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/* This file is a new (faster) implementation of mpn_rootrem.
(Will be removed once this new implementation is released in GMP.)
Copyright 2005, 2006, 2007 Free Software Foundation, Inc.
This file was written by Torbjo"rn Granlund and Paul Zimmermann.
This file is part of the MPFR Library.
The MPFR Library is free software; you can redistribute it and/or modify
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 MPFR 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 Lesser General Public
License for more details.
You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB. If not, write to
the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301, USA. */
#include <stdio.h> /* for printf */
#include <stdlib.h> /* for exit, strtoul. */
#include "gmp.h"
/* replacement for internal gmp macros/functions */
#ifndef ASSERT_ALWAYS
#define ASSERT_ALWAYS(x)
#endif
#ifndef TMP_ALLOC_LIMBS
#define TMP_ALLOC_LIMBS(x) TMP_ALLOC(x * BYTES_PER_MP_LIMB)
#endif
#ifndef mpn_incr_u
#define mpn_incr_u(p,incr) \
do { \
mp_limb_t cy = incr; \
mp_ptr q = p; \
do { \
cy = mpn_add_1 (q, q, 1, cy); \
q ++; \
} while (cy != 0); \
} while (0)
#endif
#ifndef mpn_decr_u
#define mpn_decr_u(p,incr) \
do { \
mp_limb_t cy = incr; \
mp_ptr q = p; \
do { \
cy = mpn_sub_1 (q, q, 1, cy); \
q ++; \
} while (cy != 0); \
} while (0)
#endif
/* #define DEBUG */
#define MPN_RSHIFT(cy,rp,up,un,cnt) \
do { \
if ((cnt) != 0) \
cy = mpn_rshift (rp, up, un, cnt); \
else \
{ \
MPN_COPY_INCR (rp, up, un); \
cy = 0; \
} \
} while (0)
#define MPN_LSHIFT(cy,rp,up,un,cnt) \
do { \
if ((cnt) != 0) \
cy = mpn_lshift (rp, up, un, cnt); \
else \
{ \
MPN_COPY_DECR (rp, up, un); \
cy = 0; \
} \
} while (0)
#define MAXOFF 100
int off[MAXOFF];
static mp_size_t
mpfr_mpn_rootrem (mp_ptr rootp, mp_ptr remp,
mp_srcptr up, mp_size_t un, mp_limb_t k)
{
mp_ptr pp, qp, rp, sp, tp, wp;
mp_size_t pn, qn, rn, sn, tn, wn, nl, bn;
mp_limb_t save, save2, cy;
unsigned long int unb, xnb;
unsigned int cnt;
unsigned long b, kk;
unsigned long sizes[GMP_NUMB_BITS];
int ni, i;
int c;
long B;
MPFR_TMP_DECL (marker);
ASSERT_ALWAYS (un > 0);
ASSERT_ALWAYS (up[un - 1] != 0);
ASSERT_ALWAYS (k > 1);
MPFR_TMP_MARK (marker);
#define PP_ALLOC (2 + (mp_size_t) (un*1.585))
pp = TMP_ALLOC_LIMBS (PP_ALLOC);
qp = TMP_ALLOC_LIMBS (PP_ALLOC);
rp = TMP_ALLOC_LIMBS (PP_ALLOC);
sp = TMP_ALLOC_LIMBS (PP_ALLOC);
wp = TMP_ALLOC_LIMBS (PP_ALLOC);
count_leading_zeros (cnt, up[un - 1]);
unb = un * GMP_NUMB_BITS - cnt + GMP_NAIL_BITS;
xnb = (unb - 1) / k + 1; /* ceil (unb / k) */
#ifdef DEBUG
printf ("unb=%u xnb=%u\n", unb, xnb);
#endif
if (xnb == 1)
{
if (remp == NULL)
remp = pp;
mpn_sub_1 (remp, up, un, (mp_limb_t) 1);
MPN_NORMALIZE (remp, un); /* There should be at most one zero limb,
if we demand u to be normalized */
rootp[0] = 1;
MPFR_TMP_FREE (marker);
return un;
}
tp = TMP_ALLOC_LIMBS (PP_ALLOC);
kk = k * (xnb - 1);
MPN_RSHIFT (cy, rp, up + kk / GMP_NUMB_BITS, un - kk / GMP_NUMB_BITS, kk % GMP_NUMB_BITS);
rn = un - kk / GMP_NUMB_BITS;
mpn_sub_1 (rp, rp, rn, 1);
