void
mpn_toom3_mul_n (mp_ptr c, mp_srcptr a, mp_srcptr b, mp_size_t n, mp_ptr t)
{
mp_size_t k, k1, kk1, r, twok, twor;
mp_limb_t cy, cc, saved, vinf0, cinf0;
mp_ptr trec;
int sa, sb;
mp_ptr c1, c2, c3, c4, c5;
ASSERT(GMP_NUMB_BITS >= 6);
ASSERT(n >= 17); /* so that r <> 0 and 5k+3 <= 2n */
/*
The algorithm is the following:
0. k = ceil(n/3), r = n - 2k, B = 2^(GMP_NUMB_BITS), t = B^k
1. split a and b in three parts each a0, a1, a2 and b0, b1, b2
with a0, a1, b0, b1 of k limbs, and a2, b2 of r limbs
2. v0 <- a0*b0
v1 <- (a0+a1+a2)*(b0+b1+b2)
v2 <- (a0+2*a1+4*a2)*(b0+2*b1+4*b2)
vm1 <- (a0-a1+a2)*(b0-b1+b2)
vinf <- a2*b2
t1 <- (3*v0+2*vm1+v2)/6-2*vinf
t2 <- (v1+vm1)/2
3. 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
*/
k = (n + 2) / 3; /* ceil(n/3) */
twok = 2 * k;
k1 = k + 1;
kk1 = k + k1;
r = n - twok; /* last chunk */
twor = 2 * r;
c1 = c + k;
c2 = c1 + k;
c3 = c2 + k;
c4 = c3 + k;
c5 = c4 + k;
trec = t + 4 * k + 3; /* trec = v2 + (2k+2) */
/* put a0+a2 in {c, k+1}, and b0+b2 in {c+k+1, k+1};
put a0+a1+a2 in {c+2k+2, k+1} and b0+b1+b2 in {c+3k+3,k+1}
[requires 4k+4 <= 2n, ie. n >= 8] */
cy = mpn_add_n (c, a, a + twok, r);
cc = mpn_add_n (c1 + 1, b, b + twok, r);
if (r < k)
{
__GMPN_ADD_1 (cy, c + r, a + r, k - r, cy);
__GMPN_ADD_1 (cc, c1 + 1 + r, b + r, k - r, cc);
}
c3[2] = (c1[0] = cy) + mpn_add_n (c2 + 2, c, a + k, k);
c4[3] = (c2[1] = cc) + mpn_add_n (c3 + 3, c1 + 1, b + k, k);
#define v2 (t+2*k+1)
#define vinf (t+4*k+2)
/* compute v1 := (a0+a1+a2)*(b0+b1+b2) in {t, 2k+1};
since v1 < 9*B^(2k), v1 uses only 2k+1 words if GMP_NUMB_BITS >= 4 */
TOOM3_MUL_REC (t, c2 + 2, c3 + 3, k1, trec);
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v1
*/
/* put |a0-a1+a2| in {c, k+1} and |b0-b1+b2| in {c+4k+2,k+1} */
/* sa = sign(a0-a1+a2) */
sa = (c[k] != 0) ? 1 : mpn_cmp (c, a + k, k);
c[k] = (sa >= 0) ? c[k] - mpn_sub_n (c, c, a + k, k)
: mpn_sub_n (c, a + k, c, k);
/* b0+b2 is in {c+k+1, k+1} now */
sb = (c2[1] != 0) ? 1 : mpn_cmp (c1 + 1, b + k, k);
c5[2] = (sb >= 0) ? c2[1] - mpn_sub_n (c4 + 2, c1 + 1, b + k, k)
: mpn_sub_n (c4 + 2, b + k, c1 + 1, k);
sa *= sb; /* sign of vm1 */
/* compute vm1 := (a0-a1+a2)*(b0-b1+b2) in {c+2k, 2k+1};
since |vm1| < 4*B^(2k), vm1 uses only 2k+1 limbs */
TOOM3_MUL_REC (c2, c, c4 + 2, k1, trec);
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
vm1 v1
*/
/* compute a0+2a1+4a2 in {c, k+1} and b0+2b1+4b2 in {c+4k+2, k+1}
[requires 5k+3 <= 2n, i.e. n >= 17] */
#ifdef HAVE_NATIVE_mpn_addlsh1_n
c1[0] = mpn_addlsh1_n (c, a + k, a + twok, r);
c5[2] = mpn_addlsh1_n (c4 + 2, b + k, b + twok, r);
if (r < k)
{
__GMPN_ADD_1 (c1[0], c + r, a + k + r, k - r, c1[0]);
__GMPN_ADD_1 (c5[2], c4 + 2 + r, b + k + r, k - r, c5[2]);
}
c1[0] = 2 * c1[0] + mpn_addlsh1_n (c, a, c, k);
c5[2] = 2 * c5[2] + mpn_addlsh1_n (c4 + 2, b, c4 + 2, k);
#else
c[r] = mpn_lshift (c, a + twok, r, 1);
