void
my__gmpn_tdiv_qr (mp_ptr qp, mp_ptr rp, mp_size_t qxn,
mp_srcptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn)
{
ASSERT_ALWAYS (qxn == 0);
ASSERT (nn >= 0);
ASSERT (dn >= 0);
ASSERT (dn == 0 || dp[dn - 1] != 0);
ASSERT (! MPN_OVERLAP_P (qp, nn - dn + 1 + qxn, np, nn));
ASSERT (! MPN_OVERLAP_P (qp, nn - dn + 1 + qxn, dp, dn));
int adjust;
gmp_pi1_t dinv;
TMP_DECL;
TMP_MARK;
/* conservative tests for quotient size */
adjust = np[nn - 1] >= dp[dn - 1];
mp_ptr n2p, d2p;
mp_limb_t cy;
int cnt;
qp[nn - dn] = 0; /* zero high quotient limb */
count_leading_zeros (cnt, dp[dn - 1]);
cnt -= GMP_NAIL_BITS;
d2p = TMP_ALLOC_LIMBS (dn);
mpn_lshift (d2p, dp, dn, cnt);
for (int i=0; i<dn; i+=1)
{
printf("d2p %08x\n", *( (int*) (((void*)(d2p))+(i*4))));
}
n2p = TMP_ALLOC_LIMBS (nn + 1);
cy = mpn_lshift (n2p, np, nn, cnt);
for (int i=0; i<nn; i+=1)
{
printf("n2p %08x\n", *( (int*) (((void*)(n2p))+(i*4))));
}
n2p[nn] = cy;
nn += adjust;
printf("d2p[dn-1] = %08lx\nd2p[dn-2] = %08lx\n", d2p[dn-1], d2p[dn-2]);
invert_pi1 (dinv, d2p[dn - 1], d2p[dn - 2]);
printf("dinv %08lx\n", dinv.inv32);
my_mpn_sbpi1_div_qr (qp, n2p, nn, d2p, dn, dinv.inv32);
for (int i=0; i<nn; i+=1)
{
printf("inside qp %08x\n", *( (int*) (((void*)(qp))+(i*4))));
}
n2p[nn] = cy;
mpn_rshift (rp, n2p, dn, cnt);
TMP_FREE;
return;
}
int main() {
gmp_pi1_t a;
unsigned long in[] = {0x7c2e09b7,0x847c9b5d};
invert_pi1(a, in[1], in[0]);
printf("%08lx\n", a.inv32);
return 0;
}
void
mpn_invert (mp_ptr ip, mp_srcptr dp, mp_size_t n, mp_ptr scratch)
{
ASSERT (n > 0);
ASSERT (dp[n-1] & GMP_NUMB_HIGHBIT);
ASSERT (! MPN_OVERLAP_P (ip, n, dp, n));
ASSERT (! MPN_OVERLAP_P (ip, n, scratch, mpn_invertappr_itch(n)));
ASSERT (! MPN_OVERLAP_P (dp, n, scratch, mpn_invertappr_itch(n)));
if (n == 1)
invert_limb (*ip, *dp);
else if (BELOW_THRESHOLD (n, INV_APPR_THRESHOLD))
{
/* Maximum scratch needed by this branch: 2*n */
mp_size_t i;
mp_ptr xp;
xp = scratch; /* 2 * n limbs */
/* n > 1 here */
i = n;
do
xp[--i] = GMP_NUMB_MAX;
while (i);
mpn_com (xp + n, dp, n);
if (n == 2) {
mpn_divrem_2 (ip, 0, xp, 4, dp);
} else {
gmp_pi1_t inv;
invert_pi1 (inv, dp[n-1], dp[n-2]);
/* FIXME: should we use dcpi1_div_q, for big sizes? */
mpn_sbpi1_div_q (ip, xp, 2 * n, dp, n, inv.inv32);
}
}
else { /* Use approximated inverse; correct the result if needed. */
mp_limb_t e; /* The possible error in the approximate inverse */
ASSERT ( mpn_invert_itch (n) >= mpn_invertappr_itch (n) );
e = mpn_ni_invertappr (ip, dp, n, scratch);
if (UNLIKELY (e)) { /* Assume the error can only be "0" (no error) or "1". */
/* Code to detect and correct the "off by one" approximation. */
mpn_mul_n (scratch, ip, dp, n);
e = mpn_add_n (scratch, scratch, dp, n); /* FIXME: we only need e.*/
if (LIKELY(e)) /* The high part can not give a carry by itself. */
e = mpn_add_nc (scratch + n, scratch + n, dp, n, e); /* FIXME:e */
/* If the value was wrong (no carry), correct it (increment). */
e ^= CNST_LIMB (1);
MPN_INCR_U (ip, n, e);
}
}
}
void
