void
mpn_sqr_n (mp_ptr p, mp_srcptr a, mp_size_t n)
{
ASSERT (n >= 1);
ASSERT (! MPN_OVERLAP_P (p, 2 * n, a, n));
#if 0
/* FIXME: Can this be removed? */
if (n == 0)
return;
#endif
if (BELOW_THRESHOLD (n, SQR_BASECASE_THRESHOLD))
{ /* mul_basecase is faster than sqr_basecase on small sizes sometimes */
mpn_mul_basecase (p, a, n, a, n);
}
else if (BELOW_THRESHOLD (n, SQR_KARATSUBA_THRESHOLD))
{
mpn_sqr_basecase (p, a, n);
}
else if (BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD))
{
/* Allocate workspace of fixed size on stack: fast! */
mp_limb_t ws[MPN_KARA_SQR_N_TSIZE (SQR_TOOM3_THRESHOLD_LIMIT-1)];
ASSERT (SQR_TOOM3_THRESHOLD <= SQR_TOOM3_THRESHOLD_LIMIT);
mpn_kara_sqr_n (p, a, n, ws);
}
#if WANT_FFT || TUNE_PROGRAM_BUILD
else if (BELOW_THRESHOLD (n, SQR_FFT_THRESHOLD))
#else
else if (BELOW_THRESHOLD (n, MPN_TOOM3_MAX_N))
#endif
{
mp_ptr ws;
TMP_SDECL;
TMP_SMARK;
ws = TMP_SALLOC_LIMBS (MPN_TOOM3_SQR_N_TSIZE (n));
mpn_toom3_sqr_n (p, a, n, ws);
TMP_SFREE;
}
else
#if WANT_FFT || TUNE_PROGRAM_BUILD
{
/* The current FFT code allocates its own space. That should probably
change. */
mpn_mul_fft_full (p, a, n, a, n);
}
#else
{
/* Toom3 for large operands. Use workspace from the heap, as stack space
may be limited. Since n is at least MUL_TOOM3_THRESHOLD, multiplication
will take much longer than malloc()/free(). */
mp_ptr ws; mp_size_t ws_size;
ws_size = MPN_TOOM3_SQR_N_TSIZE (n);
ws = __GMP_ALLOCATE_FUNC_LIMBS (ws_size);
mpn_toom3_sqr_n (p, a, n, ws);
__GMP_FREE_FUNC_LIMBS (ws, ws_size);
}
#endif
}
void
mpn_sqr (mp_ptr p, mp_srcptr a, mp_size_t n)
{
ASSERT (n >= 1);
ASSERT (! MPN_OVERLAP_P (p, 2 * n, a, n));
#if 0
/* FIXME: Can this be removed? */
if (n == 0)
return;
#endif
if (BELOW_THRESHOLD (n, SQR_BASECASE_THRESHOLD))
{ /* mul_basecase is faster than sqr_basecase on small sizes sometimes */
mpn_mul_basecase (p, a, n, a, n);
}
else if (BELOW_THRESHOLD (n, SQR_KARATSUBA_THRESHOLD))
{
mpn_sqr_basecase (p, a, n);
}
else if (BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD))
{
/* Allocate workspace of fixed size on stack: fast! */
mp_limb_t ws[MPN_KARA_SQR_N_TSIZE (SQR_TOOM3_THRESHOLD_LIMIT-1)];
ASSERT (SQR_TOOM3_THRESHOLD <= SQR_TOOM3_THRESHOLD_LIMIT);
mpn_kara_sqr_n (p, a, n, ws);
}
else if (BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD))
{
mp_ptr ws;
TMP_SDECL;
TMP_SMARK;
ws = TMP_SALLOC_LIMBS (MPN_TOOM3_SQR_N_TSIZE (n));
mpn_toom3_sqr_n (p, a, n, ws);
TMP_SFREE;
}
else if (BELOW_THRESHOLD (n, SQR_TOOM8_THRESHOLD))
{
mpn_toom4_sqr_n (p, a, n);
}
#if WANT_FFT || TUNE_PROGRAM_BUILD
else if (BELOW_THRESHOLD (n, SQR_FFT_FULL_THRESHOLD))
#else
else
#endif
{
mpn_toom8_sqr_n (p, a, n);
}
#if WANT_FFT || TUNE_PROGRAM_BUILD
else
{
void
mpn_mul_n (mp_ptr p, mp_srcptr a, mp_srcptr b, mp_size_t n)
{
ASSERT (n >= 1);
ASSERT (! MPN_OVERLAP_P (p, 2 * n, a, n));
ASSERT (! MPN_OVERLAP_P (p, 2 * n, b, n));
if (BELOW_THRESHOLD (n, MUL_KARATSUBA_THRESHOLD))
{
mpn_mul_basecase (p, a, n, b, n);
