/* Multiply M by M1 from the right. Since the M1 elements fit in
GMP_NUMB_BITS - 1 bits, M grows by at most one limb. Needs
temporary space M->n */
static void
ngcd_matrix_mul_1 (struct ngcd_matrix *M, const struct ngcd_matrix1 *M1)
{
unsigned row;
mp_limb_t grow;
for (row = 0, grow = 0; row < 2; row++)
{
mp_limb_t c0, c1;
/* Compute (u, u') <-- (r00 u + r10 u', r01 u + r11 u') as
t = u
u *= r00
u += r10 * u'
u' *= r11
u' += r01 * t
*/
MPN_COPY (M->tp, M->p[row][0], M->n);
c0 = mpn_mul_1 (M->p[row][0], M->p[row][0], M->n, M1->u[0][0]);
c0 += mpn_addmul_1 (M->p[row][0], M->p[row][1], M->n, M1->u[1][0]);
M->p[row][0][M->n] = c0;
c1 = mpn_mul_1 (M->p[row][1], M->p[row][1], M->n, M1->u[1][1]);
c1 += mpn_addmul_1 (M->p[row][1], M->tp, M->n, M1->u[0][1]);
M->p[row][1][M->n] = c1;
grow |= (c0 | c1);
}
M->n += (grow != 0);
ASSERT (M->n < M->alloc);
}
/* Assumes poly1 and poly2 are not length 0 and 0 < trunc <= len1 + len2 - 1 */
void
_nmod_poly_mullow_classical(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, slong trunc, nmod_t mod)
{
if (len1 == 1 || trunc == 1) /* Special case if the length of output is 1 */
{
res[0] = n_mulmod2_preinv(poly1[0], poly2[0], mod.n, mod.ninv);
}
else /* Ordinary case */
{
slong i;
slong bits = FLINT_BITS - (slong) mod.norm;
slong log_len = FLINT_BIT_COUNT(len2);
if (2 * bits + log_len <= FLINT_BITS)
{
/* Set res[i] = poly1[i]*poly2[0] */
mpn_mul_1(res, poly1, FLINT_MIN(len1, trunc), poly2[0]);
if (len2 != 1)
{
/* Set res[i+len1-1] = in1[len1-1]*in2[i] */
if (trunc > len1)
mpn_mul_1(res + len1, poly2 + 1, trunc - len1,
poly1[len1 - 1]);
/* out[i+j] += in1[i]*in2[j] */
for (i = 0; i < FLINT_MIN(len1, trunc) - 1; i++)
mpn_addmul_1(res + i + 1, poly2 + 1,
FLINT_MIN(len2, trunc - i) - 1, poly1[i]);
}
_nmod_vec_reduce(res, res, trunc, mod);
}
else
{
/* Set res[i] = poly1[i]*poly2[0] */
_nmod_vec_scalar_mul_nmod(res, poly1, FLINT_MIN(len1, trunc),
poly2[0], mod);
if (len2 == 1)
return;
/* Set res[i+len1-1] = in1[len1-1]*in2[i] */
if (trunc > len1)
_nmod_vec_scalar_mul_nmod(res + len1, poly2 + 1, trunc - len1,
poly1[len1 - 1], mod);
/* out[i+j] += in1[i]*in2[j] */
for (i = 0; i < FLINT_MIN(len1, trunc) - 1; i++)
_nmod_vec_scalar_addmul_nmod(res + i + 1, poly2 + 1,
FLINT_MIN(len2, trunc - i) - 1,
poly1[i], mod);
}
}
}
void
mpn_mullo_basecase (mp_ptr rp, mp_srcptr up, mp_srcptr vp, mp_size_t n)
{
mp_limb_t h;
h = up[0] * vp[n - 1];
if (n != 1)
{
mp_size_t i;
mp_limb_t v0;
v0 = *vp++;
h += up[n - 1] * v0 + mpn_mul_1 (rp, up, n - 1, v0);
rp++;
for (i = n - 2; i > 0; i--)
{
v0 = *vp++;
h += up[i] * v0 + mpn_addmul_1 (rp, up, i, v0);
rp++;
}
}
rp[0] = h;
}
void
mpz_mul_si(mpz_ptr prod, mpz_srcptr mult, long int small_mult)
