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F_mpz_LLL.c
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F_mpz_LLL.c
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/*
Copyright 2005, 2006 Damien Stehlé.
Copyright 2009, 2010 William Hart
Copyright 2009, 2010 Andy Novocin
This program implements ideas from the paper "Floating-point LLL Revisited",
by Phong Nguyen and Damien Stehlé, in the Proceedings of Eurocrypt'2005,
Springer-Verlag; and was partly inspired by Shoup's NTL library:
http://www.shoup.net/ntl/
This program is free software; you can redistribute it and/or modify it
under the terms of 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.
This program 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 a copy of the GNU General Public License along
with this program; see the file COPYING. If not, write to the Free
Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
02111-1307, USA.
*/
/****************************************************************************
F_mpz_LLL.c: LLL reduction on the rows of an F_mpz_mat_t
*****************************************************************************/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <time.h>
#include <float.h>
#include <sys/time.h>
#include <sys/resource.h>
#include <ctype.h>
#include <limits.h>
#include "gmp.h"
#include "flint.h"
#include "profiler.h"
#include "F_mpz_mat.h"
#include "F_mpz_LLL.h"
#include "mpfr.h"
#include "mpfr_mat.h"
#include "d_mat.h"
/****************************************************************************
The various Babai's: check_Babai, check_Babai_heuristic_d, check_Babai_heuristic
****************************************************************************/
#define PROFILE 0
#if PROFILE
// LLL profiles are on, checking babai total, time spent updating B--
// but not including the time in advanced babai which is totaled
double babai_start, babai_stop;
double babai_total = 0;
double adv_babai_start, adv_babai_stop;
double adv_babai_total = 0;
double update_start, update_stop;
double update_total = 0.0;
double convert_start, convert_stop;
double convert_total = 0.0;
double inner_start, inner_stop;
double inner_total = 0.0;
double ldexp_start, ldexp_stop;
double ldexp_total = 0.0;
double hbabai_start, hbabai_stop;
double hbabai_total = 0;
double hadv_babai_start, hadv_babai_stop;
double hadv_babai_total = 0;
double hupdate_start, hupdate_stop;
double hupdate_total = 0.0;
double hconvert_start, hconvert_stop;
double hconvert_total = 0.0;
double hinner_start, hinner_stop;
double hinner_total = 0.0;
double hldexp_start, hldexp_stop;
double hldexp_total = 0.0;
#endif
/*
Computes the scalar product of two vectors of doubles vec1 and vec2, which are
respectively double approximations (up to scaling by a power of 2) to rows k and
j in the exact integer matrix B. If massive cancellation is detected an exact
computation is made.
The exact computation is scaled by 2^-exp_adj, where exp_adj = r2 + r1 where
r2 is the exponent for row j and r1 is the exponent for row k (i.e. row j is
notionally thought of as being multiplied by 2^r2, etc).
The final scalar product computed by this function is then notionally the return
value times 2^exp_adj.
*/
double heuristic_scalar_product(double * vec1, double * vec2, ulong n,
F_mpz_mat_t B, ulong k, ulong j, long exp_adj)
{
double sum = _d_vec_scalar_product(vec1, vec2, n);
double tmp = _d_vec_norm(vec1, n);
double tmp2 = _d_vec_norm(vec2, n);
tmp = ldexp(tmp*tmp2, -70);
tmp2 = sum*sum;
if (tmp2 <= tmp)
{
F_mpz_t sp;
F_mpz_init(sp);
ulong exp;
_F_mpz_vec_scalar_product(sp, B->rows[k], B->rows[j], n);
sum = F_mpz_get_d_2exp(&exp, sp);
sum = ldexp(sum, exp - exp_adj);
F_mpz_clear(sp);
}
return sum;
}
/*
Performs floating point size reductions of the kappa-th row of B by all of
the previous rows, uses d_mats mu and r for storing the GSO data.
