void
mpn_toom4_mul_n (mp_ptr rp, mp_srcptr up,
mp_srcptr vp, mp_size_t n)
{
mp_size_t ind;
mp_limb_t cy, cy2, r30, r31;
mp_ptr tp;
mp_size_t sn, n1, n2, n3, n4, n5, n6, n7, n8, rpn, t4, h1;
TMP_DECL;
sn = (n + 3) / 4;
h1 = n - 3*sn;
#define a0 (up)
#define a1 (up + sn)
#define a2 (up + 2*sn)
#define a3 (up + 3*sn)
#define b0 (vp)
#define b1 (vp + sn)
#define b2 (vp + 2*sn)
#define b3 (vp + 3*sn)
t4 = 2*sn+2; // allows mult of 2 integers of sn + 1 limbs
TMP_MARK;
tp = TMP_ALLOC_LIMBS(4*t4 + 5*(sn + 1));
#define u2 (tp + 4*t4)
#define u3 (tp + 4*t4 + (sn+1))
#define u4 (tp + 4*t4 + 2*(sn+1))
#define u5 (tp + 4*t4 + 3*(sn+1))
#define u6 (tp + 4*t4 + 4*(sn+1))
u6[sn] = mpn_add(u6, a1, sn, a3, h1);
u5[sn] = mpn_add_n(u5, a2, a0, sn);
mpn_add_n(u3, u5, u6, sn + 1);
n4 = sn + 1;
if (mpn_cmp(u5, u6, sn + 1) >= 0)
mpn_sub_n(u4, u5, u6, sn + 1);
else
{
mpn_sub_n(u4, u6, u5, sn + 1);
n4 = -n4;
}
u6[sn] = mpn_add(u6, b1, sn, b3, h1);
u5[sn] = mpn_add_n(u5, b2, b0, sn);
mpn_add_n(r2, u5, u6, sn + 1);
n5 = sn + 1;
if (mpn_cmp(u5, u6, sn + 1) >= 0)
mpn_sub_n(u5, u5, u6, sn + 1);
else
{
mpn_sub_n(u5, u6, u5, sn + 1);
n5 = -n5;
}
MUL_TC4_UNSIGNED(r3, n3, u3, sn + 1, r2, sn + 1); /* 1 */
MUL_TC4(r4, n4, u4, n4, u5, n5); /* -1 */
#if HAVE_NATIVE_mpn_addlsh_n
r1[sn] = mpn_addlsh_n(r1, a2, a0, sn, 2);
mpn_lshift(r1, r1, sn + 1, 1);
cy = mpn_addlsh_n(r2, a3, a1, h1, 2);
#else
r1[sn] = mpn_lshift(r1, a2, sn, 1);
MPN_COPY(r2, a3, h1);
r1[sn] += mpn_addmul_1(r1, a0, sn, 8);
cy = mpn_addmul_1(r2, a1, h1, 4);
#endif
if (sn > h1)
{
cy2 = mpn_lshift(r2 + h1, a1 + h1, sn - h1, 2);
cy = cy2 + mpn_add_1(r2 + h1, r2 + h1, sn - h1, cy);
}
r2[sn] = cy;
mpn_add_n(u5, r1, r2, sn + 1);
n6 = sn + 1;
if (mpn_cmp(r1, r2, sn + 1) >= 0)
mpn_sub_n(u6, r1, r2, sn + 1);
else
{
mpn_sub_n(u6, r2, r1, sn + 1);
n6 = -n6;
}
#if HAVE_NATIVE_mpn_addlsh_n
r1[sn] = mpn_addlsh_n(r1, b2, b0, sn, 2);
mpn_lshift(r1, r1, sn + 1, 1);
cy = mpn_addlsh_n(r2, b3, b1, h1, 2);
#else
r1[sn] = mpn_lshift(r1, b2, sn, 1);
MPN_COPY(r2, b3, h1);
r1[sn] += mpn_addmul_1(r1, b0, sn, 8);
cy = mpn_addmul_1(r2, b1, h1, 4);
#endif
if (sn > h1)