}
else if (BELOW_THRESHOLD (n, MUL_TOOM3_THRESHOLD))
{
/* Allocate workspace of fixed size on stack: fast! */
mp_limb_t ws[MPN_KARA_MUL_N_TSIZE (MUL_TOOM3_THRESHOLD_LIMIT-1)];
ASSERT (MUL_TOOM3_THRESHOLD <= MUL_TOOM3_THRESHOLD_LIMIT);
mpn_kara_mul_n (p, a, b, n, ws);
}
else if (BELOW_THRESHOLD (n, MUL_TOOM4_THRESHOLD))
{
mp_ptr ws;
TMP_SDECL;
TMP_SMARK;
ws = TMP_SALLOC_LIMBS (MPN_TOOM3_MUL_N_TSIZE (n));
mpn_toom3_mul_n (p, a, b, n, ws);
TMP_SFREE;
}
else if (BELOW_THRESHOLD (n, MUL_TOOM8H_THRESHOLD))
{
mpn_toom4_mul_n (p, a, b, n);
}
#if WANT_FFT || TUNE_PROGRAM_BUILD
else if (BELOW_THRESHOLD (n, MUL_FFT_FULL_THRESHOLD))
{
mpn_toom8h_mul (p, a, n, b, n);
}
#endif
else
#if WANT_FFT || TUNE_PROGRAM_BUILD
{
mpn_mul_fft_main(p, a, n, b, n);
}
#else
{
/* Toom8 for large operands. */
mpn_toom8h_mul (p, a, n, b, n);
}
#endif
}
void
mpn_mullow_n (mp_ptr rp, mp_srcptr xp, mp_srcptr yp, mp_size_t n)
{
if (BELOW_THRESHOLD (n, MULLOW_BASECASE_THRESHOLD))
{
/* Allocate workspace of fixed size on stack: fast! */
mp_limb_t ws[MUL_BASECASE_ALLOC];
mpn_mul_basecase (ws, xp, n, yp, n);
MPN_COPY (rp, ws, n);
}
else if (BELOW_THRESHOLD (n, MULLOW_DC_THRESHOLD))
{
mpn_mullow_basecase (rp, xp, yp, n);
}
else if (BELOW_THRESHOLD (n, MULLOW_MUL_N_THRESHOLD))
{
/* Divide-and-conquer */
mp_size_t n2 = n >> 1; /* floor(n/2) */
mp_size_t n1 = n - n2; /* ceil(n/2) */
mp_ptr tp;
TMP_SDECL;
TMP_SMARK;
tp = TMP_SALLOC_LIMBS (n1);
/* Split as x = x1 2^(n1 GMP_NUMB_BITS) + x0,
y = y1 2^(n2 GMP_NUMB_BITS) + y0 */
/* x0 * y0 */
mpn_mul_n (rp, xp, yp, n2);
if (n1 != n2)
rp[2 * n2] = mpn_addmul_1 (rp + n2, yp, n2, xp[n2]);
/* x1 * y0 * 2^(n1 GMP_NUMB_BITS) */
mpn_mullow_n (tp, xp + n1, yp, n2);
mpn_add_n (rp + n1, rp + n1, tp, n2);
/* x0 * y1 * 2^(n2 GMP_NUMB_BITS) */
mpn_mullow_n (tp, yp + n2, xp, n1);
mpn_add_n (rp + n2, rp + n2, tp, n1);
TMP_SFREE;
}
else
{
void
mpn_toom53_mul (mp_ptr pp,
mp_srcptr ap, mp_size_t an,
mp_srcptr bp, mp_size_t bn,
mp_ptr scratch)
{
mp_size_t n, s, t;
int vm1_neg, vmh_neg;
mp_limb_t cy;
mp_ptr gp, hp;
mp_ptr as1, asm1, as2, ash, asmh;
mp_ptr bs1, bsm1, bs2, bsh, bsmh;
enum toom4_flags flags;
TMP_DECL;
#define a0 ap
#define a1 (ap + n)
#define a2 (ap + 2*n)
#define a3 (ap + 3*n)
#define a4 (ap + 4*n)
#define b0 bp
#define b1 (bp + n)
#define b2 (bp + 2*n)
n = 1 + (3 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 3);
s = an - 4 * n;
t = bn - 2 * n;
ASSERT (0 < s && s <= n);
ASSERT (0 < t && t <= n);
TMP_MARK;
as1 = TMP_SALLOC_LIMBS (n + 1);
asm1 = TMP_SALLOC_LIMBS (n + 1);
as2 = TMP_SALLOC_LIMBS (n + 1);
ash = TMP_SALLOC_LIMBS (n + 1);
asmh = TMP_SALLOC_LIMBS (n + 1);
bs1 = TMP_SALLOC_LIMBS (n + 1);
bsm1 = TMP_SALLOC_LIMBS (n + 1);
bs2 = TMP_SALLOC_LIMBS (n + 1);
bsh = TMP_SALLOC_LIMBS (n + 1);
bsmh = TMP_SALLOC_LIMBS (n + 1);
gp = pp;
hp = pp + n + 1;
/* Compute as1 and asm1. */
gp[n] = mpn_add_n (gp, a0, a2, n);
gp[n] += mpn_add (gp, gp, n, a4, s);
hp[n] = mpn_add_n (hp, a1, a3, n);