While the double array s will contain the size of the kappa-th row if it
were moved into position i. The d_mat appB is an approximation of
B with each row receiving an exponent stored in expo which gets populated
only when needed. The d_mat appSP is an approximation of the Gram matrix
whose entries are scalar products of the rows of B. The index a is the
smallest row index which will be reduced from the kappa-th row. Index zeros
is the number of zero rows in the matrix. Kappamax is the highest index
which has been size-reduced so far, and n is the number of columns you want to
consider. The output is the value -1 if the process fails (usually do to
insufficient precision) or 0 if everything was successful. These descriptions
will be true for the future Babai procedures as well.
*/
int check_Babai (int kappa, F_mpz_mat_t B, double **mu, double **r, double *s,
double **appB, int *expo, double **appSP,
int a, int zeros, int kappamax, int n)
{
int i, j, k, test, aa, exponent;
signed long xx;
double tmp, rtmp;
aa = (a > zeros) ? a : zeros + 1;
ctt = (4*DELTA + 1)/5;
halfplus = (4*ETA + .5)/5 ;
onedothalfplus = 1.0+halfplus;
long loops = 0;
do
{
test = 0;
loops++;
if (loops > 2){
return -1;
}
/* ************************************** */
/* Step2: compute the GSO for stage kappa */
/* ************************************** */
for (j = aa; j < kappa; j++)
{
if (appSP[kappa][j] != appSP[kappa][j]) // if appSP[kappa][j] == NAN
{
#if PROFILE
inner_start = get_cycle_counter();
#endif
appSP[kappa][j] = _d_vec_scalar_product(appB[kappa], appB[j], n);
#if PROFILE
inner_stop = get_cycle_counter();
inner_total = inner_total + inner_stop - inner_start;
#endif
}
if (j > zeros + 2)
{
tmp = mu[j][zeros+1] * r[kappa][zeros+1];
rtmp = appSP[kappa][j] - tmp;
for (k = zeros + 2; k < j - 1; k++)
{
tmp = mu[j][k] * r[kappa][k];
rtmp = rtmp - tmp;
}
tmp = mu[j][j-1] * r[kappa][j-1];
r[kappa][j] = rtmp - tmp;
} else if (j == zeros+2)
{
tmp = mu[j][zeros+1] * r[kappa][zeros+1];
r[kappa][j] = appSP[kappa][j] - tmp;
} else r[kappa][j] = appSP[kappa][j];
mu[kappa][j] = r[kappa][j] / r[j][j];
}
/* **************************** */
/* Step3--5: compute the X_j's */
/* **************************** */
for (j = kappa - 1; j > zeros; j--)
{
/* test of the relaxed size-reduction condition */
tmp = fabs(mu[kappa][j]);
#if PROFILE
ldexp_start = get_cycle_counter();
#endif
tmp = ldexp(tmp, expo[kappa] - expo[j]);
#if PROFILE
ldexp_stop = get_cycle_counter();
ldexp_total = ldexp_total + ldexp_stop - ldexp_start;
#endif
if (tmp > halfplus)
{
test = 1;
exponent = expo[j] - expo[kappa];
/* we consider separately the cases X = +-1 */
if (tmp <= onedothalfplus)
{
if (mu[kappa][j] >= 0) /* in this case, X is 1 */
{
for (k = zeros + 1; k < j; k++)
{
tmp = ldexp (mu[j][k], exponent);