{
cy2 = mpn_lshift(r2 + h1, b1 + h1, sn - h1, 2);
cy = cy2 + mpn_add_1(r2 + h1, r2 + h1, sn - h1, cy);
}
r2[sn] = cy;
mpn_add_n(u2, r1, r2, sn + 1);
n8 = sn + 1;
if (mpn_cmp(r1, r2, sn + 1) >= 0)
mpn_sub_n(r2, r1, r2, sn + 1);
else
{
mpn_sub_n(r2, r2, r1, sn + 1);
n8 = -n8;
}
r30 = r3[0];
r31 = r3[1];
MUL_TC4_UNSIGNED(r5, n5, u5, sn + 1, u2, sn + 1); /* 1/2 */
MUL_TC4(r6, n6, u6, n6, r2, n8); /* -1/2 */
r3[1] = r31;
#if HAVE_NATIVE_mpn_addlsh1_n
cy = mpn_addlsh1_n(u2, a2, a3, h1);
if (sn > h1)
cy = mpn_add_1(u2 + h1, a2 + h1, sn - h1, cy);
u2[sn] = cy;
u2[sn] = 2*u2[sn] + mpn_addlsh1_n(u2, a1, u2, sn);
u2[sn] = 2*u2[sn] + mpn_addlsh1_n(u2, a0, u2, sn);
#else
MPN_COPY(u2, a0, sn);
u2[sn] = mpn_addmul_1(u2, a1, sn, 2);
u2[sn] += mpn_addmul_1(u2, a2, sn, 4);
cy = mpn_addmul_1(u2, a3, h1, 8);
if (sn > h1) cy = mpn_add_1(u2 + h1, u2 + h1, sn - h1, cy);
u2[sn] += cy;
#endif
#if HAVE_NATIVE_mpn_addlsh1_n
cy = mpn_addlsh1_n(r1, b2, b3, h1);
if (sn > h1)
cy = mpn_add_1(r1 + h1, b2 + h1, sn - h1, cy);
r1[sn] = cy;
r1[sn] = 2*r1[sn] + mpn_addlsh1_n(r1, b1, r1, sn);
r1[sn] = 2*r1[sn] + mpn_addlsh1_n(r1, b0, r1, sn);
#else
MPN_COPY(r1, b0, sn);
r1[sn] = mpn_addmul_1(r1, b1, sn, 2);
r1[sn] += mpn_addmul_1(r1, b2, sn, 4);
cy = mpn_addmul_1(r1, b3, h1, 8);
if (sn > h1) cy = mpn_add_1(r1 + h1, r1 + h1, sn - h1, cy);
r1[sn] += cy;
#endif
MUL_TC4_UNSIGNED(r2, n2, u2, sn + 1, r1, sn + 1); /* 2 */
MUL_TC4_UNSIGNED(r1, n1, a3, h1, b3, h1); /* oo */
MUL_TC4_UNSIGNED(r7, n7, a0, sn, b0, sn); /* 0 */
TC4_DENORM(r1, n1, t4 - 1);
/* rp rp1 rp2 rp3 rp4 rp5 rp6 rp7
<----------- r7-----------><------------r5-------------->
<-------------r3------------->
<-------------r6-------------> < -----------r2------------>{ }
<-------------r4--------------> <--------------r1---->
*/
mpn_toom4_interpolate(rp, &rpn, sn, tp, t4 - 1, n4, n6, r30);
if (rpn != 2*n)
{
MPN_ZERO((rp + rpn), 2*n - rpn);
}
TMP_FREE;
}
/* Multiply {up, un} by {vp, vn} and write the result to
{prodp, un + vn} assuming vn > 2*ceil(un/5).
Note that prodp gets un + vn limbs stored, even if the actual
result only needs un + vn - 1.