c4[r + 2] = mpn_lshift (c4 + 2, b + twok, r, 1);
if (r < k)
{
MPN_ZERO(c + r + 1, k - r);
MPN_ZERO(c4 + r + 3, k - r);
}
c1[0] += mpn_add_n (c, c, a + k, k);
c5[2] += mpn_add_n (c4 + 2, c4 + 2, b + k, k);
mpn_lshift (c, c, k1, 1);
mpn_lshift (c4 + 2, c4 + 2, k1, 1);
c1[0] += mpn_add_n (c, c, a, k);
c5[2] += mpn_add_n (c4 + 2, c4 + 2, b, k);
#endif
/* compute v2 := (a0+2a1+4a2)*(b0+2b1+4b2) in {t+2k+1, 2k+1}
v2 < 49*B^k so v2 uses at most 2k+1 limbs if GMP_NUMB_BITS >= 6 */
TOOM3_MUL_REC (v2, c, c4 + 2, k1, trec);
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
vm1 v1 v2
*/
/* compute v0 := a0*b0 in {c, 2k} */
TOOM3_MUL_REC (c, a, b, k, trec);
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 vm1 v1 v2
*/
/* now compute (3v0+2vm1+v2)/6 = [v0 + (2vm1+v2)/3]/2
v2 <- v2+2vm1 = 3*(a0*b0+2*a0*b2+2*a1*b1+2*a1*b2+2*a2*b0+2*a2*b1+6*a2*b2),
thus 0 <= v2 < 51*B^(2k) < 2^6*B^(2k)
Uses temporary space {t+4k+2,2k+1}, requires T(n) >= 6k+3.
*/
if (sa >= 0)
{
#ifdef HAVE_NATIVE_mpn_addlsh1_n
mpn_addlsh1_n (v2, v2, c2, kk1);
#else
/* we can use vinf=t+4k+2 as workspace since it is not full yet */
mpn_lshift (vinf, c2, kk1, 1);
mpn_add_n (v2, v2, vinf, kk1);
#endif
}
else
{
#ifdef HAVE_NATIVE_mpn_sublsh1_n
mpn_sublsh1_n (v2, v2, c2, kk1);
#else
/* we can use vinf=t+4k+2 as workspace since it is not full yet */
mpn_lshift (vinf, c2, kk1, 1);
mpn_sub_n (v2, v2, vinf, kk1);
#endif
}
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 vm1 v1 v2+2vm1 */
/* compute vinf := a2*b2 in {t+4k+2, 2r}: first put it in {c4, 2r},
then copy it in {t+4k+2,2r} */
saved = c4[0];
TOOM3_MUL_REC (c4, a + twok, b + twok, r, trec);
cinf0 = mpn_add_n (vinf, c4, c, twor); /* {v0,2r} + {vinf,2r} */
vinf0 = c4[0];
c4[0] = saved;
toom3_interpolate (c, t, v2, c2, vinf, k, r, sa, vinf0, cinf0, vinf + twor);
#undef v2
#undef vinf
}
/* put in {c, 2n} where n = 2k+r the value of {v0,2k} (already in place)
+ B^k * [{v1, 2k+1} - {t1, 2k+1}]
+ B^(2k) * [{t2, 2k+1} - {v0+vinf, 2k}]
+ B^(3k) * [{t1, 2k+1} - {t2, 2k+1}]
+ B^(4k) * {vinf,2r} (high 2r-1 limbs already in place)
where {t1, 2k+1} = (3*{v0,2k}+2*sa*{vm1,2k+1}+{v2,2k+1})/6-2*{vinf,2r}
{t2, 2k+1} = ({v1, 2k+1} + sa * {vm1, 2k+1})/2
(sa is the sign of {vm1, 2k+1}).
{vinf, 2r} stores the content of {v0, 2r} + {vinf, 2r}, with carry in cinf0.
vinf0 is the low limb of vinf.
ws is temporary space, and should have at least 2r limbs.
Think about:
The evaluated point a-b+c stands a good chance of having a zero carry
limb, a+b+c would have a 1/4 chance, and 4*a+2*b+c a 1/8 chance, roughly.
Perhaps this could be tested and stripped. Doing so before recursing
would be better than stripping at the start of mpn_toom3_mul_n/sqr_n,
since then the recursion could be based on the new size. Although in
truth the kara vs toom3 crossover is never so exact that one limb either
way makes a difference.