mu[kappa][k] = mu[kappa][k] - tmp;
}
#if PROFILE
update_start = get_cycle_counter();
#endif
_F_mpz_vec_sub(B->rows[kappa], B->rows[kappa], B->rows[j], n);
#if PROFILE
update_stop = get_cycle_counter();
update_total = update_total + update_stop - update_start;
#endif
} else /* otherwise X is -1 */
{
for (k=zeros+1; k<j; k++)
{
tmp = ldexp (mu[j][k], exponent);
mu[kappa][k] = mu[kappa][k] + tmp;
}
#if PROFILE
update_start = get_cycle_counter();
#endif
_F_mpz_vec_add(B->rows[kappa], B->rows[kappa], B->rows[j], n);
#if PROFILE
update_stop = get_cycle_counter();
update_total = update_total + update_stop - update_start;
#endif
}
} else /* we must have |X| >= 2 */
{
#if PROFILE
ldexp_start = get_cycle_counter();
#endif
tmp = ldexp (mu[kappa][j] , -exponent);
#if PROFILE
ldexp_stop = get_cycle_counter();
ldexp_total = ldexp_total + ldexp_stop - ldexp_start;
#endif
if ((tmp < (double) MAX_LONG) &&(tmp > (double) -MAX_LONG))
{
tmp = rint (tmp);
for (k = zeros + 1; k < j; k++)
{
rtmp = tmp * mu[j][k];
#if PROFILE
ldexp_start = get_cycle_counter();
#endif
rtmp = ldexp (rtmp, exponent);
#if PROFILE
ldexp_stop = get_cycle_counter();
ldexp_total = ldexp_total + ldexp_stop - ldexp_start;
#endif
mu[kappa][k] = mu[kappa][k] - rtmp;
}
xx = (long) tmp;
if (xx > 0L)
{
#if PROFILE
update_start = get_cycle_counter();
#endif
_F_mpz_vec_submul_ui(B->rows[kappa], B->rows[j], n, (ulong) xx);
#if PROFILE
update_stop = get_cycle_counter();
update_total = update_total + update_stop - update_start;
#endif
} else
{
#if PROFILE
update_start = get_cycle_counter();
#endif
_F_mpz_vec_addmul_ui(B->rows[kappa], B->rows[j], n, (ulong) -xx);
#if PROFILE
update_stop = get_cycle_counter();
update_total = update_total + update_stop - update_start;
#endif
}
} else
{
#if PROFILE
ldexp_start = get_cycle_counter();
#endif
tmp = frexp(mu[kappa][j], &exponent);
#if PROFILE
ldexp_stop = get_cycle_counter();
ldexp_total = ldexp_total + ldexp_stop - ldexp_start;
#endif
tmp = tmp * MAX_LONG;
xx = (long) tmp;
exponent += expo[kappa] - expo[j] - CPU_SIZE_1;
/* This case is extremely rare: never happened for me */
if (exponent <= 0)
{
// printf("rare case kappa = %d, j = %d ******\n", kappa, j);
xx = xx << -exponent;
exponent = 0;
if (xx > 0)
{
#if PROFILE
update_start = get_cycle_counter();
#endif
_F_mpz_vec_submul_ui(B->rows[kappa], B->rows[j], n, xx);
#if PROFILE
update_stop = get_cycle_counter();
update_total = update_total + update_stop - update_start;
#endif
} else
{
#if PROFILE
update_start = get_cycle_counter();
#endif
_F_mpz_vec_addmul_ui(B->rows[kappa], B->rows[j], n, -xx);
#if PROFILE
update_stop = get_cycle_counter();
update_total = update_total + update_stop - update_start;
#endif
}
for (k = zeros + 1; k < j; k++)
{
rtmp = ((double) xx) * mu[j][k];
#if PROFILE
ldexp_start = get_cycle_counter();