{
mp_size_t size = mult->_mp_size;
mp_size_t sign_product = size;
mp_limb_t cy;
mp_size_t prod_size;
mp_ptr prod_ptr;
if(size == 0 || small_mult == 0)
{
prod->_mp_size = 0;
return;
}
size = ABS(size);
prod_size = size + 1;
if(prod->_mp_alloc < prod_size)
{
_mpz_realloc(prod, prod_size);
}
prod_ptr = prod->_mp_d;
cy = mpn_mul_1(prod_ptr, mult->_mp_d, size, (mp_limb_t)ABS(small_mult));
if(cy != 0)
{
prod_ptr[size] = cy;
size++;
}
prod->_mp_size = ((sign_product < 0) ^ (small_mult < 0)) ? -size : size;
}
/* (rp, 2n) = (xp, n)*(yp, n) / B^n */
inline static void
mpn_mulshort_n_basecase(mp_ptr rp, mp_srcptr xp, mp_srcptr yp, mp_size_t n)
{
mp_size_t i, k;
#if GMP_NAIL_BITS==0
mp_limb_t t1, t2, t3;
#endif
ASSERT(n >= 3); /* this restriction doesn't make a lot of sense in general */
ASSERT_MPN(xp, n);
ASSERT_MPN(yp, n);
ASSERT(!MPN_OVERLAP_P (rp, 2 * n, xp, n));
ASSERT(!MPN_OVERLAP_P (rp, 2 * n, yp, n));
k = n - 2; /* so want short product sum_(i + j >= k) x[i]y[j]B^(i + j) */
#if GMP_NAIL_BITS!=0
rp[n] = mpn_mul_1(rp + k, xp + k, 2, yp[0]);
#else
umul_ppmm(t1, rp[k], xp[k], yp[0]);
umul_ppmm(t3, t2, xp[k + 1], yp[0]);
add_ssaaaa(rp[n], rp[k + 1], t3, t2, 0, t1);
#endif
for (i = 1; i <= n - 2; i++)
rp[n + i] = mpn_addmul_1 (rp + k, xp + k - i, 2 + i, yp[i]);
rp[n + n - 1] = mpn_addmul_1 (rp + n - 1, xp, n, yp[n - 1]);
return;
}
mp_limb_t mpn_addadd_n(mp_ptr t,mp_srcptr x,mp_srcptr y,mp_srcptr z,mp_size_t n)
{mp_limb_t ret;
mp_srcptr a=x,b=y,c=z;
ASSERT(n>0);
ASSERT_MPN(x,n);ASSERT_MPN(y,n);ASSERT_MPN(z,n);//ASSERT_SPACE(t,n);
ASSERT(MPN_SAME_OR_SEPARATE_P(t,x,n));
ASSERT(MPN_SAME_OR_SEPARATE_P(t,y,n));
ASSERT(MPN_SAME_OR_SEPARATE_P(t,z,n));
if(t==x)
{if(t==y)
{if(t==z)
{
#ifdef HAVE_NATIVE_mpn_addlsh1_n
return mpn_addlsh1_n(t,x,y,n);
#else
return mpn_mul_1(t,x,n,3);
#endif
}
}
else
{MP_SRCPTR_SWAP(b,c);}
}
else
{MP_SRCPTR_SWAP(a,c);if(t==y)MP_SRCPTR_SWAP(a,b);}
ret=mpn_add_n(t,a,b,n);return ret+mpn_add_n(t,t,c,n);}
void
check_one (const char *desc, mpf_ptr got, mpf_srcptr u, mpir_ui v)
{
mp_size_t usize, usign;
mp_ptr wp;
mpf_t want;
MPF_CHECK_FORMAT (got);
/* this code not nailified yet */
ASSERT_ALWAYS (BITS_PER_UI <= GMP_NUMB_BITS);
usign = SIZ (u);
usize = ABS (usign);
wp = refmpn_malloc_limbs (usize + 1);
wp[usize] = mpn_mul_1 (wp, PTR(u), usize, (mp_limb_t) v);
PTR(want) = wp;
SIZ(want) = (usign >= 0 ? usize+1 : -(usize+1));
EXP(want) = EXP(u) + 1;
refmpf_normalize (want);
if (! refmpf_validate ("mpf_mul_ui", got, want))
{
mp_trace_base = -16;
printf (" %s\n", desc);
mpf_trace (" u", u);
printf (" v %ld 0x%lX\n", v, v);
abort ();
}
free (wp);
}
/* puts in {rp, n} the low part of {np, n} times {mp, n}, i.e. equivalent to:
