/*
Toom 4 interpolation. Interpolates the value at 2^(sn*B) of a
polynomial p(x) with 7 coefficients given the values
p(oo), p(2), p(1), p(-1), 2^6*p(1/2), 2^6*p(-1/2), p(0).
The output is placed in rp and the final number of limbs of the
output is given in rpn.
The 4th and 6th values may be negative, and if so, n4 and n6
should be set to a negative value respectively.
To save space we pass r3, r5, r7 in place in the output rp.
The other r's are stored separately in space tp.
The low limb of r3 is stored in r30, as it will be overwritten
by the high limb of r5.
rp rp1 rp2 rp3 rp4 rp5 rp6 rp7
<----------- r7-----------><------------r5-------------->
<-------------r3------------->
We assume that r1 is stored at tp, r2 at (tp + t4), r4 at (tp + 2*t4)
and r6 (tp + 3*t4). Each of these r's has t4 = s4 + 1 limbs allocated.
*/
void mpn_toom4_interpolate(mp_ptr rp, mp_size_t * rpn, mp_size_t sn,
mp_ptr tp, mp_size_t s4, mp_size_t n4, mp_size_t n6, mp_limb_t r30)
{
mp_size_t n1, n2, n3, n5, n7, t4;
mp_limb_t saved, saved2, cy;
t4 = s4 + 1;
mpn_add_n(r2, r2, r5, s4);
if (n6 < 0)
mpn_add_n(r6, r5, r6, s4);
else
mpn_sub_n(r6, r5, r6, s4);
/* r6 is now in twos complement format */
saved = r3[0];
r3[0] = r30;
if (n4 < 0)
mpn_add_n(r4, r3, r4, s4);
else
mpn_sub_n(r4, r3, r4, s4);
r3[0] = saved;
/* r4 is now in twos complement format */
mpn_sub_n(r5, r5, r1, s4);
#if HAVE_NATIVE_mpn_sublsh_n
r5[s4-1] -= mpn_sublsh_n(r5, r5, r7, s4-1, 6);
#else
r5[s4-1] -= mpn_submul_1(r5, r7, s4-1, 64);
#endif
TC4_RSHIFT1(r4, s4);
saved = r3[0];
r3[0] = r30;
mpn_sub_n(r3, r3, r4, s4);
r30 = r3[0];
r3[0] = saved;
mpn_double(r5, s4);
mpn_sub_n(r5, r5, r6, s4);
saved = r3[0];
r3[0] = r30;
mpn_submul_1(r2, r3, s4, 65);
r3[0] = saved;
saved2 = r7[s4-1];
r7[s4-1] = CNST_LIMB(0); // r7 is always positive so no sign extend needed
saved = r3[0];
r3[0] = r30;
#if HAVE_NATIVE_mpn_subadd_n
mpn_subadd_n(r3, r3, r7, r1, s4);
#else
mpn_sub_n(r3, r3, r7, s4);
mpn_sub_n(r3, r3, r1, s4);
#endif
r7[s4-1] = saved2;
r30 = r3[0];
mpn_addmul_1(r2, r3, s4, 45);
#if HAVE_NATIVE_mpn_sublsh_n
cy = mpn_sublsh_n(r5, r5, r3, s4 - 1, 3);
#else
cy = mpn_submul_1(r5, r3, s4 - 1, 8);
#endif
r3[0] = saved;
r3[0] -= (cy + 8*r3[s4-1]);
mpn_rshift(r5, r5, s4, 3);
mpn_divexact_by3(r5, r5, s4);
mpn_sub_n(r6, r6, r2, s4);
#if HAVE_NATIVE_mpn_sublsh_n
mpn_sublsh_n(r2, r2, r4, s4, 4);
#else
mpn_submul_1(r2, r4, s4, 16);
#endif
mpn_rshift(r2, r2, s4, 1);
mpn_divexact_by3(r2, r2, s4);
mpn_divexact_by3(r2, r2, s4);
saved = r3[0];
r3[0] = r30;
cy = mpn_sub_n(r3, r3, r5, s4 - 1);
r30 = r3[0];
r3[0] = saved;
r3[s4-1] -= (cy + r5[s4-1]);
mpn_sub_n(r4, r4, r2, s4);
mpn_addmul_1(r6, r2, s4, 30);
mpn_divexact_byfobm1(r6, r6, s4, CNST_LIMB(15), CNST_LIMB(~0/15));
mpn_rshift(r6, r6, s4, 2);
mpn_sub_n(r2, r2, r6, s4);
TC4_NORM(r1, n1, s4);
TC4_NORM(r2, n2, s4);
(*rpn) = 6*sn+1;
cy = mpn_add_1(r3, r3, *rpn - 4*sn, r30); /* don't forget to add r3[0] back in */