#endif
rtmp = ldexp (rtmp, expo[j] - expo[kappa]);
#if PROFILE
ldexp_stop = get_cycle_counter();
ldexp_total = ldexp_total + ldexp_stop - ldexp_start;
#endif
mu[kappa][k] = mu[kappa][k] - rtmp;
}
} else
{
if (xx > 0)
{
#if PROFILE
update_start = get_cycle_counter();
#endif
_F_mpz_vec_submul_2exp_ui(B->rows[kappa], B->rows[j], n, (ulong) xx, exponent);
#if PROFILE
update_stop = get_cycle_counter();
update_total = update_total + update_stop - update_start;
#endif
} else
{
#if PROFILE
update_start = get_cycle_counter();
#endif
_F_mpz_vec_addmul_2exp_ui(B->rows[kappa], B->rows[j], n, (ulong) -xx, exponent);
#if PROFILE
update_stop = get_cycle_counter();
update_total = update_total + update_stop - update_start;
#endif
}
for (k = zeros + 1; k < j; k++)
{
rtmp = ((double) xx) * mu[j][k];
#if PROFILE
ldexp_start = get_cycle_counter();
#endif
rtmp = ldexp (rtmp, exponent + expo[j] - expo[kappa]);
#if PROFILE
ldexp_stop = get_cycle_counter();
ldexp_total = ldexp_total + ldexp_stop - ldexp_start;
#endif
mu[kappa][k] = mu[kappa][k] - rtmp;
}
}
}
}
}
}
if (test) /* Anything happened? */
{
#if PROFILE
convert_start = get_cycle_counter();
#endif
expo[kappa] = _F_mpz_vec_to_d_vec_2exp(appB[kappa], B->rows[kappa], n);
#if PROFILE
convert_stop = get_cycle_counter();
convert_total = convert_total + convert_stop - convert_start;
#endif
aa = zeros + 1;
for (i = zeros + 1; i <= kappa; i++)
appSP[kappa][i] = NAN;//0.0/0.0;
for (i = kappa + 1; i <= kappamax; i++)
appSP[i][kappa] = NAN;//0.0/0.0;
}
} while (test);
if (appSP[kappa][kappa] != appSP[kappa][kappa])
{
#if PROFILE
inner_start = get_cycle_counter();
#endif
appSP[kappa][kappa] = _d_vec_norm(appB[kappa], n);
#if PROFILE
inner_stop = get_cycle_counter();
inner_total = inner_total + inner_stop - inner_start;
#endif
}
s[zeros + 1] = appSP[kappa][kappa];
for (k = zeros + 1; k < kappa - 1; k++)
{
tmp = mu[kappa][k] * r[kappa][k];
s[k+1] = s[k] - tmp;
}
return 0;
}
/*
Same as check_Babai but using the heuristic inner product rather than a purely
floating point inner product. The heuristic will compute at full precision
when there is cancellation.
*/
int check_Babai_heuristic_d (int kappa, F_mpz_mat_t B, double **mu, double **r, double *s,
double **appB, int *expo, double **appSP,
int a, int zeros, int kappamax, int n)
{
int i, j, k, test, aa, exponent;
signed long xx;
double tmp, rtmp;
aa = (a > zeros) ? a : zeros + 1;
ctt = (4*DELTA + 1)/5;
halfplus = (4*ETA + .5)/5 ;
onedothalfplus = 1.0+halfplus;
int loops = 0;
do
{
test = 0;
loops++;
if (loops > 10)
return -1;
/* ************************************** */
/* Step2: compute the GSO for stage kappa */
/* ************************************** */
for (j = aa; j < kappa; j++)
{
if (appSP[kappa][j] != appSP[kappa][j]) // if appSP[kappa][j] == NAN