mpn_invert (mp_ptr ip, mp_srcptr dp, mp_size_t n, mp_ptr scratch)
{
ASSERT (n > 0);
ASSERT (dp[n-1] & GMP_NUMB_HIGHBIT);
ASSERT (! MPN_OVERLAP_P (ip, n, dp, n));
ASSERT (! MPN_OVERLAP_P (ip, n, scratch, mpn_invertappr_itch(n)));
ASSERT (! MPN_OVERLAP_P (dp, n, scratch, mpn_invertappr_itch(n)));
if (n == 1)
invert_limb (*ip, *dp);
else {
TMP_DECL;
TMP_MARK;
if (BELOW_THRESHOLD (n, INV_APPR_THRESHOLD))
{
/* Maximum scratch needed by this branch: 2*n */
mp_size_t i;
mp_ptr xp;
xp = scratch; /* 2 * n limbs */
for (i = n - 1; i >= 0; i--)
xp[i] = GMP_NUMB_MAX;
mpn_com (xp + n, dp, n);
if (n == 2) {
mpn_divrem_2 (ip, 0, xp, 4, dp);
} else {
gmp_pi1_t inv;
invert_pi1 (inv, dp[n-1], dp[n-2]);
/* FIXME: should we use dcpi1_div_q, for big sizes? */
mpn_sbpi1_div_q (ip, xp, 2 * n, dp, n, inv.inv32);
}
}
else { /* Use approximated inverse; correct the result if needed. */
mp_limb_t e; /* The possible error in the approximate inverse */
ASSERT ( mpn_invert_itch (n) >= mpn_invertappr_itch (n) );
e = mpn_ni_invertappr (ip, dp, n, scratch);
if (UNLIKELY (e)) { /* Assume the error can only be "0" (no error) or "1". */
/* Code to detect and correct the "off by one" approximation. */
mpn_mul_n (scratch, ip, dp, n);
ASSERT_NOCARRY (mpn_add_n (scratch + n, scratch + n, dp, n));
if (! mpn_add (scratch, scratch, 2*n, dp, n))
MPN_INCR_U (ip, n, 1); /* The value was wrong, correct it. */
}
}
TMP_FREE;
}
}
mp_limb_t
mpfr_divhigh_n (mpfr_limb_ptr qp, mpfr_limb_ptr np, mpfr_limb_ptr dp,
mp_size_t n)
{
mp_size_t k, l;
mp_limb_t qh, cy;
mpfr_limb_ptr tp;
MPFR_TMP_DECL(marker);
MPFR_ASSERTN (MPFR_MULHIGH_TAB_SIZE >= 15); /* so that 2*(n/3) >= (n+4)/2 */
k = MPFR_LIKELY (n < MPFR_DIVHIGH_TAB_SIZE) ? divhigh_ktab[n] : 2*(n/3);
if (k == 0)
#if defined(WANT_GMP_INTERNALS) && defined(HAVE___GMPN_SBPI1_DIVAPPR_Q)
{
mpfr_pi1_t dinv2;
invert_pi1 (dinv2, dp[n - 1], dp[n - 2]);
return __gmpn_sbpi1_divappr_q (qp, np, n + n, dp, n, dinv2.inv32);
}
#else /* use our own code for base-case short division */
return mpfr_divhigh_n_basecase (qp, np, dp, n);
#endif
else if (k == n)
/* Put in Q={qp, n} an approximation of N={np, 2*n} divided by D={dp, n},
with the most significant limb of the quotient as return value (0 or 1).
Assumes the most significant bit of D is set. Clobbers N.
The approximate quotient Q satisfies - 2(n-1) < N/D - Q <= 4.
*/
static mp_limb_t
mpfr_divhigh_n_basecase (mpfr_limb_ptr qp, mpfr_limb_ptr np,
mpfr_limb_srcptr dp, mp_size_t n)
{
mp_limb_t qh, d1, d0, dinv, q2, q1, q0;
mpfr_pi1_t dinv2;
np += n;
if ((qh = (mpn_cmp (np, dp, n) >= 0)))
mpn_sub_n (np, np, dp, n);
/* now {np, n} is less than D={dp, n}, which implies np[n-1] <= dp[n-1] */
d1 = dp[n - 1];
if (n == 1)
{
invert_limb (dinv, d1);
umul_ppmm (q1, q0, np[0], dinv);
qp[0] = np[0] + q1;
return qh;
}
/* now n >= 2 */
d0 = dp[n - 2];
invert_pi1 (dinv2, d1, d0);
/* dinv2.inv32 = floor ((B^3 - 1) / (d0 + d1 B)) - B */
while (n > 1)
{
/* Invariant: it remains to reduce n limbs from N (in addition to the
initial low n limbs).