#if HAVE_NATIVE_mpn_addsub_n
if (mpn_cmp (gp, hp, n + 1) < 0)
{
mpn_addsub_n (as1, asm1, hp, gp, n + 1);
vm1_neg = 1;
}
else
{
mpn_addsub_n (as1, asm1, gp, hp, n + 1);
vm1_neg = 0;
}
#else
mpn_add_n (as1, gp, hp, n + 1);
if (mpn_cmp (gp, hp, n + 1) < 0)
{
mpn_sub_n (asm1, hp, gp, n + 1);
vm1_neg = 1;
}
else
{
mpn_sub_n (asm1, gp, hp, n + 1);
vm1_neg = 0;
}
#endif
/* Compute as2. */
#if !HAVE_NATIVE_mpn_addlsh_n
ash[n] = mpn_lshift (ash, a2, n, 2); /* 4a2 */
#endif
#if HAVE_NATIVE_mpn_addlsh1_n
cy = mpn_addlsh1_n (as2, a3, a4, s);
if (s != n)
cy = mpn_add_1 (as2 + s, a3 + s, n - s, cy);
cy = 2 * cy + mpn_addlsh1_n (as2, a2, as2, n);
cy = 2 * cy + mpn_addlsh1_n (as2, a1, as2, n);
as2[n] = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
#else
cy = mpn_lshift (as2, a4, s, 1);
cy += mpn_add_n (as2, a3, as2, s);
if (s != n)
cy = mpn_add_1 (as2 + s, a3 + s, n - s, cy);
cy = 4 * cy + mpn_lshift (as2, as2, n, 2);
cy += mpn_add_n (as2, a1, as2, n);
cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
as2[n] = cy + mpn_add_n (as2, a0, as2, n);
mpn_add_n (as2, ash, as2, n + 1);
#endif
/* Compute ash and asmh. */
#if HAVE_NATIVE_mpn_addlsh_n
cy = mpn_addlsh_n (gp, a2, a0, n, 2); /* 4a0 + a2 */
cy = 4 * cy + mpn_addlsh_n (gp, a4, gp, n, 2); /* 16a0 + 4a2 + a4 */ /* FIXME s */
gp[n] = cy;
cy = mpn_addlsh_n (hp, a3, a1, n, 2); /* 4a1 + a3 */
cy = 2 * cy + mpn_lshift (hp, hp, n, 1); /* 8a1 + 2a3 */
hp[n] = cy;
#else
gp[n] = mpn_lshift (gp, a0, n, 4); /* 16a0 */
mpn_add (gp, gp, n + 1, a4, s); /* 16a0 + a4 */
mpn_add_n (gp, ash, gp, n+1); /* 16a0 + 4a2 + a4 */
cy = mpn_lshift (hp, a1, n, 3); /* 8a1 */
cy += mpn_lshift (ash, a3, n, 1); /* 2a3 */
cy += mpn_add_n (hp, ash, hp, n); /* 8a1 + 2a3 */
hp[n] = cy;
#endif
#if HAVE_NATIVE_mpn_addsub_n
if (mpn_cmp (gp, hp, n + 1) < 0)
{
mpn_addsub_n (ash, asmh, hp, gp, n + 1);
vmh_neg = 1;
}
else
{
mpn_addsub_n (ash, asmh, gp, hp, n + 1);
vmh_neg = 0;
}
#else
mpn_add_n (ash, gp, hp, n + 1);
if (mpn_cmp (gp, hp, n + 1) < 0)
{
mpn_sub_n (asmh, hp, gp, n + 1);
vmh_neg = 1;
}
else
{
mpn_sub_n (asmh, gp, hp, n + 1);
vmh_neg = 0;
}
#endif
/* Compute bs1 and bsm1. */
bs1[n] = mpn_add (bs1, b0, n, b2, t); /* b0 + b2 */
#if HAVE_NATIVE_mpn_addsub_n
if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0)
{
bs1[n] = mpn_addsub_n (bs1, bsm1, b1, bs1, n) >> 1;
bsm1[n] = 0;
vm1_neg ^= 1;
}
mp_limb_t
mpn_dcpi1_divappr_q (mp_ptr qp, mp_ptr np, mp_size_t nn,
mp_srcptr dp, mp_size_t dn, gmp_pi1_t *dinv)
{
mp_size_t qn;
mp_limb_t qh, cy, qsave;
mp_ptr tp;
TMP_DECL;
TMP_MARK;
ASSERT (dn >= 6);
ASSERT (nn > dn);
ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT);
qn = nn - dn;
qp += qn;
np += nn;
dp += dn;
if (qn >= dn)
{
qn++; /* pretend we'll need an extra limb */
/* Reduce qn mod dn without division, optimizing small operations. */
do
qn -= dn;
while (qn > dn);
qp -= qn; /* point at low limb of next quotient block */
np -= qn; /* point in the middle of partial remainder */