{
#if PROFILE
hinner_start = get_cycle_counter();
#endif
//### This is different -----
appSP[kappa][j] = heuristic_scalar_product(appB[kappa], appB[j],
n, B, kappa, j, expo[kappa]+expo[j]);
#if PROFILE
hinner_stop = get_cycle_counter();
hinner_total = hinner_total + hinner_stop - hinner_start;
#endif
}
if (j > zeros + 2)
{
tmp = mu[j][zeros+1] * r[kappa][zeros+1];
rtmp = appSP[kappa][j] - tmp;
for (k = zeros + 2; k < j - 1; k++)
{
tmp = mu[j][k] * r[kappa][k];
rtmp = rtmp - tmp;
}
tmp = mu[j][j-1] * r[kappa][j-1];
r[kappa][j] = rtmp - tmp;
} else if (j == zeros+2)
{
tmp = mu[j][zeros+1] * r[kappa][zeros+1];
r[kappa][j] = appSP[kappa][j] - tmp;
} else r[kappa][j] = appSP[kappa][j];
mu[kappa][j] = r[kappa][j] / r[j][j];
}
/* **************************** */
/* Step3--5: compute the X_j's */
/* **************************** */
for (j = kappa - 1; j > zeros; j--)
{
/* test of the relaxed size-reduction condition */
tmp = fabs(mu[kappa][j]);
#if PROFILE
hldexp_start = get_cycle_counter();
#endif
tmp = ldexp(tmp, expo[kappa] - expo[j]);
#if PROFILE
hldexp_stop = get_cycle_counter();
hldexp_total = hldexp_total + hldexp_stop - hldexp_start;
#endif
if (tmp > halfplus)
{
test = 1;
exponent = expo[j] - expo[kappa];
/* we consider separately the cases X = +-1 */
if (tmp <= onedothalfplus)
{
if (mu[kappa][j] >= 0) /* in this case, X is 1 */
{
for (k = zeros + 1; k < j; k++)
{
#if PROFILE
hldexp_start = get_cycle_counter();
#endif
tmp = ldexp (mu[j][k], exponent);
#if PROFILE
hldexp_stop = get_cycle_counter();
hldexp_total = hldexp_total + hldexp_stop - hldexp_start;
#endif
mu[kappa][k] = mu[kappa][k] - tmp;
}
#if PROFILE
hupdate_start = get_cycle_counter();
#endif
_F_mpz_vec_sub(B->rows[kappa], B->rows[kappa], B->rows[j], n);
#if PROFILE
hupdate_stop = get_cycle_counter();
hupdate_total = hupdate_total + hupdate_stop - hupdate_start;
#endif
} else /* otherwise X is -1 */
{
for (k=zeros+1; k<j; k++)
{
#if PROFILE
hldexp_start = get_cycle_counter();
#endif
tmp = ldexp (mu[j][k], exponent);
#if PROFILE
hldexp_stop = get_cycle_counter();
hldexp_total = hldexp_total + hldexp_stop - hldexp_start;
#endif
mu[kappa][k] = mu[kappa][k] + tmp;
}
#if PROFILE
hupdate_start = get_cycle_counter();
#endif
_F_mpz_vec_add(B->rows[kappa], B->rows[kappa], B->rows[j], n);
#if PROFILE
hupdate_stop = get_cycle_counter();
hupdate_total = hupdate_total + hupdate_stop - hupdate_start;
#endif
}
} else /* we must have |X| >= 2 */
{
#if PROFILE
hldexp_start = get_cycle_counter();
#endif
tmp = ldexp (mu[kappa][j] , -exponent);
#if PROFILE
hldexp_stop = get_cycle_counter();
hldexp_total = hldexp_total + hldexp_stop - hldexp_start;
#endif
if ((tmp < (double) MAX_LONG) && (tmp > (double) -MAX_LONG))
{
tmp = rint (tmp);
for (k = zeros + 1; k < j; k++)
{
rtmp = tmp * mu[j][k];