mp_ptr tp;
TMP_DECL(marker);
TMP_MARK(marker);
tp = TMP_ALLOC_LIMBS (2 * n);
mpn_mul_n (tp, np, mp, n);
MPN_COPY (rp, tp, n);
TMP_FREE(marker);
*/
void
ecm_mul_lo_basecase (mp_ptr rp, mp_srcptr np, mp_srcptr mp, mp_size_t n)
{
mpn_mul_1 (rp, np, n, mp[0]);
for (; --n;)
mpn_addmul_1 (++rp, np, n, (++mp)[0]);
}
long
_fmpr_mul_mpn(fmpr_t z,
mp_srcptr xman, mp_size_t xn, const fmpz_t xexp,
mp_srcptr yman, mp_size_t yn, const fmpz_t yexp,
int negative, long prec, fmpr_rnd_t rnd)
{
long zn, alloc, ret, shift;
mp_limb_t tmp_stack[MUL_STACK_ALLOC];
mp_ptr tmp;
zn = xn + yn;
alloc = zn;
MUL_TMP_ALLOC
if (yn == 1)
{
mp_limb_t cy = mpn_mul_1(tmp, xman, xn, yman[0]);
tmp[zn - 1] = cy;
zn = zn - (cy == 0);
}
else
{
mpn_mul(tmp, xman, xn, yman, yn);
zn = zn - (tmp[zn - 1] == 0);
}
ret = _fmpr_set_round_mpn(&shift, fmpr_manref(z), tmp, zn, negative, prec, rnd);
fmpz_add2_fmpz_si_inline(fmpr_expref(z), xexp, yexp, shift);
MUL_TMP_FREE
return ret;
}
void
mpn_mullow_basecase (mp_ptr rp, mp_srcptr up, mp_srcptr vp, mp_size_t n)
{
mp_size_t i;
mpn_mul_1 (rp, up, n, vp[0]);
for (i = 1; i < n; i++)
mpn_addmul_1 (rp + i, up, n - i, vp[i]);
}
/* Put in rp[0..n] the n+1 low limbs of {up, n} * {vp, n}.
Assume 2n limbs are allocated at rp. */
static void
mpfr_mullow_n_basecase (mpfr_limb_ptr rp, mpfr_limb_srcptr up,
mpfr_limb_srcptr vp, mp_size_t n)
{
mp_size_t i;
rp[n] = mpn_mul_1 (rp, up, n, vp[0]);
for (i = 1 ; i < n ; i++)
mpn_addmul_1 (rp + i, up, n - i + 1, vp[i]);
}
void
mpz_lcm (mpz_ptr r, mpz_srcptr u, mpz_srcptr v)
{
mpz_t g;
mp_size_t usize, vsize;
TMP_DECL;
usize = SIZ (u);
vsize = SIZ (v);
if (usize == 0 || vsize == 0)
{
SIZ (r) = 0;
return;
}
usize = ABS (usize);
vsize = ABS (vsize);
if (vsize == 1 || usize == 1)
{
mp_limb_t vl, gl, c;
mp_srcptr up;
mp_ptr rp;
if (usize == 1)
{
usize = vsize;
MPZ_SRCPTR_SWAP (u, v);
}
MPZ_REALLOC (r, usize+1);
up = PTR(u);
vl = PTR(v)[0];
gl = mpn_gcd_1 (up, usize, vl);
vl /= gl;
rp = PTR(r);
c = mpn_mul_1 (rp, up, usize, vl);
rp[usize] = c;
usize += (c != 0);
SIZ(r) = usize;
return;
}
TMP_MARK;
MPZ_TMP_INIT (g, usize); /* v != 0 implies |gcd(u,v)| <= |u| */
mpz_gcd (g, u, v);
mpz_divexact (g, u, g);
mpz_mul (r, g, v);
SIZ (r) = ABS (SIZ (r)); /* result always positive */
TMP_FREE;
}
static void fp_mul_si(element_ptr e, element_ptr a, signed long int op) {
fp_field_data_ptr p = e->field->data;
size_t t = p->limbs;
mp_limb_t *tmp = _alloca((t + 1) * sizeof(mp_limb_t));
mp_limb_t qp[2];
tmp[t] = mpn_mul_1(tmp, a->data, t, labs(op));
mpn_tdiv_qr(qp, e->data, 0, tmp, t + 1, p->primelimbs, t);
if (op < 0) {
fp_neg(e, e);
}
}
/* Compute r such that r^2 * y = 1 (mod 2^{b+1}).