tp = TMP_SALLOC_LIMBS (dn);
/* Perform the typically smaller block first. */
if (qn == 1)
{
mp_limb_t q, n2, n1, n0, d1, d0;
/* Handle qh up front, for simplicity. */
qh = mpn_cmp (np - dn + 1, dp - dn, dn) >= 0;
if (qh)
ASSERT_NOCARRY (mpn_sub_n (np - dn + 1, np - dn + 1, dp - dn, dn));
/* A single iteration of schoolbook: One 3/2 division,
followed by the bignum update and adjustment. */
n2 = np[0];
n1 = np[-1];
n0 = np[-2];
d1 = dp[-1];
d0 = dp[-2];
ASSERT (n2 < d1 || (n2 == d1 && n1 <= d0));
if (UNLIKELY (n2 == d1) && n1 == d0)
{
q = GMP_NUMB_MASK;
cy = mpn_submul_1 (np - dn, dp - dn, dn, q);
ASSERT (cy == n2);
}
else
{
udiv_qr_3by2 (q, n1, n0, n2, n1, n0, d1, d0, dinv->inv32);
if (dn > 2)
{
mp_limb_t cy, cy1;
cy = mpn_submul_1 (np - dn, dp - dn, dn - 2, q);
cy1 = n0 < cy;
n0 = (n0 - cy) & GMP_NUMB_MASK;
cy = n1 < cy1;
n1 = (n1 - cy1) & GMP_NUMB_MASK;
np[-2] = n0;
if (UNLIKELY (cy != 0))
{
n1 += d1 + mpn_add_n (np - dn, np - dn, dp - dn, dn - 1);
qh -= (q == 0);
q = (q - 1) & GMP_NUMB_MASK;
}
}
else
np[-2] = n0;
np[-1] = n1;
}
qp[0] = q;
}
else
{
if (qn == 2)
qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2);
else if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
qh = mpn_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32);
else
qh = mpn_dcpi1_div_qr_n (qp, np - qn, dp - qn, qn, dinv, tp);
if (qn != dn)
{
if (qn > dn - qn)
mpn_mul (tp, qp, qn, dp - dn, dn - qn);
else
mpn_mul (tp, dp - dn, dn - qn, qp, qn);
cy = mpn_sub_n (np - dn, np - dn, tp, dn);
if (qh != 0)
cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);
while (cy != 0)
{
qh -= mpn_sub_1 (qp, qp, qn, 1);
cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);
}
}
}
qn = nn - dn - qn + 1;
while (qn > dn)
{
qp -= dn;
np -= dn;
mpn_dcpi1_div_qr_n (qp, np - dn, dp - dn, dn, dinv, tp);
qn -= dn;
}
/* Since we pretended we'd need an extra quotient limb before, we now
have made sure the code above left just dn-1=qn quotient limbs to
develop. Develop that plus a guard limb. */
qn--;
qp -= qn;
np -= dn;
qsave = qp[qn];
mpn_dcpi1_divappr_q_n (qp, np - dn, dp - dn, dn, dinv, tp);
MPN_COPY_INCR (qp, qp + 1, qn);
qp[qn] = qsave;
}
else /* (qn < dn) */
{
mp_ptr q2p;
#if 0 /* not possible since we demand nn > dn */
if (qn == 0)
{
qh = mpn_cmp (np - dn, dp - dn, dn) >= 0;
if (qh)
mpn_sub_n (np - dn, np - dn, dp - dn, dn);
TMP_FREE;
return qh;
}
#endif
qp -= qn; /* point at low limb of next quotient block */
np -= qn; /* point in the middle of partial remainder */
q2p = TMP_SALLOC_LIMBS (qn + 1);
/* Should we at all check DC_DIVAPPR_Q_THRESHOLD here, or reply on
callers not to be silly? */
if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD))
{
qh = mpn_sbpi1_divappr_q (q2p, np - qn - 2, 2 * (qn + 1),
dp - (qn + 1), qn + 1, dinv->inv32);
}
else
{
/* It is tempting to use qp for recursive scratch and put quotient in
tp, but the recursive scratch needs one limb too many. */
tp = TMP_SALLOC_LIMBS (qn + 1);
