_steps;
! 111: }
! 112: else
! 113: {
! 114: mp_limb_t divisor_limb_inverted;
! 115:
! 116: /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB. The
! 117: result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
! 118: most significant bit (with weight 2**N) implicit. */
! 119:
! 120: /* Special case for DIVISOR_LIMB == 100...000. */
! 121: if (divisor_limb << 1 == 0)
! 122: divisor_limb_inverted = ~(mp_limb_t) 0;
! 123: else
! 124: udiv_qrnnd (divisor_limb_inverted, dummy,
! 125: -divisor_limb, 0, divisor_limb);
! 126:
! 127: i = dividend_size - 1;
! 128: r = dividend_ptr[i];
! 129:
! 130: if (r >= divisor_limb)
! 131: r = 0;
! 132: else
! 133: i--;
! 134:
! 135: for (; i >= 0; i--)
! 136: {
! 137: n0 = dividend_ptr[i];
! 138: udiv_qrnnd_preinv (dummy, r, r,
! 139: n0, divisor_limb, divisor_limb_inverted);
! 140: }
! 141: return r;
! 142: }
! 143: }
! 144: else
! 145: {
! 146: if (UDIV_NEEDS_NORMALIZATION)
! 147: {
! 148: int normalization_steps;
! 149:
! 150: count_leading_zeros (normalization_steps, divisor_limb);
! 151: if (normalization_steps != 0)
! 152: {
! 153: divisor_limb <<= normalization_steps;
! 154:
! 155: n1 = dividend_ptr[dividend_size - 1];
! 156: r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
! 157:
! 158: /* Possible optimization:
! 159: if (r == 0
! 160: && divisor_limb > ((n1 << normalization_steps)
! 161: | (dividend_ptr[dividend_size - 2] >> ...)))
! 162: ...one division less... */
! 163:
! 164: for (i = dividend_size - 2; i >= 0; i--)
! 165: {
! 166: n0 = dividend_ptr[i];
! 167: udiv_qrnnd (dummy, r, r,
! 168: ((n1 << normalization_steps)
! 169: | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
! 170: divisor_limb);
! 171: n1 = n0;
! 172: }
! 173: udiv_qrnnd (dummy, r, r,
! 174: n1 << normalization_steps,
! 175: divisor_limb);
! 176: return r >> normalization_steps;
! 177: }
! 178: }
! 179: /* No normalization needed, either because udiv_qrnnd doesn't require
! 180: it, or because DIVISOR_LIMB is already normalized. */
! 181:
! 182: i = dividend_size - 1;
! 183: r = dividend_ptr[i];
! 184:
! 185: if (r >= divisor_limb)
! 186: r = 0;
! 187: else
! 188: i--;
! 189:
! 190: for (; i >= 0; i--)
! 191: {
! 192: n0 = dividend_ptr[i];
! 193: udiv_qrnnd (dummy, r, r, n0, divisor_limb);
! 194: }
! 195: return r;
! 196: }
! 197: }
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