A small value like 1 or 2 for the carry could perhaps also be handled
with an add_n or addlsh1_n. Would that be faster than an extra limb on a
(recursed) multiply/square?
*/
static void
toom3_interpolate (mp_ptr c, mp_srcptr v1, mp_ptr v2, mp_ptr vm1,
mp_ptr vinf, mp_size_t k, mp_size_t r, int sa,
mp_limb_t vinf0, mp_limb_t cinf0, mp_ptr ws)
{
mp_limb_t cy, saved;
unsigned long twok = k + k;
unsigned long kk1 = twok + 1;
unsigned long twor = r + r;
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+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 |vm1| hi(vinf) v1 v2+2vm1 vinf
+lo(v0) */
ASSERT_NOCARRY (mpn_divexact_by3 (v2, v2, kk1)); /* v2 <- v2 / 3 */
#ifdef HAVE_NATIVE_mpn_rsh1add_n
mpn_rsh1add_n (v2, v2, v0, twok); /* v2 <- (lo(v2)+v0) / 2, exact */
cy = v2[twok] & 1; /* add high limb of v2 divided by 2 */
v2[twok] >>= 1;
MPN_INCR_U (v2 + twok - 1, 2, cy << (GMP_NUMB_BITS - 1));
#else
v2[twok] += mpn_add_n (v2, v2, v0, twok);
mpn_rshift (v2, v2, kk1, 1);
#endif
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 |vm1| hi(vinf) v1 (3v0+2vm1+v2) vinf
/6 +lo(v0) */
/* vm1 <- t2 := (v1 + sa*vm1) / 2
t2 = a0*b0+a0*b2+a1*b1+a2*b0+a2*b2 >= 0
No carry comes out from {v1, kk1} +/- {vm1, kk1},
and the division by two is exact */
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_rshift (vm1, vm1, kk1, 1);
#endif
}
else
{
#ifdef HAVE_NATIVE_mpn_rsh1sub_n
mpn_rsh1sub_n (vm1, v1, vm1, kk1);
#else
mpn_sub_n (vm1, v1, vm1, kk1);
mpn_rshift (vm1, vm1, kk1, 1);
#endif
}
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 t2 hi(vinf) v1 t1 vinf+lo(v0) */
/* subtract 2*vinf to v2,
result is t1 := a0*b0+a0*b2+a1*b1+a1*b2+a2*b0+a2*b1+a2*b2 >= 0 */
saved = c4[0];
c4[0] = vinf0;
#ifdef HAVE_NATIVE_mpn_sublsh1_n
cy = mpn_sublsh1_n (v2, v2, c4, twor);
#else
cy = mpn_lshift (ws, c4, twor, 1);
cy += mpn_sub_n (v2, v2, ws, twor);
#endif
MPN_DECR_U (v2 + twor, kk1 - twor, cy);
c4[0] = saved;
/* subtract {t2, 2k+1} in {c+3k, 2k+1} i.e. in {t2+k, 2k+1}:
by chunks of k limbs from right to left to avoid overlap */
#define t2 (vm1)
/* a borrow may occur in one of the 2 following __GMPN_SUB_1 calls, but since
the final result is nonnegative, it will be compensated later on */
__GMPN_SUB_1 (cout, c5, c5, twor - k, t2[twok]);
cy = mpn_sub_n (c4, c4, t2 + k, k);
__GMPN_SUB_1 (cout, c5, c5, twor - k, cy);
cy = mpn_sub_n (c3, c3, t2, k);
__GMPN_SUB_1 (cout, c4, c4, twor, cy);
/* don't forget to add vinf0 in {c+4k, ...} */
__GMPN_ADD_1 (cout, c4, c4, twor, vinf0);
/* c c+k c+2k c+3k c+4k+1 t t+2k+1 t+4k+2
v0 t2 hi(vinf) v1 t1 vinf
-t2 +lo(v0)
*/
/* c c+k c+2k c+3k c+4k t t+2k+1 t+4k+2
v0 t2 vinf v1 t1 vinf
-t2 +lo(v0)
*/
/* subtract v0+vinf in {c+2k, ...} */
cy = cinf0 + mpn_sub_n (c2, c2, vinf, twor);
if (twor < twok)
{
__GMPN_SUB_1 (cy, c2 + twor, c2 + twor, twok - twor, cy);
cy += mpn_sub_n (c2 + twor, c2 + twor, v0 + twor, twok - twor);