Return non-zero if such an integer r exists.
Iterates
r' <-- (3r - r^3 y) / 2
using Hensel lifting. Since we divide by two, the Hensel lifting is
somewhat degenerates. Therefore, we lift from 2^b to 2^{b+1}-1.
FIXME:
(1) Simplify to do precision book-keeping in limbs rather than bits.
(2) Rewrite iteration as
r' <-- r - r (r^2 y - 1) / 2
and take advantage of zero low part of r^2 y - 1.
(3) Use wrap-around trick.
(4) Use a small table to get starting value.
*/
int
mpn_bsqrtinv (mp_ptr rp, mp_srcptr yp, mp_bitcnt_t bnb, mp_ptr tp)
{
mp_ptr tp2, tp3;
mp_limb_t k;
mp_size_t bn, order[GMP_LIMB_BITS + 1];
int i, d;
ASSERT (bnb > 0);
bn = 1 + bnb / GMP_LIMB_BITS;
tp2 = tp + bn;
tp3 = tp + 2 * bn;
k = 3;
rp[0] = 1;
if (bnb == 1)
{
if ((yp[0] & 3) != 1)
return 0;
}
else
{
if ((yp[0] & 7) != 1)
return 0;
d = 0;
for (; bnb != 2; bnb = (bnb + 2) >> 1)
order[d++] = bnb;
for (i = d - 1; i >= 0; i--)
{
bnb = order[i];
bn = 1 + bnb / GMP_LIMB_BITS;
mpn_mul_1 (tp, rp, bn, k);
mpn_powlo (tp2, rp, &k, 1, bn, tp3);
mpn_mullo_n (rp, yp, tp2, bn);
#if HAVE_NATIVE_mpn_rsh1sub_n
mpn_rsh1sub_n (rp, tp, rp, bn);
#else
mpn_sub_n (tp2, tp, rp, bn);
mpn_rshift (rp, tp2, bn, 1);
#endif
}
}
return 1;
}
void
ecc_modp_mul_1 (const struct ecc_curve *ecc, mp_limb_t *rp,
const mp_limb_t *ap, mp_limb_t b)
{
mp_limb_t hi;
assert (b <= 0xffffffff);
hi = mpn_mul_1 (rp, ap, ecc->size, b);
hi = mpn_addmul_1 (rp, ecc->Bmodp, ecc->size, hi);
assert (hi <= 1);
hi = cnd_add_n (hi, rp, ecc->Bmodp, ecc->size);
/* Sufficient if b < B^size / p */
assert (hi == 0);
}
void
mpn_mullo_basecase (mp_ptr rp, mp_srcptr up, mp_srcptr vp, mp_size_t n)
{
mp_size_t i;
mpn_mul_1 (rp, up, n, vp[0]);
for (i = n - 1; i > 0; i--)
{
vp++;
rp++;
mpn_addmul_1 (rp, up, i, vp[0]);
}
}
mp_limb_t
mpn_submul_1 (mp_ptr rp, mp_srcptr s1p, mp_size_t n, mp_limb_t s2d)
{
mp_ptr tp;
mp_limb_t cy;
TMP_DECL;
TMP_MARK;
tp = TMP_ALLOC_LIMBS (n);
cy = mpn_mul_1 (tp, s1p, n, s2d);
cy += mpn_sub_n (rp, rp, tp, n);
TMP_FREE;
return cy;
}
/* Define our own squaring function, which uses mpn_sqr_basecase for its
allowed sizes, but its own code for larger sizes. */
static void
mpn_local_sqr (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_ptr tp)
{
mp_size_t i;
ASSERT (n >= 1);
ASSERT (! MPN_OVERLAP_P (rp, 2*n, up, n));
if (BELOW_THRESHOLD (n, SQR_BASECASE_LIM))
{
mpn_sqr_basecase (rp, up, n);
return;
}
{
mp_limb_t ul, lpl;
ul = up[0];