qh = mpn_dcpi1_divappr_q_n (q2p, np - qn - 2, dp - (qn + 1), qn + 1, dinv, tp);
}
MPN_COPY (qp, q2p + 1, qn);
}
TMP_FREE;
return qh;
}
mp_limb_t
mpn_dcpi1_div_qr (mp_ptr qp,
mp_ptr np, mp_size_t nn,
mp_srcptr dp, mp_size_t dn,
gmp_pi1_t *dinv)
{
mp_size_t qn;
mp_limb_t qh, cy;
mp_ptr tp;
TMP_DECL;
TMP_MARK;
ASSERT (dn >= 6); /* to adhere to mpn_sbpi1_div_qr's limits */
ASSERT (nn - dn >= 3); /* to adhere to mpn_sbpi1_div_qr's limits */
ASSERT (dp[dn-1] & GMP_NUMB_HIGHBIT);
tp = TMP_SALLOC_LIMBS (dn);
qn = nn - dn;
qp += qn;
np += nn;
dp += dn;
if (qn > dn)
{
/* Reduce qn mod dn without division, optimizing small operations. */
do
qn -= dn;
while (qn > dn);
qp -= qn; /* point at low limb of next quotient block */
np -= qn; /* point in the middle of partial remainder */
/* Perform the typically smaller block first. */
if (qn == 1)
{
mp_limb_t q, n2, n1, n0, d1, d0;
/* Handle qh up front, for simplicity. */
qh = mpn_cmp (np - dn + 1, dp - dn, dn) >= 0;
if (qh)
ASSERT_NOCARRY (mpn_sub_n (np - dn + 1, np - dn + 1, dp - dn, dn));
/* A single iteration of schoolbook: One 3/2 division,
followed by the bignum update and adjustment. */
n2 = np[0];
n1 = np[-1];
n0 = np[-2];
d1 = dp[-1];
d0 = dp[-2];
ASSERT (n2 < d1 || (n2 == d1 && n1 <= d0));
if (UNLIKELY (n2 == d1) && n1 == d0)
{
q = GMP_NUMB_MASK;
cy = mpn_submul_1 (np - dn, dp - dn, dn, q);
ASSERT (cy == n2);
}
else
{
udiv_qr_3by2 (q, n1, n0, n2, n1, n0, d1, d0, dinv->inv32);
if (dn > 2)
{
mp_limb_t cy, cy1;
cy = mpn_submul_1 (np - dn, dp - dn, dn - 2, q);
cy1 = n0 < cy;
n0 = (n0 - cy) & GMP_NUMB_MASK;
cy = n1 < cy1;
n1 = (n1 - cy1) & GMP_NUMB_MASK;
np[-2] = n0;
if (UNLIKELY (cy != 0))
{
n1 += d1 + mpn_add_n (np - dn, np - dn, dp - dn, dn - 1);
qh -= (q == 0);
q = (q - 1) & GMP_NUMB_MASK;
}
}
else
np[-2] = n0;
np[-1] = n1;
}
qp[0] = q;
}
else
{
/* Do a 2qn / qn division */
if (qn == 2)
qh = mpn_divrem_2 (qp, 0L, np - 2, 4, dp - 2); /* FIXME: obsolete function. Use 5/3 division? */
else if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
qh = mpn_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32);
else
qh = mpn_dcpi1_div_qr_n (qp, np - qn, dp - qn, qn, dinv, tp);
if (qn != dn)
{
if (qn > dn - qn)
mpn_mul (tp, qp, qn, dp - dn, dn - qn);
else
mpn_mul (tp, dp - dn, dn - qn, qp, qn);
cy = mpn_sub_n (np - dn, np - dn, tp, dn);
if (qh != 0)
cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);
while (cy != 0)
{
qh -= mpn_sub_1 (qp, qp, qn, 1);
cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);
}
}
}
qn = nn - dn - qn;
do
{
qp -= dn;
np -= dn;
mpn_dcpi1_div_qr_n (qp, np - dn, dp - dn, dn, dinv, tp);
qn -= dn;
}
while (qn > 0);
}
else
{
qp -= qn; /* point at low limb of next quotient block */
np -= qn; /* point in the middle of partial remainder */
if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
qh = mpn_sbpi1_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dinv->inv32);
else
qh = mpn_dcpi1_div_qr_n (qp, np - qn, dp - qn, qn, dinv, tp);