}
__GMPN_SUB_1 (cout, c4, c4, twor, cy); /* 2n-4k = 2r */
/* c c+k c+2k c+3k c+4k t t+2k+1 t+4k+2
v0 t2 vinf v1 t1 vinf
-v0 -t2 +lo(v0)
-vinf */
/* subtract t1 in {c+k, ...} */
cy = mpn_sub_n (c1, c1, v2, kk1);
__GMPN_SUB_1 (cout, c3 + 1, c3 + 1, twor + k - 1, cy); /* 2n-(3k+1)=k+2r-1 */
/* c c+k c+2k c+3k c+4k t t+2k+1 t+4k+2
v0 t2 vinf v1 t1 vinf
-t1 -v0 -t2
-vinf */
/* add t1 in {c+3k, ...} */
cy = mpn_add_n (c3, c3, v2, kk1);
__GMPN_ADD_1 (cout, c5 + 1, c5 + 1, twor - k - 1, cy); /* 2n-(5k+1) = 2r-k-1 */
/* c c+k c+2k c+3k c+4k t t+2k+1 t+4k+2
v0 t2 t1 vinf v1 t1 vinf
-t1 -v0 -t2
-vinf */
/* add v1 in {c+k, ...} */
cy = mpn_add_n (c1, c1, v1, kk1);
__GMPN_ADD_1 (cout, c3 + 1, c3 + 1, twor + k - 1, cy); /* 2n-(3k+1) = 2r+k-1 */
/* c c+k c+2k c+3k c+4k t t+2k+1 t+4k+2
v0 v1 t2 t1 vinf v1 t1 vinf
-t1 -v0 -t2
-vinf */
#undef v0
#undef t2
}
void
mpn_toom_interpolate_5pts (mp_ptr c, mp_ptr v2, mp_ptr vm1,
mp_size_t k, mp_size_t twor, 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, v1, c3, vinf, c5;
mp_limb_t cout; /* final carry, should be zero at the end */
c1 = c + k;
v1 = c1 + k;
c3 = v1 + k;
vinf = c3 + k;
c5 = vinf + k;
#define v0 (c)
/* (1) v2 <- v2-vm1 < v2+|vm1|, (16 8 4 2 1) - (1 -1 1 -1 1) =
thus 0 <= v2 < 50*B^(2k) < 2^6*B^(2k) (15 9 3 3 0)
*/
if (sa <= 0)
mpn_add_n (v2, v2, vm1, kk1);
else
mpn_sub_n (v2, v2, vm1, kk1);
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1 hi(vinf) |vm1| v2-vm1 EMPTY */
ASSERT_NOCARRY (mpn_divexact_by3 (v2, v2, kk1)); /* v2 <- v2 / 3 */
/* (5 3 1 1 0)*/
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1 hi(vinf) |vm1| (v2-vm1)/3 EMPTY */
/* (2) vm1 <- tm1 := (v1 - sa*vm1) / 2 [(1 1 1 1 1) - (1 -1 1 -1 1)] / 2 =
tm1 >= 0 (0 1 0 1 0)
No carry comes out from {v1, kk1} +/- {vm1, kk1},
and the division by two is exact */
if (sa <= 0)
{
#ifdef HAVE_NATIVE_mpn_rsh1add_n
mpn_rsh1add_n (vm1, v1, vm1, kk1);
#else
mpn_add_n (vm1, v1, vm1, kk1);
mpn_rshift (vm1, vm1, kk1, 1);
#endif
}
else
{
#ifdef HAVE_NATIVE_mpn_rsh1sub_n
mpn_rsh1sub_n (vm1, v1, vm1, kk1);
#else
mpn_sub_n (vm1, v1, vm1, kk1);
mpn_rshift (vm1, vm1, kk1, 1);
#endif
}
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1 hi(vinf) tm1 (v2-vm1)/3 EMPTY */
/* (3) v1 <- t1 := v1 - v0 (1 1 1 1 1) - (0 0 0 0 1) = (1 1 1 1 0)
t1 >= 0
*/
vinf[0] -= mpn_sub_n (v1, v1, c, twok);
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1-v0 hi(vinf) tm1 (v2-vm1)/3 EMPTY */
/* (4) v2 <- t2 := ((v2-vm1)/3-t1)/2 = (v2-vm1-3*t1)/6
t2 >= 0 [(5 3 1 1 0) - (1 1 1 1 0)]/2 = (2 1 0 0 0)
*/
#ifdef HAVE_NATIVE_mpn_rsh1sub_n
mpn_rsh1sub_n (v2, v2, v1, kk1);
#else
mpn_sub_n (v2, v2, v1, kk1);
mpn_rshift (v2, v2, kk1, 1);
#endif
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1-v0 hi(vinf) tm1 (v2-vm1-3t1)/6 EMPTY */