Since n >= 2 here, necessarily we had n >= 2 initially, which means
that in addition to the limb np[n-1] to reduce, we have at least 2
extra limbs, thus accessing np[n-3] is valid. */
/* warning: we can have np[n-1]=d1 and np[n-2]=d0, but since {np,n} < D,
the largest possible partial quotient is B-1 */
if (MPFR_UNLIKELY(np[n - 1] == d1 && np[n - 2] == d0))
q2 = ~ (mp_limb_t) 0;
else
udiv_qr_3by2 (q2, q1, q0, np[n - 1], np[n - 2], np[n - 3],
d1, d0, dinv2.inv32);
/* since q2 = floor((np[n-1]*B^2+np[n-2]*B+np[n-3])/(d1*B+d0)),
we have q2 <= (np[n-1]*B^2+np[n-2]*B+np[n-3])/(d1*B+d0),
thus np[n-1]*B^2+np[n-2]*B+np[n-3] >= q2*(d1*B+d0)
and {np-1, n} >= q2*D - q2*B^(n-2) >= q2*D - B^(n-1)
thus {np-1, n} - (q2-1)*D >= D - B^(n-1) >= 0
which proves that at most one correction is needed */
q0 = mpn_submul_1 (np - 1, dp, n, q2);
if (MPFR_UNLIKELY(q0 > np[n - 1]))
{
mpn_add_n (np - 1, np - 1, dp, n);
q2 --;
}
qp[--n] = q2;
dp ++;
}
/* we have B+dinv2 = floor((B^3-1)/(d1*B+d0)) < B^2/d1
q1 = floor(np[0]*(B+dinv2)/B) <= floor(np[0]*B/d1)
<= floor((np[0]*B+np[1])/d1)
thus q1 is not larger than the true quotient.
q1 > np[0]*(B+dinv2)/B - 1 > np[0]*(B^3-1)/(d1*B+d0)/B - 2
For d1*B+d0 <> B^2/2, we have B+dinv2 = floor(B^3/(d1*B+d0))
thus q1 > np[0]*B^2/(d1*B+d0) - 2, i.e.,
(d1*B+d0)*q1 > np[0]*B^2 - 2*(d1*B+d0)
d1*B*q1 > np[0]*B^2 - 2*d1*B - 2*d0 - d0*q1 >= np[0]*B^2 - 2*d1*B - B^2
thus q1 > np[0]*B/d1 - 2 - B/d1 > np[0]*B/d1 - 4.
For d1*B+d0 = B^2/2, dinv2 = B-1 thus q1 > np[0]*(2B-1)/B - 1 >
np[0]*B/d1 - 2.
In all cases, if q = floor((np[0]*B+np[1])/d1), we have:
q - 4 <= q1 <= q
*/
umul_ppmm (q1, q0, np[0], dinv2.inv32);
qp[0] = np[0] + q1;
return qh;
}
int
main (int argc, char **argv)
{
gmp_randstate_ptr rands;
unsigned long maxnbits, maxdbits, nbits, dbits;
mpz_t n, d, q, r, tz, junk;
mp_size_t maxnn, maxdn, nn, dn, clearn, i;
mp_ptr np, dup, dnp, qp, rp, junkp;
mp_limb_t t;
gmp_pi1_t dinv;
long count = COUNT;
mp_ptr scratch;
mp_limb_t ran;
mp_size_t alloc, itch;
mp_limb_t rran0, rran1, qran0, qran1;
TMP_DECL;
if (argc > 1)
{
char *end;
count = strtol (argv[1], &end, 0);
if (*end || count <= 0)
{
fprintf (stderr, "Invalid test count: %s.\n", argv[1]);
return 1;
}
}
maxdbits = MAX_DN;
maxnbits = MAX_NN;
tests_start ();
rands = RANDS;
mpz_init (n);
mpz_init (d);
mpz_init (q);
mpz_init (r);
mpz_init (tz);
mpz_init (junk);
maxnn = maxnbits / GMP_NUMB_BITS + 1;
maxdn = maxdbits / GMP_NUMB_BITS + 1;
TMP_MARK;
qp = TMP_ALLOC_LIMBS (maxnn + 2) + 1;
rp = TMP_ALLOC_LIMBS (maxnn + 2) + 1;
dnp = TMP_ALLOC_LIMBS (maxdn);
alloc = 1;
scratch = __GMP_ALLOCATE_FUNC_LIMBS (alloc);
for (test = -300; test < count; test++)
{
nbits = random_word (rands) % (maxnbits - GMP_NUMB_BITS) + 2 * GMP_NUMB_BITS;
if (test < 0)
dbits = (test + 300) % (nbits - 1) + 1;
else
dbits = random_word (rands) % (nbits - 1) % maxdbits + 1;
#if RAND_UNIFORM