if (qn != dn)
{
if (qn > dn - qn)
mpn_mul (tp, qp, qn, dp - dn, dn - qn);
else
mpn_mul (tp, dp - dn, dn - qn, qp, qn);
cy = mpn_sub_n (np - dn, np - dn, tp, dn);
if (qh != 0)
cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);
while (cy != 0)
{
qh -= mpn_sub_1 (qp, qp, qn, 1);
cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);
}
}
}
TMP_FREE;
return qh;
}
int
main (int argc, char **argv)
{
mp_ptr ap, bp, rp, refp;
mp_size_t max_n, n;
gmp_randstate_ptr rands;
long test, reps = 1000;
TMP_SDECL;
TMP_SMARK;
tests_start ();
TESTS_REPS (reps, argv, argc);
rands = RANDS;
max_n = 32;
ap = TMP_SALLOC_LIMBS (max_n);
bp = TMP_SALLOC_LIMBS (max_n);
rp = TMP_SALLOC_LIMBS (max_n);
refp = TMP_SALLOC_LIMBS (max_n);
for (test = 0; test < reps; test++)
{
for (n = 1; n <= max_n; n++)
{
mpn_random2 (ap, n);
mpn_random2 (bp, n);
refmpn_and_n (refp, ap, bp, n);
mpn_and_n (rp, ap, bp, n);
check_one (refp, rp, ap, bp, n, "and_n");
refmpn_ior_n (refp, ap, bp, n);
mpn_ior_n (rp, ap, bp, n);
check_one (refp, rp, ap, bp, n, "ior_n");
refmpn_xor_n (refp, ap, bp, n);
mpn_xor_n (rp, ap, bp, n);
check_one (refp, rp, ap, bp, n, "xor_n");
refmpn_andn_n (refp, ap, bp, n);
mpn_andn_n (rp, ap, bp, n);
check_one (refp, rp, ap, bp, n, "andn_n");
refmpn_iorn_n (refp, ap, bp, n);
mpn_iorn_n (rp, ap, bp, n);
check_one (refp, rp, ap, bp, n, "iorn_n");
refmpn_nand_n (refp, ap, bp, n);
mpn_nand_n (rp, ap, bp, n);
check_one (refp, rp, ap, bp, n, "nand_n");
refmpn_nior_n (refp, ap, bp, n);
mpn_nior_n (rp, ap, bp, n);
check_one (refp, rp, ap, bp, n, "nior_n");
refmpn_xnor_n (refp, ap, bp, n);
mpn_xnor_n (rp, ap, bp, n);
check_one (refp, rp, ap, bp, n, "xnor_n");
refmpn_com (refp, ap, n);
mpn_com (rp, ap, n);
check_one (refp, rp, ap, bp, n, "com");
}
}
TMP_SFREE;
tests_end ();
return 0;
}
void
mpn_dcpi1_bdiv_q (mp_ptr qp,
mp_ptr np, mp_size_t nn,
mp_srcptr dp, mp_size_t dn,
mp_limb_t dinv)
{
mp_size_t qn;
mp_limb_t cy;
mp_ptr tp;
TMP_DECL;
TMP_MARK;
ASSERT (dn >= 2);
ASSERT (nn - dn >= 0);
ASSERT (dp[0] & 1);
tp = TMP_SALLOC_LIMBS (dn);
qn = nn;
if (qn > dn)
{
/* Reduce qn mod dn in a super-efficient manner. */
do
qn -= dn;
while (qn > dn);
/* Perform the typically smaller block first. */
if (BELOW_THRESHOLD (qn, DC_BDIV_QR_THRESHOLD))
cy = mpn_sbpi1_bdiv_qr (qp, np, 2 * qn, dp, qn, dinv);
else
cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, qn, dinv, tp);
if (qn != dn)
{
if (qn > dn - qn)
mpn_mul (tp, qp, qn, dp + qn, dn - qn);
else
mpn_mul (tp, dp + qn, dn - qn, qp, qn);
mpn_incr_u (tp + qn, cy);
mpn_sub (np + qn, np + qn, nn - qn, tp, dn);
cy = 0;
}
np += qn;
qp += qn;
qn = nn - qn;
while (qn > dn)
{
mpn_sub_1 (np + dn, np + dn, qn - dn, cy);
cy = mpn_dcpi1_bdiv_qr_n (qp, np, dp, dn, dinv, tp);
qp += dn;
np += dn;
qn -= dn;
}
mpn_dcpi1_bdiv_q_n (qp, np, dp, dn, dinv, tp);
}
else
{
if (BELOW_THRESHOLD (qn, DC_BDIV_Q_THRESHOLD))
mpn_sbpi1_bdiv_q (qp, np, qn, dp, qn, dinv);
else