/* (5) v1 <- t1-tm1 (1 1 1 1 0) - (0 1 0 1 0) = (1 0 1 0 0)
result is v1 >= 0
*/
mpn_sub_n (v1, v1, vm1, kk1);
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1-v0-tm1 hi(vinf) tm1 (v2-vm1-3t1)/6 EMPTY */
/* (6) v2 <- v2 - 2*vinf, (2 1 0 0 0) - 2*(1 0 0 0 0) = (0 1 0 0 0)
result is v2 >= 0 */
saved = vinf[0]; /* Remember v1's highest byte (will be overwritten). */
vinf[0] = vinf0; /* Set the right value for vinf0 */
#ifdef HAVE_NATIVE_mpn_sublsh1_n
cy = mpn_sublsh1_n (v2, v2, vinf, twor);
#else
cy = mpn_lshift (ws, vinf, twor, 1);
cy += mpn_sub_n (v2, v2, ws, twor);
#endif
MPN_DECR_U (v2 + twor, kk1 - twor, cy);
/* (7) v1 <- v1 - vinf, (1 0 1 0 0) - (1 0 0 0 0) = (0 0 1 0 0)
result is >= 0 */
cy = mpn_sub_n (v1, v1, vinf, twor); /* vinf is at most twor long. */
vinf[0] = saved;
MPN_DECR_U (v1 + twor, kk1 - twor, cy); /* Treat the last bytes. */
__GMPN_ADD_1 (cout, vinf, vinf, twor, vinf0); /* Add vinf0, propagate carry. */
/* (8) vm1 <- vm1-t2 (0 1 0 1 0) - (0 1 0 0 0) = (0 0 0 1 0)
vm1 >= 0
*/
mpn_sub_n (vm1, vm1, v2, kk1); /* No overlapping here. */
/********************* Beginning the final phase **********************/
/* {c,2k} {c+2k,2k } {c+4k ,2r } {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 t1 hi(t1)+vinf tm1 (v2-vm1-3t1)/6 EMPTY */
/* (9) add t2 in {c+3k, ...} */
cy = mpn_add_n (c3, c3, v2, kk1);
__GMPN_ADD_1 (cout, c5 + 1, c5 + 1, twor - k - 1, cy); /* 2n-(5k+1) = 2r-k-1 */
/* {c,2k} {c+2k,2k } {c+4k ,2r } {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 t1 hi(t1)+vinf tm1 (v2-vm1-3t1)/6 EMPTY */
/* c c+k c+2k c+3k c+4k t t+2k+1 t+4k+2
v0 t1 vinf tm1 t2
+t2 */
/* add vm1 in {c+k, ...} */
cy = mpn_add_n (c1, c1, vm1, kk1);
__GMPN_ADD_1 (cout, c3 + 1, c3 + 1, twor + k - 1, cy); /* 2n-(3k+1) = 2r+k-1 */
/* c c+k c+2k c+3k c+4k t t+2k+1 t+4k+2
v0 t1 vinf tm1 t2
+tm1 +t2 */
#undef v0
#undef t2
}
void
mpn_toom_interpolate_5pts (mp_ptr c, mp_ptr v2, mp_ptr vm1,
mp_size_t k, mp_size_t twor, int sa,
mp_limb_t vinf0)
{
mp_limb_t cy, saved;
mp_size_t twok;
mp_size_t kk1;
mp_ptr c1, v1, c3, vinf;
twok = k + k;
kk1 = twok + 1;
c1 = c + k;
v1 = c1 + k;
c3 = v1 + k;
vinf = c3 + k;
#define v0 (c)
/* (1) v2 <- v2-vm1 < v2+|vm1|, (16 8 4 2 1) - (1 -1 1 -1 1) =
thus 0 <= v2 < 50*B^(2k) < 2^6*B^(2k) (15 9 3 3 0)
*/
if (sa)
ASSERT_NOCARRY (mpn_add_n (v2, v2, vm1, kk1));
else
ASSERT_NOCARRY (mpn_sub_n (v2, v2, vm1, kk1));
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1 hi(vinf) |vm1| v2-vm1 EMPTY */
ASSERT_NOCARRY (mpn_divexact_by3 (v2, v2, kk1)); /* v2 <- v2 / 3 */
/* (5 3 1 1 0)*/
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1 hi(vinf) |vm1| (v2-vm1)/3 EMPTY */
/* (2) vm1 <- tm1 := (v1 - vm1) / 2 [(1 1 1 1 1) - (1 -1 1 -1 1)] / 2 =
tm1 >= 0 (0 1 0 1 0)
No carry comes out from {v1, kk1} +/- {vm1, kk1},
and the division by two is exact.