#if PROFILE
hldexp_start = get_cycle_counter();
#endif
rtmp = ldexp (rtmp, exponent);
#if PROFILE
hldexp_stop = get_cycle_counter();
hldexp_total = hldexp_total + hldexp_stop - hldexp_start;
#endif
mu[kappa][k] = mu[kappa][k] - rtmp;
}
xx = (long) tmp;
if (xx > 0L)
{
#if PROFILE
hupdate_start = get_cycle_counter();
#endif
_F_mpz_vec_submul_ui(B->rows[kappa], B->rows[j], n, (ulong) xx);
#if PROFILE
hupdate_stop = get_cycle_counter();
hupdate_total = hupdate_total + hupdate_stop - hupdate_start;
#endif
} else
{
#if PROFILE
hupdate_start = get_cycle_counter();
#endif
_F_mpz_vec_addmul_ui(B->rows[kappa], B->rows[j], n, (ulong) -xx);
#if PROFILE
hupdate_stop = get_cycle_counter();
hupdate_total = hupdate_total + hupdate_stop - hupdate_start;
#endif
}
} else
{
#if PROFILE
hldexp_start = get_cycle_counter();
#endif
tmp = frexp(mu[kappa][j], &exponent);
#if PROFILE
hldexp_stop = get_cycle_counter();
hldexp_total = hldexp_total + hldexp_stop - hldexp_start;
#endif
tmp = tmp * MAX_LONG;
xx = (long) tmp;
exponent += expo[kappa] - expo[j] - CPU_SIZE_1;
/* This case is extremely rare: never happened for me */
if (exponent <= 0)
{
xx = xx << -exponent;
exponent = 0;
if (xx > 0)
{
#if PROFILE
hupdate_start = get_cycle_counter();
#endif
_F_mpz_vec_submul_ui(B->rows[kappa], B->rows[j], n, xx);
#if PROFILE
hupdate_stop = get_cycle_counter();
hupdate_total = hupdate_total + hupdate_stop - hupdate_start;
#endif
} else
{
#if PROFILE
hupdate_start = get_cycle_counter();
#endif
_F_mpz_vec_addmul_ui(B->rows[kappa], B->rows[j], n, -xx);
#if PROFILE
hupdate_stop = get_cycle_counter();
hupdate_total = hupdate_total + hupdate_stop - hupdate_start;
#endif
}
for (k = zeros + 1; k < j; k++)
{
rtmp = ((double) xx) * mu[j][k];
#if PROFILE
hldexp_start = get_cycle_counter();
#endif
rtmp = ldexp (rtmp, expo[j] - expo[kappa]);
#if PROFILE
hldexp_stop = get_cycle_counter();
hldexp_total = hldexp_total + hldexp_stop - hldexp_start;
#endif
mu[kappa][k] = mu[kappa][k] - rtmp;
}
} else
{
if (xx > 0)
{
#if PROFILE
hupdate_start = get_cycle_counter();
#endif
_F_mpz_vec_submul_2exp_ui(B->rows[kappa], B->rows[j], n, (ulong) xx, exponent);
#if PROFILE
hupdate_stop = get_cycle_counter();
hupdate_total = hupdate_total + hupdate_stop - hupdate_start;
#endif
} else
{
#if PROFILE
hupdate_start = get_cycle_counter();
#endif
_F_mpz_vec_addmul_2exp_ui(B->rows[kappa], B->rows[j], n, (ulong) -xx, exponent);
#if PROFILE
hupdate_stop = get_cycle_counter();
hupdate_total = hupdate_total + hupdate_stop - hupdate_start;
#endif
}
for (k = zeros + 1; k < j; k++)
{
rtmp = ((double) xx) * mu[j][k];
#if PROFILE
hldexp_start = get_cycle_counter();
#endif
rtmp = ldexp (rtmp, exponent + expo[j] - expo[kappa]);
#if PROFILE
hldexp_stop = get_cycle_counter();
hldexp_total = hldexp_total + hldexp_stop - hldexp_start;
