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;
}
}