If (sa!=0) the sign of vm1 is negative */
if (sa)
{
#ifdef HAVE_NATIVE_mpn_rsh1add_n
mpn_rsh1add_n (vm1, v1, vm1, kk1);
#else
ASSERT_NOCARRY (mpn_add_n (vm1, v1, vm1, kk1));
ASSERT_NOCARRY (mpn_rshift (vm1, vm1, kk1, 1));
#endif
}
else
{
#ifdef HAVE_NATIVE_mpn_rsh1sub_n
mpn_rsh1sub_n (vm1, v1, vm1, kk1);
#else
ASSERT_NOCARRY (mpn_sub_n (vm1, v1, vm1, kk1));
ASSERT_NOCARRY (mpn_rshift (vm1, vm1, kk1, 1));
#endif
}
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1 hi(vinf) tm1 (v2-vm1)/3 EMPTY */
/* (3) v1 <- t1 := v1 - v0 (1 1 1 1 1) - (0 0 0 0 1) = (1 1 1 1 0)
t1 >= 0
*/
vinf[0] -= mpn_sub_n (v1, v1, c, twok);
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1-v0 hi(vinf) tm1 (v2-vm1)/3 EMPTY */
/* (4) v2 <- t2 := ((v2-vm1)/3-t1)/2 = (v2-vm1-3*t1)/6
t2 >= 0 [(5 3 1 1 0) - (1 1 1 1 0)]/2 = (2 1 0 0 0)
*/
#ifdef HAVE_NATIVE_mpn_rsh1sub_n
mpn_rsh1sub_n (v2, v2, v1, kk1);
#else
ASSERT_NOCARRY (mpn_sub_n (v2, v2, v1, kk1));
ASSERT_NOCARRY (mpn_rshift (v2, v2, kk1, 1));
#endif
/* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
v0 v1-v0 hi(vinf) tm1 (v2-vm1-3t1)/6 EMPTY */
/* (5) v1 <- t1-tm1 (1 1 1 1 0) - (0 1 0 1 0) = (1 0 1 0 0)
result is v1 >= 0
*/
ASSERT_NOCARRY (mpn_sub_n (v1, v1, vm1, kk1));
/* We do not need to read the value in vm1, so we add it in {c+k, ...} */
cy = mpn_add_n (c1, c1, vm1, kk1);
MPN_INCR_U (c3 + 1, twor + k - 1, cy); /* 2n-(3k+1) = 2r+k-1 */
/* Memory allocated for vm1 is now free, it can be recycled ...*/
/* (6) v2 <- v2 - 2*vinf, (2 1 0 0 0) - 2*(1 0 0 0 0) = (0 1 0 0 0)
result is v2 >= 0 */
saved = vinf[0]; /* Remember v1's highest byte (will be overwritten). */
vinf[0] = vinf0; /* Set the right value for vinf0 */
#ifdef HAVE_NATIVE_mpn_sublsh1_n
cy = mpn_sublsh1_n (v2, v2, vinf, twor);
#else
/* Overwrite unused vm1 */
cy = mpn_lshift (vm1, vinf, twor, 1);
cy += mpn_sub_n (v2, v2, vm1, twor);
#endif
MPN_DECR_U (v2 + twor, kk1 - twor, cy);
/* Current matrix is
[1 0 0 0 0; vinf
0 1 0 0 0; v2
1 0 1 0 0; v1
0 1 0 1 0; vm1
0 0 0 0 1] v0
Some vaues already are in-place (we added vm1 in the correct position)
| vinf| v1 | v0 |
| vm1 |
One still is in a separated area
| +v2 |
We have to compute v1-=vinf; vm1 -= v2,
|-vinf|
| -v2 |
Carefully reordering operations we can avoid to compute twice the sum
of the high half of v2 plus the low half of vinf.
*/
/* Add the high half of t2 in {vinf} */
if ( LIKELY(twor > k + 1) ) { /* This is the expected flow */
cy = mpn_add_n (vinf, vinf, v2 + k, k + 1);
MPN_INCR_U (c3 + kk1, twor - k - 1, cy); /* 2n-(5k+1) = 2r-k-1 */
} else { /* triggered only by very unbalanced cases like
(k+k+(k-2))x(k+k+1) , should be handled by toom32 */
ASSERT_NOCARRY (mpn_add_n (vinf, vinf, v2 + k, twor));
}
/* (7) v1 <- v1 - vinf, (1 0 1 0 0) - (1 0 0 0 0) = (0 0 1 0 0)
result is >= 0 */
/* Side effect: we also subtracted (high half) vm1 -= v2 */
cy = mpn_sub_n (v1, v1, vinf, twor); /* vinf is at most twor long. */
vinf0 = vinf[0]; /* Save again the right value for vinf0 */
vinf[0] = saved;
MPN_DECR_U (v1 + twor, kk1 - twor, cy); /* Treat the last bytes. */
/* (8) vm1 <- vm1-v2 (0 1 0 1 0) - (0 1 0 0 0) = (0 0 0 1 0)
Operate only on the low half.