#endif
mu[kappa][k] = mu[kappa][k] - rtmp;
}
}
}
}
}
}
if (test) /* Anything happened? */
{
#if PROFILE
hconvert_start = get_cycle_counter();
#endif
expo[kappa] = _F_mpz_vec_to_d_vec_2exp(appB[kappa], B->rows[kappa], n);
#if PROFILE
hconvert_stop = get_cycle_counter();
hconvert_total = hconvert_total + hconvert_stop - hconvert_start;
#endif
aa = zeros + 1;
for (i = zeros + 1; i <= kappa; i++)
appSP[kappa][i] = NAN;//0.0/0.0;
for (i = kappa + 1; i <= kappamax; i++)
appSP[i][kappa] = NAN;//0.0/0.0;
}
} while (test);
if (appSP[kappa][kappa] != appSP[kappa][kappa])
{
// ### This is different -------
#if PROFILE
hinner_start = get_cycle_counter();
#endif
appSP[kappa][kappa] = _d_vec_norm(appB[kappa], n);
#if PROFILE
hinner_stop = get_cycle_counter();
hinner_total = hinner_total + hinner_stop - hinner_start;
#endif
}
s[zeros + 1] = appSP[kappa][kappa];
for (k = zeros + 1; k < kappa - 1; k++)
{
tmp = mu[kappa][k] * r[kappa][k];
s[k+1] = s[k] - tmp;
}
return 0;
}
/* The mpfr version of check_Babai_heuristic_d, also inherits some temp variables.*/
int check_Babai_heuristic(int kappa, F_mpz_mat_t B, __mpfr_struct **mu, __mpfr_struct **r, __mpfr_struct *s,
__mpfr_struct **appB, __mpfr_struct **appSP,
int a, int zeros, int kappamax, int n, mpfr_t tmp, mpfr_t rtmp, mp_prec_t prec)
{
int i, j, k, test, aa, exponent;
signed long xx;
F_mpz_t ztmp, X;
F_mpz_init(ztmp);
F_mpz_init(X);
aa = (a > zeros) ? a : zeros + 1;
ctt = (4*DELTA + 1)/5;
halfplus = (4*ETA + .5)/5 ;
onedothalfplus = 1.0+halfplus;
long loops = 0;
do
{
test = 0;
loops++;
if (loops > 20)
return -1;
/* ************************************** */
/* Step2: compute the GSO for stage kappa */
/* ************************************** */
for (j = aa; j < kappa; j++)
{
if ( mpfr_nan_p(appSP[kappa] + j) ) // if appSP[kappa] + j == NAN
{
if (!(_mpfr_vec_scalar_product2(appSP[kappa] + j, appB[kappa], appB[j], n, prec) ) ){
//In this case a heuristic told us that some cancelation probably happened so we just compute the scalar product at full precision
_F_mpz_vec_scalar_product(ztmp, B->rows[kappa], B->rows[j], n);
F_mpz_get_mpfr(appSP[kappa] + j, ztmp);
}
}
if (j > zeros + 2)
{
mpfr_mul(tmp, mu[j] + zeros + 1, r[kappa] + zeros + 1, GMP_RNDN);
mpfr_sub(rtmp, appSP[kappa] + j, tmp, GMP_RNDN);
for (k = zeros + 2; k < j - 1; k++)
{
mpfr_mul(tmp, mu[j] + k, r[kappa] + k, GMP_RNDN);
mpfr_sub(rtmp, rtmp, tmp, GMP_RNDN);
}
mpfr_mul(tmp, mu[j] + j - 1, r[kappa] + j - 1, GMP_RNDN);
mpfr_sub(r[kappa] + j, rtmp, tmp, GMP_RNDN);
} else if (j == zeros+2)
{
mpfr_mul(tmp, mu[j] + zeros + 1, r[kappa] + zeros + 1, GMP_RNDN);
mpfr_sub(r[kappa] + j, appSP[kappa] + j, tmp, GMP_RNDN);
} else mpfr_set(r[kappa] + j, appSP[kappa] + j, GMP_RNDN);
mpfr_div(mu[kappa] + j, r[kappa] + j, r[j] + j, GMP_RNDN);
}