#define RANDFUNC mpz_urandomb
#else
#define RANDFUNC mpz_rrandomb
#endif
do
RANDFUNC (d, rands, dbits);
while (mpz_sgn (d) == 0);
dn = SIZ (d);
dup = PTR (d);
MPN_COPY (dnp, dup, dn);
dnp[dn - 1] |= GMP_NUMB_HIGHBIT;
if (test % 2 == 0)
{
RANDFUNC (n, rands, nbits);
nn = SIZ (n);
ASSERT_ALWAYS (nn >= dn);
}
else
{
do
{
RANDFUNC (q, rands, random_word (rands) % (nbits - dbits + 1));
RANDFUNC (r, rands, random_word (rands) % mpz_sizeinbase (d, 2));
mpz_mul (n, q, d);
mpz_add (n, n, r);
nn = SIZ (n);
}
while (nn > maxnn || nn < dn);
}
ASSERT_ALWAYS (nn <= maxnn);
ASSERT_ALWAYS (dn <= maxdn);
mpz_urandomb (junk, rands, nbits);
junkp = PTR (junk);
np = PTR (n);
mpz_urandomb (tz, rands, 32);
t = mpz_get_ui (tz);
if (t % 17 == 0)
{
dnp[dn - 1] = GMP_NUMB_MAX;
dup[dn - 1] = GMP_NUMB_MAX;
}
switch ((int) t % 16)
{
case 0:
clearn = random_word (rands) % nn;
for (i = clearn; i < nn; i++)
np[i] = 0;
break;
case 1:
mpn_sub_1 (np + nn - dn, dnp, dn, random_word (rands));
break;
case 2:
mpn_add_1 (np + nn - dn, dnp, dn, random_word (rands));
break;
}
if (dn >= 2)
invert_pi1 (dinv, dnp[dn - 1], dnp[dn - 2]);
rran0 = random_word (rands);
rran1 = random_word (rands);
qran0 = random_word (rands);
qran1 = random_word (rands);
qp[-1] = qran0;
qp[nn - dn + 1] = qran1;
rp[-1] = rran0;
ran = random_word (rands);
if ((double) (nn - dn) * dn < 1e5)
{
/* Test mpn_sbpi1_div_qr */
if (dn > 2)
{
MPN_COPY (rp, np, nn);
if (nn > dn)
MPN_COPY (qp, junkp, nn - dn);
qp[nn - dn] = mpn_sbpi1_div_qr (qp, rp, nn, dnp, dn, dinv.inv32);
check_one (qp, rp, np, nn, dnp, dn, "mpn_sbpi1_div_qr", 0);
}
/* Test mpn_sbpi1_divappr_q */
if (dn > 2)
{
MPN_COPY (rp, np, nn);
if (nn > dn)
MPN_COPY (qp, junkp, nn - dn);
qp[nn - dn] = mpn_sbpi1_divappr_q (qp, rp, nn, dnp, dn, dinv.inv32);
check_one (qp, NULL, np, nn, dnp, dn, "mpn_sbpi1_divappr_q", 1);
}
/* Test mpn_sbpi1_div_q */
if (dn > 2)
{
MPN_COPY (rp, np, nn);
if (nn > dn)
MPN_COPY (qp, junkp, nn - dn);
qp[nn - dn] = mpn_sbpi1_div_q (qp, rp, nn, dnp, dn, dinv.inv32);
check_one (qp, NULL, np, nn, dnp, dn, "mpn_sbpi1_div_q", 0);
}
/* Test mpn_sb_div_qr_sec */
itch = 3 * nn + 4;
if (itch + 1 > alloc)
{
scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
alloc = itch + 1;
}
scratch[itch] = ran;
MPN_COPY (rp, np, nn);
if (nn >= dn)
MPN_COPY (qp, junkp, nn - dn + 1);
mpn_sb_div_qr_sec (qp, rp, nn, dup, dn, scratch);
ASSERT_ALWAYS (ran == scratch[itch]);
check_one (qp, rp, np, nn, dup, dn, "mpn_sb_div_qr_sec", 0);
/* Test mpn_sb_div_r_sec */
itch = nn + 2 * dn + 2;
if (itch + 1 > alloc)
{
scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
alloc = itch + 1;
}
scratch[itch] = ran;
MPN_COPY (rp, np, nn);
mpn_sb_div_r_sec (rp, nn, dup, dn, scratch);
ASSERT_ALWAYS (ran == scratch[itch]);
/* Note: Since check_one cannot cope with random-only functions, we
pass qp[] from the previous function, mpn_sb_div_qr_sec. */