*/
cy = mpn_sub_n (c1, c1, v2, k);
MPN_DECR_U (v1, kk1, cy);
/********************* Beginning the final phase **********************/
/* Most of the recomposition was done */
/* add t2 in {c+3k, ...}, but only the low half */
cy = mpn_add_n (c3, c3, v2, k);
vinf[0] += cy;
ASSERT(vinf[0] >= cy); /* No carry */
MPN_INCR_U (vinf, twor, vinf0); /* Add vinf0, propagate carry. */
#undef v0
}
void
check (void)
{
mp_limb_t wp[100], xp[100], yp[100];
mp_size_t size = 100;
refmpn_zero (xp, size);
refmpn_zero (yp, size);
refmpn_zero (wp, size);
pre ("mpn_add_n");
mpn_add_n (wp, xp, yp, size);
post ();
#if HAVE_NATIVE_mpn_add_nc
pre ("mpn_add_nc");
mpn_add_nc (wp, xp, yp, size, CNST_LIMB(0));
post ();
#endif
#if HAVE_NATIVE_mpn_addlsh1_n
pre ("mpn_addlsh1_n");
mpn_addlsh1_n (wp, xp, yp, size);
post ();
#endif
#if HAVE_NATIVE_mpn_and_n
pre ("mpn_and_n");
mpn_and_n (wp, xp, yp, size);
post ();
#endif
#if HAVE_NATIVE_mpn_andn_n
pre ("mpn_andn_n");
mpn_andn_n (wp, xp, yp, size);
post ();
#endif
pre ("mpn_addmul_1");
mpn_addmul_1 (wp, xp, size, yp[0]);
post ();
#if HAVE_NATIVE_mpn_addmul_1c
pre ("mpn_addmul_1c");
mpn_addmul_1c (wp, xp, size, yp[0], CNST_LIMB(0));
post ();
#endif
#if HAVE_NATIVE_mpn_com_n
pre ("mpn_com_n");
mpn_com_n (wp, xp, size);
post ();
#endif
#if HAVE_NATIVE_mpn_copyd
pre ("mpn_copyd");
mpn_copyd (wp, xp, size);
post ();
#endif
#if HAVE_NATIVE_mpn_copyi
pre ("mpn_copyi");
mpn_copyi (wp, xp, size);
post ();
#endif
pre ("mpn_divexact_1");
mpn_divexact_1 (wp, xp, size, CNST_LIMB(123));
post ();
pre ("mpn_divexact_by3c");
mpn_divexact_by3c (wp, xp, size, CNST_LIMB(0));
post ();
pre ("mpn_divrem_1");
mpn_divrem_1 (wp, (mp_size_t) 0, xp, size, CNST_LIMB(123));
post ();
#if HAVE_NATIVE_mpn_divrem_1c
pre ("mpn_divrem_1c");
mpn_divrem_1c (wp, (mp_size_t) 0, xp, size, CNST_LIMB(123), CNST_LIMB(122));
post ();
#endif
pre ("mpn_gcd_1");
xp[0] |= 1;
notdead += (unsigned long) mpn_gcd_1 (xp, size, CNST_LIMB(123));
post ();
#if HAVE_NATIVE_mpn_gcd_finda
pre ("mpn_gcd_finda");
xp[0] |= 1;
xp[1] |= 1;
notdead += mpn_gcd_finda (xp);
post ();
#endif
pre ("mpn_hamdist");
notdead += mpn_hamdist (xp, yp, size);
post ();
#if HAVE_NATIVE_mpn_ior_n
pre ("mpn_ior_n");
mpn_ior_n (wp, xp, yp, size);
post ();
#endif
#if HAVE_NATIVE_mpn_iorn_n
pre ("mpn_iorn_n");
mpn_iorn_n (wp, xp, yp, size);
post ();
#endif
pre ("mpn_lshift");
mpn_lshift (wp, xp, size, 1);
post ();
pre ("mpn_mod_1");
notdead += mpn_mod_1 (xp, size, CNST_LIMB(123));
post ();
#if HAVE_NATIVE_mpn_mod_1c
pre ("mpn_mod_1c");
notdead += mpn_mod_1c (xp, size, CNST_LIMB(123), CNST_LIMB(122));
post ();
#endif
#if GMP_NUMB_BITS % 4 == 0
pre ("mpn_mod_34lsub1");
notdead += mpn_mod_34lsub1 (xp, size);