mpn_dcpi1_bdiv_q_n (qp, np, dp, qn, dinv, tp);
}
TMP_FREE;
}
mp_limb_t
mpn_preinv_dc_divappr_q (mp_ptr qp,
mp_ptr np, mp_size_t nn,
mp_srcptr dp, mp_size_t dn,
mp_srcptr dip)
{
mp_size_t qn;
mp_limb_t qh, cy, qsave;
mp_ptr tp;
TMP_DECL;
TMP_MARK;
tp = TMP_SALLOC_LIMBS (dn+1);
qn = nn - dn;
qp += qn;
np += nn;
dp += dn;
if (qn > dn)
{
qn++; /* pretend we'll need an extra limb */
/* Reduce qn mod dn without division, optimizing small operations. */
do
qn -= dn;
while (qn > dn);
qp -= qn; /* point at low limb of next quotient block */
np -= qn; /* point in the middle of partial remainder */
/* Perform the typically smaller block first. */
if (BELOW_THRESHOLD (qn, DC_DIV_QR_THRESHOLD))
qh = mpn_sb_div_qr (qp, np - qn, 2 * qn, dp - qn, qn, dip);
else
qh = mpn_dc_div_qr_n (qp, np - qn, dp - qn, qn, dip, tp);
if (qn != dn)
{
if (qn > dn - qn)
mpn_mul (tp, qp, qn, dp - dn, dn - qn);
else
mpn_mul (tp, dp - dn, dn - qn, qp, qn);
cy = mpn_sub_n (np - dn, np - dn, tp, dn);
if (qh != 0)
cy += mpn_sub_n (np - dn + qn, np - dn + qn, dp - dn, dn - qn);
while (cy != 0)
{
qh -= mpn_sub_1 (qp, qp, qn, 1);
cy -= mpn_add_n (np - dn, np - dn, dp - dn, dn);
}
}
qn = nn - dn - qn + 1;
while (qn > dn)
{
qp -= dn;
np -= dn;
mpn_dc_div_qr_n (qp, np - dn, dp - dn, dn, dip, tp);
qn -= dn;
}
/* Since we pretended we'd need an extra quotient limb before, we now
have made sure the code above left just dn-1=qn quotient limbs to
develop. Develop that plus a guard limb. */
qn--;
qp -= qn;
np -= dn;
qsave = qp[qn];
mpn_dc_divappr_q_n (qp, np - dn, dp - dn, dn, dip, tp);
MPN_COPY_INCR (qp, qp + 1, qn);
qp[qn] = qsave;
}
else
{
if (qn == 0)
{
qh = mpn_cmp (np - dn, dp - dn, dn) >= 0;
if (qh)
mpn_sub_n (np - dn, np - dn, dp - dn, dn);
TMP_FREE;
return qh;
}
qp -= qn; /* point at low limb of next quotient block */
np -= qn; /* point in the middle of partial remainder */
if (BELOW_THRESHOLD (qn, DC_DIVAPPR_Q_THRESHOLD))
/* Full precision. Optimal? */
qh = mpn_sb_divappr_q (qp, np - dn, nn, dp - dn, dn, dip);
else
{
/* Put quotient in tp, use qp as temporary, since qp lacks a limb. */
qh = mpn_dc_divappr_q_n (tp, np - qn - 2, dp - (qn + 1), qn + 1, dip, qp);
MPN_COPY (qp, tp + 1, qn);
}
}
TMP_FREE;
return qh;
}
void
mpn_sqr (mp_ptr p, mp_srcptr a, mp_size_t n)
{
ASSERT (n >= 1);
ASSERT (! MPN_OVERLAP_P (p, 2 * n, a, n));
if (BELOW_THRESHOLD (n, SQR_BASECASE_THRESHOLD))
{ /* mul_basecase is faster than sqr_basecase on small sizes sometimes */
mpn_mul_basecase (p, a, n, a, n);
}
else if (BELOW_THRESHOLD (n, SQR_TOOM2_THRESHOLD))
{
mpn_sqr_basecase (p, a, n);
}
else if (BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD))
{
/* Allocate workspace of fixed size on stack: fast! */
mp_limb_t ws[mpn_toom2_sqr_itch (SQR_TOOM3_THRESHOLD_LIMIT-1)];
ASSERT (SQR_TOOM3_THRESHOLD <= SQR_TOOM3_THRESHOLD_LIMIT);
mpn_toom2_sqr (p, a, n, ws);
}
else if (BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD))
{
mp_ptr ws;
TMP_SDECL;
TMP_SMARK;