check_one (qp, rp, np, nn, dup, dn, "mpn_sb_div_r_sec", 0);
}
/* Test mpn_dcpi1_div_qr */
if (dn >= 6 && nn - dn >= 3)
{
MPN_COPY (rp, np, nn);
if (nn > dn)
MPN_COPY (qp, junkp, nn - dn);
qp[nn - dn] = mpn_dcpi1_div_qr (qp, rp, nn, dnp, dn, &dinv);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0);
check_one (qp, rp, np, nn, dnp, dn, "mpn_dcpi1_div_qr", 0);
}
/* Test mpn_dcpi1_divappr_q */
if (dn >= 6 && nn - dn >= 3)
{
MPN_COPY (rp, np, nn);
if (nn > dn)
MPN_COPY (qp, junkp, nn - dn);
qp[nn - dn] = mpn_dcpi1_divappr_q (qp, rp, nn, dnp, dn, &dinv);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0);
check_one (qp, NULL, np, nn, dnp, dn, "mpn_dcpi1_divappr_q", 1);
}
/* Test mpn_dcpi1_div_q */
if (dn >= 6 && nn - dn >= 3)
{
MPN_COPY (rp, np, nn);
if (nn > dn)
MPN_COPY (qp, junkp, nn - dn);
qp[nn - dn] = mpn_dcpi1_div_q (qp, rp, nn, dnp, dn, &dinv);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0);
check_one (qp, NULL, np, nn, dnp, dn, "mpn_dcpi1_div_q", 0);
}
/* Test mpn_mu_div_qr */
if (nn - dn > 2 && dn >= 2)
{
itch = mpn_mu_div_qr_itch (nn, dn, 0);
if (itch + 1 > alloc)
{
scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
alloc = itch + 1;
}
scratch[itch] = ran;
MPN_COPY (qp, junkp, nn - dn);
MPN_ZERO (rp, dn);
rp[dn] = rran1;
qp[nn - dn] = mpn_mu_div_qr (qp, rp, np, nn, dnp, dn, scratch);
ASSERT_ALWAYS (ran == scratch[itch]);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
ASSERT_ALWAYS (rp[-1] == rran0); ASSERT_ALWAYS (rp[dn] == rran1);
check_one (qp, rp, np, nn, dnp, dn, "mpn_mu_div_qr", 0);
}
/* Test mpn_mu_divappr_q */
if (nn - dn > 2 && dn >= 2)
{
itch = mpn_mu_divappr_q_itch (nn, dn, 0);
if (itch + 1 > alloc)
{
scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
alloc = itch + 1;
}
scratch[itch] = ran;
MPN_COPY (qp, junkp, nn - dn);
qp[nn - dn] = mpn_mu_divappr_q (qp, np, nn, dnp, dn, scratch);
ASSERT_ALWAYS (ran == scratch[itch]);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
check_one (qp, NULL, np, nn, dnp, dn, "mpn_mu_divappr_q", 4);
}
/* Test mpn_mu_div_q */
if (nn - dn > 2 && dn >= 2)
{
itch = mpn_mu_div_q_itch (nn, dn, 0);
if (itch + 1> alloc)
{
scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
alloc = itch + 1;
}
scratch[itch] = ran;
MPN_COPY (qp, junkp, nn - dn);
qp[nn - dn] = mpn_mu_div_q (qp, np, nn, dnp, dn, scratch);
ASSERT_ALWAYS (ran == scratch[itch]);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
check_one (qp, NULL, np, nn, dnp, dn, "mpn_mu_div_q", 0);
}
if (1)
{
itch = nn + 1;
if (itch + 1> alloc)
{
scratch = __GMP_REALLOCATE_FUNC_LIMBS (scratch, alloc, itch + 1);
alloc = itch + 1;
}
scratch[itch] = ran;
mpn_div_q (qp, np, nn, dup, dn, scratch);
ASSERT_ALWAYS (ran == scratch[itch]);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - dn + 1] == qran1);
check_one (qp, NULL, np, nn, dup, dn, "mpn_div_q", 0);