if (cy)
{
rp[*rpn] = cy;
(*rpn)++;
}
tc4_copy(rp, rpn, 5*sn, r2, n2);
tc4_copy(rp, rpn, 6*sn, r1, n1);
tc4_copy(rp, rpn, sn, r6, s4);
tc4_copy(rp, rpn, 3*sn, r4, s4);
}
/*
We have
{v0,2k} {v1,2k+1} {c+4k+1,r+r2-1}
v0 v1 {-}vinf
vinf0 is the first limb of vinf, which is overwritten by v1
{vm1,2k+1} {v2, 2k+1}
ws is temporary space
sa is the sign of vm1
rr2 is r+r2
We want to compute
t1 <- (3*v0+2*vm1+v2)/6-2*vinf
t2 <- (v1+vm1)/2
then the result is c0+c1*t+c2*t^2+c3*t^3+c4*t^4 where
c0 <- v0
c1 <- v1 - t1
c2 <- t2 - v0 - vinf
c3 <- t1 - t2
c4 <- vinf
*/
void
mpn_toom3_interpolate (mp_ptr c, mp_ptr v1, mp_ptr v2, mp_ptr vm1,
mp_ptr vinf, mp_size_t k, mp_size_t rr2, int sa,
mp_limb_t vinf0, mp_ptr ws)
{
mp_limb_t cy, saved;
mp_size_t twok = k + k;
mp_size_t kk1 = twok + 1;
mp_ptr c1, c2, c3, c4, c5;
mp_limb_t cout; /* final carry, should be zero at the end */
c1 = c + k;
c2 = c1 + k;
c3 = c2 + k;
c4 = c3 + k;
c5 = c4 + k;
#define v0 (c)
/* {c,2k} {c+2k,2k+1} {c+4k+1,r+r2-1}
v0 v1 {-}vinf
{vm1,2k+1} {v2, 2k+1}
*/
/* v2 <- v2 - vm1 */
if (sa < 0)
{
mpn_add_n(v2, v2, vm1, kk1);
} else
{
mpn_sub_n(v2, v2, vm1, kk1);
}
ASSERT_NOCARRY (mpn_divexact_by3 (v2, v2, kk1)); /* v2 <- v2 / 3 */
/* vm1 <- t2 := (v1 - sa*vm1) / 2
*/
if (sa < 0)
{
#ifdef HAVE_NATIVE_mpn_rsh1add_n
mpn_rsh1add_n (vm1, v1, vm1, kk1);
#else
mpn_add_n (vm1, vm1, v1, kk1);
mpn_half (vm1, kk1);
#endif
}
else
{
#ifdef HAVE_NATIVE_mpn_rsh1sub_n
mpn_rsh1sub_n (vm1, v1, vm1, kk1);
#else
mpn_sub_n (vm1, v1, vm1, kk1);
mpn_half (vm1, kk1);
#endif
}
/* v1 <- v1 - v0 - vinf */
saved = c4[0];
c4[0] = vinf0;
#if HAVE_NATIVE_mpn_subadd_n
cy = mpn_subadd_n(v1, v1, v0, c4, rr2);
#else
cy = mpn_sub_n(v1, v1, v0, rr2);
cy += mpn_sub_n(v1, v1, c4, rr2);
#endif
c4[0] = saved;
if (rr2 < twok)
{
v1[twok] -= mpn_sub_n(v1 + rr2, v1 + rr2, v0 + rr2, twok - rr2);
MPN_DECR_U(v1 + rr2, kk1 - rr2, cy);
}
else v1[twok] -= cy;
saved = c4[0];
c4[0] = vinf0;
/* subtract 5*vinf from v2,
*/
cy = mpn_submul_1 (v2, c4, rr2, CNST_LIMB(5));
MPN_DECR_U (v2 + rr2, kk1 - rr2, cy);
c4[0] = saved;
/* v2 = (v2 - v1)/2 (exact)
*/
#ifdef HAVE_NATIVE_mpn_rsh1sub_n
mpn_rsh1sub_n (v2, v2, v1, kk1);
#else
mpn_sub_n (v2, v2, v1, kk1);
mpn_half (v2, kk1);
#endif
/* v1 = v1 - vm1
*/
mpn_sub_n(v1, v1, vm1, kk1);
/* vm1 = vm1 - v2 and add vm1 in {c+k, ...} */
#if HAVE_NATIVE_mpn_addsub_n
cy = mpn_addsub_n(c1, c1, vm1, v2, kk1);
#else
mpn_sub_n(vm1, vm1, v2, kk1);
cy = mpn_add_n (c1, c1, vm1, kk1);
#endif
ASSERT_NOCARRY (mpn_add_1(c3 + 1, c3 + 1, rr2 + k - 1, cy)); /* 4k+rr2-(3k+1) = rr2+k-1 */
/* don't forget to add vinf0 in {c+4k, ...} */
ASSERT_NOCARRY (mpn_add_1(c4, c4, rr2, vinf0));
/* add v2 in {c+3k, ...} */
if (rr2 <= k + 1)
ASSERT_NOCARRY (mpn_add_n (c3, c3, v2, k+rr2));
else
{
cy = mpn_add_n (c3, c3, v2, kk1);
if (cy) ASSERT_NOCARRY (mpn_add_1(c5 + 1, c5 + 1, rr2 - k - 1, cy)); /* 4k+rr2-(5k+1) = rr2-k-1 */
}
#undef v0
}