*/
void
mpn_toom53_mul (mp_ptr rp, mp_srcptr up, mp_size_t un,
mp_srcptr vp, mp_size_t vn)
{
mp_size_t ind;
mp_limb_t cy, r30, r31;
mp_ptr tp;
mp_size_t a0n, a1n, a2n, a3n, a4n, b0n, b1n, b2n, sn, n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, rpn, t4;
sn = (un + 4) / 5;
ASSERT (vn > 2*sn);
#define a0 (up)
#define a1 (up + sn)
#define a2 (up + 2*sn)
#define a3 (up + 3*sn)
#define a4 (up + 4*sn)
#define b0 (vp)
#define b1 (vp + sn)
#define b2 (vp + 2*sn)
TC4_NORM(a0, a0n, sn);
TC4_NORM(a1, a1n, sn);
TC4_NORM(a2, a2n, sn);
TC4_NORM(a3, a3n, sn);
TC4_NORM(a4, a4n, un - 4*sn);
TC4_NORM(b0, b0n, sn);
TC4_NORM(b1, b1n, sn);
TC4_NORM(b2, b2n, vn - 2*sn);
t4 = 2*sn+2; // allows mult of 2 integers of sn + 1 limbs
tp = __GMP_ALLOCATE_FUNC_LIMBS(4*t4 + 4*(sn + 1));
#define u2 (tp + 4*t4)
#define u3 (tp + 4*t4 + (sn+1))
#define u4 (tp + 4*t4 + 2*(sn+1))
#define u5 (tp + 4*t4 + 3*(sn+1))
tc4_add_unsigned(u2, &n2, a3, a3n, a1, a1n);
tc4_add_unsigned(u5, &n5, a2, a2n, a0, a0n);
tc4_add_unsigned(u5, &n5, u5, n5, a4, a4n);
tc4_add_unsigned(u3, &n3, u5, n5, u2, n2);
tc4_sub(u4, &n4, u5, n5, u2, n2);
tc4_add_unsigned(u5, &n5, b2, b2n, b0, b0n);
tc4_add_unsigned(r2, &n8, u5, n5, b1, b1n);
tc4_sub(u5, &n5, u5, n5, b1, b1n);
MUL_TC4_UNSIGNED(r3, n3, u3, n3, r2, n8); /* 1 */
MUL_TC4(r4, n4, u4, n4, u5, n5); /* -1 */
tc4_lshift(r1, &n1, a0, a0n, 4);
tc4_lshift(u3, &n9, a2, a2n, 2);
tc4_add_unsigned(r1, &n1, r1, n1, u3, n9);
tc4_add_unsigned(r1, &n1, r1, n1, a4, a4n);
tc4_lshift(r2, &n8, a1, a1n, 3);
tc4_addlsh1_unsigned(r2, &n8, a3, a3n);
tc4_add_unsigned(u5, &n5, r1, n1, r2, n8);
tc4_sub(u3, &n9, r1, n1, r2, n8);
tc4_lshift(r1, &n1, b0, b0n, 2);
tc4_add_unsigned(r1, &n1, r1, n1, b2, b2n);
tc4_lshift(u4, &n10, b1, b1n, 1);
tc4_add_unsigned(u2, &n2, r1, n1, u4, n10);
tc4_sub(r2, &n8, r1, n1, u4, n10);
r30 = r3[0];
if (!n3) r30 = CNST_LIMB(0);
r31 = r3[1];
MUL_TC4_UNSIGNED(r5, n5, u5, n5, u2, n2); /* 1/2 */
MUL_TC4(r6, n6, u3, n9, r2, n8); /* -1/2 */
r3[1] = r31;
tc4_lshift(u2, &n2, a4, a4n, 4);
tc4_addmul_1(u2, &n2, a3, a3n, 8);
tc4_addmul_1(u2, &n2, a2, a2n, 4);
tc4_addlsh1_unsigned(u2, &n2, a1, a1n);
tc4_add(u2, &n2, u2, n2, a0, a0n);
tc4_lshift(r1, &n1, b2, b2n, 2);
tc4_addlsh1_unsigned(r1, &n1, b1, b1n);
tc4_add(r1, &n1, r1, n1, b0, b0n);
MUL_TC4_UNSIGNED(r2, n2, u2, n2, r1, n1); /* 2 */
MUL_TC4_UNSIGNED(r1, n1, a4, a4n, b2, b2n); /* oo */
MUL_TC4_UNSIGNED(r7, n7, a0, a0n, b0, b0n); /* 0 */
TC4_DENORM(r1, n1, t4 - 1);
TC4_DENORM(r2, n2, t4 - 1);
if (n3)
TC4_DENORM(r3, n3, t4 - 1);
else {
/* MPN_ZERO defeats gcc 4.1.2 here, hence the explicit for loop */
for (ind = 1 ; ind < t4 - 1; ind++)
(r3)[ind] = CNST_LIMB(0);
}
TC4_DENORM(r4, n4, t4 - 1);
TC4_DENORM(r5, n5, t4 - 1);
TC4_DENORM(r6, n6, t4 - 1);
TC4_DENORM(r7, n7, t4 - 2); // we treat r7 differently (it cannot exceed t4-2 in length)
/* rp rp1 rp2 rp3 rp4 rp5 rp6 rp7
<----------- r7-----------><------------r5-------------->
<-------------r3------------->
<-------------r6-------------> < -----------r2------------>{ }
<-------------r4--------------> <--------------r1---->
*/
mpn_toom4_interpolate(rp, &rpn, sn, tp, t4 - 1, n4, n6, r30);
if (rpn != un + vn)
{
MPN_ZERO((rp + rpn), un + vn - rpn);
}
__GMP_FREE_FUNC_LIMBS (tp, 4*t4 + 4*(sn+1));
}