sp[0] = 1;
sn = 1;
b = 1;
B = 1;
b = xnb - 1;
ni = 0;
while (b != 1)
{
sizes[ni] = b;
b = (b + 1) / 2;
ni ++;
}
sizes[ni++] = 1;
sizes[ni] = 0;
for (i = ni; i != 0; i--)
{
b = sizes[i - 1] - sizes[i];
/* Reinsert a low zero limb if we normalized away the entire remainder. */
if (rn == 0)
{
rp[0] = 0;
rn = 1;
}
MPN_LSHIFT (cy, rp + b / GMP_NUMB_BITS, rp, rn, b % GMP_NUMB_BITS);
rn = rn + b / GMP_NUMB_BITS;
rp[rn] = cy;
rn += cy != 0;
kk = kk - b;
/* Now insert more bits from U. The lowest bit is kk, then get b higher bits. */
bn = b / GMP_NUMB_BITS; /* lowest limb from high part of rp[] */
save = rp[bn];
/* we have to save rp[bn] up to rp[nl-1], i.e. 1 or 2 limbs */
nl = 1 + (kk + b - 1) / GMP_NUMB_BITS - (kk / GMP_NUMB_BITS);
if (nl - 1 > bn)
save2 = rp[bn + 1];
MPN_RSHIFT (cy, rp, up + kk / GMP_NUMB_BITS, nl, kk % GMP_NUMB_BITS);
rp[bn] &= ((mp_limb_t) 1 << (b % GMP_NUMB_BITS)) - 1;
rp[bn] |= save;
if (nl - 1 > bn)
rp[bn + 1] = save2; /* the low b bits go in rp[0..bn] only */
if (i == ni)
wn = mpn_pow_1 (wp, sp, sn, k - 1, tp);
cy = mpn_mul_1 (pp, wp, wn, k);
pn = wn;
pp[pn] = cy;
pn += cy != 0;
if (rn < pn)
{
qn = 0;
}
else
{
mp_size_t cut;
qn = rn - pn;
cut = (pn < qn + 2) ? 0 : pn - (qn + 2);
/* printf ("%5ld %5ld %5ld %5ld\n", rn, pn, qn, cut); */
mpn_tdiv_qr (qp, tp, 0, rp + cut, rn - cut, pp + cut, pn - cut);
qn += qp[qn] != 0;
}
bn = (b - 1) / GMP_NUMB_BITS + 1; /* number of limbs used by b bits,
when least significant bit is
aligned to least limb */
/* q should be smaller than 2^b */
if (qn > bn || (qn == bn && (b % GMP_NUMB_BITS != 0) &&
qp[qn - 1] >= ((mp_limb_t) 1 << (b % GMP_NUMB_BITS))))
{
qn = b / GMP_NUMB_BITS + 1; /* b+1 bits */
MPN_ZERO (qp, qn);
qp[qn - 1] = (mp_limb_t) 1 << (b % GMP_NUMB_BITS);
mpn_sub_1 (qp, qp, qn, (mp_limb_t) 1);
qn -= qp[qn - 1] == 0;
}
MPN_LSHIFT (cy, sp + b / GMP_NUMB_BITS, sp, sn, b % GMP_NUMB_BITS);
sn = sn + b / GMP_NUMB_BITS;
sp[sn] = cy;
sn += cy != 0;
ASSERT_ALWAYS (bn >= qn);
MPN_ZERO (qp + qn, bn - qn);
/* Combine sB and q to form sB + q. */
save = sp[b / GMP_NUMB_BITS];
MPN_COPY (sp, qp, bn);
if (b % GMP_NUMB_BITS) /* if b is a multiple of GMP_NUMB_BITS,
there is no overlap */
mpn_incr_u (sp + b / GMP_NUMB_BITS, save);
kk -= (k - 1) * b;
MPN_RSHIFT (cy, tp, up + kk / GMP_NUMB_BITS, un - kk / GMP_NUMB_BITS, kk % GMP_NUMB_BITS);
tn = un - kk / GMP_NUMB_BITS;
tn -= tp[tn - 1] == 0;
for (c = 0;; c++)
{
/* Compute T. */
if (i == 1)
{
/* Last iteration */
pn = mpn_pow_1 (pp, sp, sn, k, qp);
}
else
{
wn = mpn_pow_1 (wp, sp, sn, k - 1, qp);
mpn_mul (pp, wp, wn, sp, sn);
pn = wn + sn;
pn -= pp[pn - 1] == 0;
}
if (pn > tn || (pn == tn && mpn_cmp (pp, tp, pn) > 0))
mpn_decr_u (sp, 1);
else
break;
}
if (c < MAXOFF)
off[c]++;
#ifdef DEBUG
if (c > 1)
{
printf ("b =%5lu B =%5ld k =%6ld c =%5d un =%7ld\n", b, B, k, c, un);
}
#endif
B += b;
ASSERT_ALWAYS (tn >= pn);
mpn_sub (rp, tp, tn, pp, pn);
rn = tn;
MPN_NORMALIZE (rp, rn);
}
MPN_COPY (rootp, sp, sn);
if (remp != NULL)
MPN_COPY (remp, rp, rn);
MPFR_TMP_FREE (marker);
return rn;
}
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