}
if (dn >= 2 && nn >= 2)
{
mp_limb_t qh;
/* mpn_divrem_2 */
MPN_COPY (rp, np, nn);
qp[nn - 2] = qp[nn-1] = qran1;
qh = mpn_divrem_2 (qp, 0, rp, nn, dnp + dn - 2);
ASSERT_ALWAYS (qp[nn - 2] == qran1);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - 1] == qran1);
qp[nn - 2] = qh;
check_one (qp, rp, np, nn, dnp + dn - 2, 2, "mpn_divrem_2", 0);
/* Missing: divrem_2 with fraction limbs. */
/* mpn_div_qr_2 */
qp[nn - 2] = qran1;
qh = mpn_div_qr_2 (qp, rp, np, nn, dup + dn - 2);
ASSERT_ALWAYS (qp[nn - 2] == qran1);
ASSERT_ALWAYS (qp[-1] == qran0); ASSERT_ALWAYS (qp[nn - 1] == qran1);
qp[nn - 2] = qh;
check_one (qp, rp, np, nn, dup + dn - 2, 2, "mpn_div_qr_2", 0);
}
}
__GMP_FREE_FUNC_LIMBS (scratch, alloc);
TMP_FREE;
mpz_clear (n);
mpz_clear (d);
mpz_clear (q);
mpz_clear (r);
mpz_clear (tz);
mpz_clear (junk);
tests_end ();
return 0;
}
void
mpz_powm_ui (mpz_ptr r, mpz_srcptr b, unsigned long int el, mpz_srcptr m)
{
if (el < 20)
{
mp_ptr xp, tp, mp, bp, scratch;
mp_size_t xn, tn, mn, bn;
int m_zero_cnt;
int c;
mp_limb_t e, m2;
gmp_pi1_t dinv;
TMP_DECL;
mp = PTR(m);
mn = ABSIZ(m);
if (UNLIKELY (mn == 0))
DIVIDE_BY_ZERO;
if (el == 0)
{
/* Exponent is zero, result is 1 mod M, i.e., 1 or 0 depending on if
M equals 1. */
SIZ(r) = (mn == 1 && mp[0] == 1) ? 0 : 1;
PTR(r)[0] = 1;
return;
}
TMP_MARK;
/* Normalize m (i.e. make its most significant bit set) as required by
division functions below. */
count_leading_zeros (m_zero_cnt, mp[mn - 1]);
m_zero_cnt -= GMP_NAIL_BITS;
if (m_zero_cnt != 0)
{
mp_ptr new_mp = TMP_ALLOC_LIMBS (mn);
mpn_lshift (new_mp, mp, mn, m_zero_cnt);
mp = new_mp;
}
m2 = mn == 1 ? 0 : mp[mn - 2];
invert_pi1 (dinv, mp[mn - 1], m2);
bn = ABSIZ(b);
bp = PTR(b);
if (bn > mn)
{
/* Reduce possibly huge base. Use a function call to reduce, since we
don't want the quotient allocation to live until function return. */
mp_ptr new_bp = TMP_ALLOC_LIMBS (mn);
reduce (new_bp, bp, bn, mp, mn, &dinv);
bp = new_bp;
bn = mn;
/* Canonicalize the base, since we are potentially going to multiply with
it quite a few times. */
MPN_NORMALIZE (bp, bn);
}
if (bn == 0)
{
SIZ(r) = 0;
TMP_FREE;
return;
}
tp = TMP_ALLOC_LIMBS (2 * mn + 1);
xp = TMP_ALLOC_LIMBS (mn);
scratch = TMP_ALLOC_LIMBS (mn + 1);
MPN_COPY (xp, bp, bn);
xn = bn;
e = el;
count_leading_zeros (c, e);
e = (e << c) << 1; /* shift the exp bits to the left, lose msb */
c = GMP_LIMB_BITS - 1 - c;
if (c == 0)
{
/* If m is already normalized (high bit of high limb set), and b is
the same size, but a bigger value, and e==1, then there's no
modular reductions done and we can end up with a result out of
range at the end. */
if (xn == mn && mpn_cmp (xp, mp, mn) >= 0)
mpn_sub_n (xp, xp, mp, mn);
}
else
{
/* Main loop. */
do
{
mpn_sqr (tp, xp, xn);
tn = 2 * xn; tn -= tp[tn - 1] == 0;
if (tn < mn)
{
MPN_COPY (xp, tp, tn);
xn = tn;
}
else
{