/* **************************** */
/* Step3--5: compute the X_j's */
/* **************************** */
for (j = kappa - 1; j > zeros; j--)
{
/* test of the relaxed size-reduction condition */
mpfr_abs(tmp, mu[kappa] + j, GMP_RNDN);
if (mpfr_cmp_d(tmp, halfplus) > 0)
{
test = 1;
/* we consider separately the cases X = +-1 */
if (mpfr_cmp_d(tmp, onedothalfplus) <= 0)
{
int sgn = mpfr_sgn(mu[kappa] + j);
if (sgn >= 0) /* in this case, X is 1 */
{
for (k = zeros + 1; k < j; k++)
{
mpfr_sub(mu[kappa] + k, mu[kappa] + k, mu[j] + k, GMP_RNDN);
}
_F_mpz_vec_sub(B->rows[kappa], B->rows[kappa], B->rows[j], n);
} else /* otherwise X is -1 */
{
for (k=zeros+1; k<j; k++)
{
mpfr_add(mu[kappa] + k, mu[kappa] + k, mu[j] + k, GMP_RNDN);
}
_F_mpz_vec_add(B->rows[kappa], B->rows[kappa], B->rows[j], n);
}
} else /* we must have |X| >= 2 */
{
mpfr_round(tmp, mu[kappa] + j);
for (k = zeros + 1; k < j; k++)
{
mpfr_mul(rtmp, tmp, mu[j] + k, GMP_RNDN);
mpfr_sub(mu[kappa] + k, mu[kappa] + k, rtmp, GMP_RNDN);
}
if (mpfr_get_exp(tmp) < CPU_SIZE_1 - 2)
{
/* X is stored in a long signed int */
xx = mpfr_get_si(tmp, GMP_RNDN);
if (xx > 0L)
{
_F_mpz_vec_submul_ui(B->rows[kappa], B->rows[j], n, (ulong) xx);
} else
{
_F_mpz_vec_addmul_ui(B->rows[kappa], B->rows[j], n, (ulong) -xx);
}
} else
{
exponent = F_mpz_set_mpfr_2exp(ztmp, tmp);
if (exponent <= 0)
{
F_mpz_div_2exp(ztmp, ztmp, -exponent);
_F_mpz_vec_submul_F_mpz(B->rows[kappa], B->rows[j], n, ztmp);
} else
{
_F_mpz_vec_submul_2exp_F_mpz(B->rows[kappa], B->rows[j], n, ztmp, exponent);
}
}
}
}
}
if (test) /* Anything happened? */
{
_F_mpz_vec_to_mpfr_vec(appB[kappa], B->rows[kappa], n);
aa = zeros + 1;
for (i = zeros + 1; i <= kappa; i++)
mpfr_set_nan(appSP[kappa] + i);//0.0/0.0;
for (i = kappa + 1; i <= kappamax; i++)
mpfr_set_nan(appSP[i] + kappa);//0.0/0.0;
}
} while (test);
if (mpfr_nan_p(appSP[kappa] + kappa))
{
_mpfr_vec_norm2(appSP[kappa] + kappa, appB[kappa], n, prec);
}
mpfr_set(s + zeros + 1, appSP[kappa] + kappa, GMP_RNDN);
for (k = zeros + 1; k < kappa - 1; k++)
{
mpfr_mul( tmp, mu[kappa] + k, r[kappa] + k, GMP_RNDN);
mpfr_sub( s + k + 1, s + k, tmp, GMP_RNDN);
}
mpfr_set(r[kappa] + kappa, s + kappa - 1, GMP_RNDN);
F_mpz_clear(ztmp);
F_mpz_clear(X);
return 0;
}
/*
takes the scalar product of two dpe vectors with the same exponents by entry,
mantissas in vec1 and vec2, n entries to be considered, while cexpo holds the
exponents.
*/
double d_2exp_vec_scalar_product(double * vec1, double * vec2, int n, int *cexpo)
{
double sum;
sum = vec1[0] * vec2[0];
for (long i = 1; i < n; i++)
sum += ldexp(vec1[i] * vec2[i], 2*cexpo[i]);
return sum;
}
/* same as above but returning the square of the l_2 norm of a single vector */
double d_2exp_vec_norm(double * vec, int n, int *cexpo)
{
double sum;
sum = vec[0] * vec[0];