ws = TMP_SALLOC_LIMBS (mpn_toom3_sqr_itch (n));
mpn_toom3_sqr (p, a, n, ws);
TMP_SFREE;
}
else if (BELOW_THRESHOLD (n, SQR_TOOM6_THRESHOLD))
{
mp_ptr ws;
TMP_SDECL;
TMP_SMARK;
ws = TMP_SALLOC_LIMBS (mpn_toom4_sqr_itch (n));
mpn_toom4_sqr (p, a, n, ws);
TMP_SFREE;
}
else if (BELOW_THRESHOLD (n, SQR_TOOM8_THRESHOLD))
{
mp_ptr ws;
TMP_SDECL;
TMP_SMARK;
ws = TMP_SALLOC_LIMBS (mpn_toom6_sqr_itch (n));
mpn_toom6_sqr (p, a, n, ws);
TMP_SFREE;
}
else if (BELOW_THRESHOLD (n, SQR_FFT_THRESHOLD))
{
mp_ptr ws;
TMP_DECL;
TMP_MARK;
ws = TMP_ALLOC_LIMBS (mpn_toom8_sqr_itch (n));
mpn_toom8_sqr (p, a, n, ws);
TMP_FREE;
}
else
{
/* The current FFT code allocates its own space. That should probably
change. */
mpn_fft_mul (p, a, n, a, n);
}
}
void
mpn_toom53_mul (mp_ptr pp,
mp_srcptr ap, mp_size_t an,
mp_srcptr bp, mp_size_t bn,
mp_ptr scratch)
{
mp_size_t n, s, t;
mp_limb_t cy;
mp_ptr gp;
mp_ptr as1, asm1, as2, asm2, ash;
mp_ptr bs1, bsm1, bs2, bsm2, bsh;
enum toom7_flags flags;
TMP_DECL;
#define a0 ap
#define a1 (ap + n)
#define a2 (ap + 2*n)
#define a3 (ap + 3*n)
#define a4 (ap + 4*n)
#define b0 bp
#define b1 (bp + n)
#define b2 (bp + 2*n)
n = 1 + (3 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 3);
s = an - 4 * n;
t = bn - 2 * n;
ASSERT (0 < s && s <= n);
ASSERT (0 < t && t <= n);
TMP_MARK;
as1 = TMP_SALLOC_LIMBS (n + 1);
asm1 = TMP_SALLOC_LIMBS (n + 1);
as2 = TMP_SALLOC_LIMBS (n + 1);
asm2 = TMP_SALLOC_LIMBS (n + 1);
ash = TMP_SALLOC_LIMBS (n + 1);
bs1 = TMP_SALLOC_LIMBS (n + 1);
bsm1 = TMP_SALLOC_LIMBS (n + 1);
bs2 = TMP_SALLOC_LIMBS (n + 1);
bsm2 = TMP_SALLOC_LIMBS (n + 1);
bsh = TMP_SALLOC_LIMBS (n + 1);
gp = pp;
/* Compute as1 and asm1. */
flags = (enum toom7_flags) (toom7_w3_neg & mpn_toom_eval_pm1 (as1, asm1, 4, ap, n, s, gp));
/* Compute as2 and asm2. */
flags = (enum toom7_flags) (flags | (toom7_w1_neg & mpn_toom_eval_pm2 (as2, asm2, 4, ap, n, s, gp)));
/* Compute ash = 16 a0 + 8 a1 + 4 a2 + 2 a3 + a4
= 2*(2*(2*(2*a0 + a1) + a2) + a3) + a4 */
#if HAVE_NATIVE_mpn_addlsh1_n
cy = mpn_addlsh1_n (ash, a1, a0, n);
cy = 2*cy + mpn_addlsh1_n (ash, a2, ash, n);
cy = 2*cy + mpn_addlsh1_n (ash, a3, ash, n);
if (s < n)
{
mp_limb_t cy2;
cy2 = mpn_addlsh1_n (ash, a4, ash, s);
ash[n] = 2*cy + mpn_lshift (ash + s, ash + s, n - s, 1);
MPN_INCR_U (ash + s, n+1-s, cy2);
}
else
ash[n] = 2*cy + mpn_addlsh1_n (ash, a4, ash, n);
#else
cy = mpn_lshift (ash, a0, n, 1);
cy += mpn_add_n (ash, ash, a1, n);
cy = 2*cy + mpn_lshift (ash, ash, n, 1);
cy += mpn_add_n (ash, ash, a2, n);
cy = 2*cy + mpn_lshift (ash, ash, n, 1);
cy += mpn_add_n (ash, ash, a3, n);
cy = 2*cy + mpn_lshift (ash, ash, n, 1);
ash[n] = cy + mpn_add (ash, ash, n, a4, s);
#endif
/* Compute bs1 and bsm1. */
bs1[n] = mpn_add (bs1, b0, n, b2, t); /* b0 + b2 */
#if HAVE_NATIVE_mpn_add_n_sub_n
if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0)
{
bs1[n] = mpn_add_n_sub_n (bs1, bsm1, b1, bs1, n) >> 1;
bsm1[n] = 0;
flags = (enum toom7_flags) (flags ^ toom7_w3_neg);
}