mod (tp, tn, mp, mn, &dinv, scratch);
MPN_COPY (xp, tp, mn);
xn = mn;
}
if ((mp_limb_signed_t) e < 0)
{
mpn_mul (tp, xp, xn, bp, bn);
tn = xn + bn; tn -= tp[tn - 1] == 0;
if (tn < mn)
{
MPN_COPY (xp, tp, tn);
xn = tn;
}
else
{
mod (tp, tn, mp, mn, &dinv, scratch);
MPN_COPY (xp, tp, mn);
xn = mn;
}
}
e <<= 1;
c--;
}
while (c != 0);
}
/* We shifted m left m_zero_cnt steps. Adjust the result by reducing it
with the original M. */
if (m_zero_cnt != 0)
{
mp_limb_t cy;
cy = mpn_lshift (tp, xp, xn, m_zero_cnt);
tp[xn] = cy; xn += cy != 0;
if (xn < mn)
{
MPN_COPY (xp, tp, xn);
}
else
{
mod (tp, xn, mp, mn, &dinv, scratch);
MPN_COPY (xp, tp, mn);
xn = mn;
}
mpn_rshift (xp, xp, xn, m_zero_cnt);
}
MPN_NORMALIZE (xp, xn);
if ((el & 1) != 0 && SIZ(b) < 0 && xn != 0)
{
mp = PTR(m); /* want original, unnormalized m */
mpn_sub (xp, mp, mn, xp, xn);
xn = mn;
MPN_NORMALIZE (xp, xn);
}
MPZ_REALLOC (r, xn);
SIZ (r) = xn;
MPN_COPY (PTR(r), xp, xn);
TMP_FREE;
}
else
{
/* For large exponents, fake a mpz_t exponent and deflect to the more
sophisticated mpz_powm. */
mpz_t e;
mp_limb_t ep[LIMBS_PER_ULONG];
MPZ_FAKE_UI (e, ep, el);
mpz_powm (r, b, e, m);
}
}
void
mpn_div_q (mp_ptr qp,
mp_srcptr np, mp_size_t nn,
mp_srcptr dp, mp_size_t dn, mp_ptr scratch)
{
mp_ptr new_dp, new_np, tp, rp;
mp_limb_t cy, dh, qh;
mp_size_t new_nn, qn;
gmp_pi1_t dinv;
int cnt;
TMP_DECL;
TMP_MARK;
ASSERT (nn >= dn);
ASSERT (dn > 0);
ASSERT (dp[dn - 1] != 0);
ASSERT (! MPN_OVERLAP_P (qp, nn - dn + 1, np, nn));
ASSERT (! MPN_OVERLAP_P (qp, nn - dn + 1, dp, dn));
ASSERT (MPN_SAME_OR_SEPARATE_P (np, scratch, nn));
ASSERT_ALWAYS (FUDGE >= 2);
if (dn == 1)
{
mpn_divrem_1 (qp, 0L, np, nn, dp[dn - 1]);
return;
}
qn = nn - dn + 1; /* Quotient size, high limb might be zero */
if (qn + FUDGE >= dn)
{
/* |________________________|
|_______| */
new_np = scratch;
dh = dp[dn - 1];
if (LIKELY ((dh & GMP_NUMB_HIGHBIT) == 0))
{
count_leading_zeros (cnt, dh);
cy = mpn_lshift (new_np, np, nn, cnt);
new_np[nn] = cy;
new_nn = nn + (cy != 0);
new_dp = TMP_ALLOC_LIMBS (dn);
mpn_lshift (new_dp, dp, dn, cnt);
if (dn == 2)
{
qh = mpn_divrem_2 (qp, 0L, new_np, new_nn, new_dp);
}
else if (BELOW_THRESHOLD (dn, DC_DIV_Q_THRESHOLD) ||
BELOW_THRESHOLD (new_nn - dn, DC_DIV_Q_THRESHOLD))
{
invert_pi1 (dinv, new_dp[dn - 1], new_dp[dn - 2]);
qh = mpn_sbpi1_div_q (qp, new_np, new_nn, new_dp, dn, dinv.inv32);
}
else if (BELOW_THRESHOLD (dn, MUPI_DIV_Q_THRESHOLD) || /* fast condition */
BELOW_THRESHOLD (nn, 2 * MU_DIV_Q_THRESHOLD) || /* fast condition */
(double) (2 * (MU_DIV_Q_THRESHOLD - MUPI_DIV_Q_THRESHOLD)) * dn /* slow... */
+ (double) MUPI_DIV_Q_THRESHOLD * nn > (double) dn * nn) /* ...condition */
{
invert_pi1 (dinv, new_dp[dn - 1], new_dp[dn - 2]);
qh = mpn_dcpi1_div_q (qp, new_np, new_nn, new_dp, dn, &dinv);
}
else
{
mp_size_t itch = mpn_mu_div_q_itch (new_nn, dn, 0);
mp_ptr scratch = TMP_ALLOC_LIMBS (itch);