post ();
#endif
pre ("mpn_modexact_1_odd");
notdead += mpn_modexact_1_odd (xp, size, CNST_LIMB(123));
post ();
pre ("mpn_modexact_1c_odd");
notdead += mpn_modexact_1c_odd (xp, size, CNST_LIMB(123), CNST_LIMB(456));
post ();
pre ("mpn_mul_1");
mpn_mul_1 (wp, xp, size, yp[0]);
post ();
#if HAVE_NATIVE_mpn_mul_1c
pre ("mpn_mul_1c");
mpn_mul_1c (wp, xp, size, yp[0], CNST_LIMB(0));
post ();
#endif
#if HAVE_NATIVE_mpn_mul_2
pre ("mpn_mul_2");
mpn_mul_2 (wp, xp, size-1, yp);
post ();
#endif
pre ("mpn_mul_basecase");
mpn_mul_basecase (wp, xp, (mp_size_t) 3, yp, (mp_size_t) 3);
post ();
#if HAVE_NATIVE_mpn_nand_n
pre ("mpn_nand_n");
mpn_nand_n (wp, xp, yp, size);
post ();
#endif
#if HAVE_NATIVE_mpn_nior_n
pre ("mpn_nior_n");
mpn_nior_n (wp, xp, yp, size);
post ();
#endif
pre ("mpn_popcount");
notdead += mpn_popcount (xp, size);
post ();
pre ("mpn_preinv_mod_1");
notdead += mpn_preinv_mod_1 (xp, size, GMP_NUMB_MAX,
refmpn_invert_limb (GMP_NUMB_MAX));
post ();
#if USE_PREINV_DIVREM_1 || HAVE_NATIVE_mpn_preinv_divrem_1
pre ("mpn_preinv_divrem_1");
mpn_preinv_divrem_1 (wp, (mp_size_t) 0, xp, size, GMP_NUMB_MAX,
refmpn_invert_limb (GMP_NUMB_MAX), 0);
post ();
#endif
#if HAVE_NATIVE_mpn_rsh1add_n
pre ("mpn_rsh1add_n");
mpn_rsh1add_n (wp, xp, yp, size);
post ();
#endif
#if HAVE_NATIVE_mpn_rsh1sub_n
pre ("mpn_rsh1sub_n");
mpn_rsh1sub_n (wp, xp, yp, size);
post ();
#endif
pre ("mpn_rshift");
mpn_rshift (wp, xp, size, 1);
post ();
pre ("mpn_sqr_basecase");
mpn_sqr_basecase (wp, xp, (mp_size_t) 3);
post ();
pre ("mpn_submul_1");
mpn_submul_1 (wp, xp, size, yp[0]);
post ();
#if HAVE_NATIVE_mpn_submul_1c
pre ("mpn_submul_1c");
mpn_submul_1c (wp, xp, size, yp[0], CNST_LIMB(0));
post ();
#endif
pre ("mpn_sub_n");
mpn_sub_n (wp, xp, yp, size);
post ();
#if HAVE_NATIVE_mpn_sub_nc
pre ("mpn_sub_nc");
mpn_sub_nc (wp, xp, yp, size, CNST_LIMB(0));
post ();
#endif
#if HAVE_NATIVE_mpn_sublsh1_n
pre ("mpn_sublsh1_n");
mpn_sublsh1_n (wp, xp, yp, size);
post ();
#endif
#if HAVE_NATIVE_mpn_udiv_qrnnd
pre ("mpn_udiv_qrnnd");
mpn_udiv_qrnnd (&wp[0], CNST_LIMB(122), xp[0], CNST_LIMB(123));
post ();
#endif
#if HAVE_NATIVE_mpn_udiv_qrnnd_r
pre ("mpn_udiv_qrnnd_r");
mpn_udiv_qrnnd (CNST_LIMB(122), xp[0], CNST_LIMB(123), &wp[0]);
post ();
#endif
#if HAVE_NATIVE_mpn_umul_ppmm
pre ("mpn_umul_ppmm");
mpn_umul_ppmm (&wp[0], xp[0], yp[0]);
post ();
#endif
#if HAVE_NATIVE_mpn_umul_ppmm_r
pre ("mpn_umul_ppmm_r");
mpn_umul_ppmm_r (&wp[0], xp[0], yp[0]);
post ();
#endif
#if HAVE_NATIVE_mpn_xor_n
pre ("mpn_xor_n");
mpn_xor_n (wp, xp, yp, size);
post ();
#endif
#if HAVE_NATIVE_mpn_xnor_n
pre ("mpn_xnor_n");
mpn_xnor_n (wp, xp, yp, size);
post ();
#endif
}