qh = mpn_mu_div_q (qp, new_np, new_nn, new_dp, dn, scratch);
}
if (cy == 0)
qp[qn - 1] = qh;
else if (UNLIKELY (qh != 0))
{
/* This happens only when the quotient is close to B^n and
mpn_*_divappr_q returned B^n. */
mp_size_t i, n;
n = new_nn - dn;
for (i = 0; i < n; i++)
qp[i] = GMP_NUMB_MAX;
qh = 0; /* currently ignored */
}
}
else /* divisor is already normalised */
{
if (new_np != np)
MPN_COPY (new_np, np, nn);
if (dn == 2)
{
qh = mpn_divrem_2 (qp, 0L, new_np, nn, dp);
}
else if (BELOW_THRESHOLD (dn, DC_DIV_Q_THRESHOLD) ||
BELOW_THRESHOLD (nn - dn, DC_DIV_Q_THRESHOLD))
{
invert_pi1 (dinv, dh, dp[dn - 2]);
qh = mpn_sbpi1_div_q (qp, new_np, nn, dp, dn, dinv.inv32);
}
else if (BELOW_THRESHOLD (dn, MUPI_DIV_Q_THRESHOLD) || /* fast condition */
BELOW_THRESHOLD (nn, 2 * MU_DIV_Q_THRESHOLD) || /* fast condition */
(double) (2 * (MU_DIV_Q_THRESHOLD - MUPI_DIV_Q_THRESHOLD)) * dn /* slow... */
+ (double) MUPI_DIV_Q_THRESHOLD * nn > (double) dn * nn) /* ...condition */
{
invert_pi1 (dinv, dh, dp[dn - 2]);
qh = mpn_dcpi1_div_q (qp, new_np, nn, dp, dn, &dinv);
}
else
{
mp_size_t itch = mpn_mu_div_q_itch (nn, dn, 0);
mp_ptr scratch = TMP_ALLOC_LIMBS (itch);
qh = mpn_mu_div_q (qp, np, nn, dp, dn, scratch);
}
qp[nn - dn] = qh;
}
}
else
{
/* |________________________|
|_________________| */
tp = TMP_ALLOC_LIMBS (qn + 1);
new_np = scratch;
new_nn = 2 * qn + 1;
if (new_np == np)
/* We need {np,nn} to remain untouched until the final adjustment, so
we need to allocate separate space for new_np. */
new_np = TMP_ALLOC_LIMBS (new_nn + 1);
dh = dp[dn - 1];
if (LIKELY ((dh & GMP_NUMB_HIGHBIT) == 0))
{
count_leading_zeros (cnt, dh);
cy = mpn_lshift (new_np, np + nn - new_nn, new_nn, cnt);
new_np[new_nn] = cy;
new_nn += (cy != 0);
new_dp = TMP_ALLOC_LIMBS (qn + 1);
mpn_lshift (new_dp, dp + dn - (qn + 1), qn + 1, cnt);
new_dp[0] |= dp[dn - (qn + 1) - 1] >> (GMP_NUMB_BITS - cnt);
if (qn + 1 == 2)
{
qh = mpn_divrem_2 (tp, 0L, new_np, new_nn, new_dp);
}
else if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD - 1))
{
invert_pi1 (dinv, new_dp[qn], new_dp[qn - 1]);
qh = mpn_sbpi1_divappr_q (tp, new_np, new_nn, new_dp, qn + 1, dinv.inv32);
}
else if (BELOW_THRESHOLD (qn, MU_DIVAPPR_Q_THRESHOLD - 1))
{
invert_pi1 (dinv, new_dp[qn], new_dp[qn - 1]);
qh = mpn_dcpi1_divappr_q (tp, new_np, new_nn, new_dp, qn + 1, &dinv);
}
else
{
mp_size_t itch = mpn_mu_divappr_q_itch (new_nn, qn + 1, 0);
mp_ptr scratch = TMP_ALLOC_LIMBS (itch);
qh = mpn_mu_divappr_q (tp, new_np, new_nn, new_dp, qn + 1, scratch);
}
if (cy == 0)
tp[qn] = qh;
else if (UNLIKELY (qh != 0))
{
/* This happens only when the quotient is close to B^n and
mpn_*_divappr_q returned B^n. */
mp_size_t i, n;
n = new_nn - (qn + 1);
for (i = 0; i < n; i++)
tp[i] = GMP_NUMB_MAX;
qh = 0; /* currently ignored */
}
}
else /* divisor is already normalised */
{