umul_ppmm (rp[1], lpl, ul, ul << GMP_NAIL_BITS);
rp[0] = lpl >> GMP_NAIL_BITS;
}
if (n > 1)
{
mp_limb_t cy;
cy = mpn_mul_1 (tp, up + 1, n - 1, up[0]);
tp[n - 1] = cy;
for (i = 2; i < n; i++)
{
mp_limb_t cy;
cy = mpn_addmul_1 (tp + 2 * i - 2, up + i, n - i, up[i - 1]);
tp[n + i - 2] = cy;
}
MPN_SQR_DIAGONAL (rp + 2, up + 1, n - 1);
{
mp_limb_t cy;
#if HAVE_NATIVE_mpn_addlsh1_n
cy = mpn_addlsh1_n (rp + 1, rp + 1, tp, 2 * n - 2);
#else
cy = mpn_lshift (tp, tp, 2 * n - 2, 1);
cy += mpn_add_n (rp + 1, rp + 1, tp, 2 * n - 2);
#endif
rp[2 * n - 1] += cy;
}
}
}
void _nmod_vec_scalar_mul_nmod(mp_ptr res, mp_srcptr vec,
slong len, mp_limb_t c, nmod_t mod)
{
if (mod.norm >= FLINT_BITS/2) /* products will fit in a limb */
{
mpn_mul_1(res, vec, len, c);
_nmod_vec_reduce(res, res, len, mod);
} else /* products may take two limbs */
{
slong i;
for (i = 0; i < len; i++)
{
mp_limb_t hi, lo;
umul_ppmm(hi, lo, vec[i], c);
NMOD_RED2(res[i], hi, lo, mod); /* hi already reduced mod n */
}
}
}
void
impn_mul_n_basecase (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size)
{
mp_size_t i;
mp_limb_t cy_limb;
mp_limb_t v_limb;
/* Multiply by the first limb in V separately, as the result can be
stored (not added) to PROD. We also avoid a loop for zeroing. */
v_limb = vp[0];
if (v_limb <= 1)
{
if (v_limb == 1)
MPN_COPY (prodp, up, size);
else
MPN_ZERO (prodp, size);
cy_limb = 0;
}
else
cy_limb = mpn_mul_1 (prodp, up, size, v_limb);
prodp[size] = cy_limb;
prodp++;
/* For each iteration in the outer loop, multiply one limb from
U with one limb from V, and add it to PROD. */
for (i = 1; i < size; i++)
{
v_limb = vp[i];
if (v_limb <= 1)
{
cy_limb = 0;
if (v_limb == 1)
cy_limb = mpn_add_n (prodp, prodp, up, size);
}
else
cy_limb = mpn_addmul_1 (prodp, up, size, v_limb);
prodp[size] = cy_limb;
prodp++;
}
}
static void
print_mpn_fp (const mp_limb_t *x, unsigned int dp, unsigned int base)
{
unsigned int i;
mp1 tx;
memcpy (tx, x, sizeof (mp1));
if (base == 16)
fputs ("0x", stdout);
assert (x[SZ-1] < base);
fputc (hexdig[x[SZ - 1]], stdout);
fputc ('.', stdout);
for (i = 0; i < dp; i++)
{
tx[SZ - 1] = 0;
mpn_mul_1 (tx, tx, SZ, base);
assert (tx[SZ - 1] < base);
fputc (hexdig[tx[SZ - 1]], stdout);
}
}
void fmpz_mul_ui(fmpz_t output, const fmpz_t input, const unsigned long x)
{
if (x == 0)
{
output[0] = 0;
return;
}
mp_limb_t mslimb;
if (output[0] = input[0]) // This isn't a typo
{
mslimb = mpn_mul_1(output+1, input+1, FLINT_ABS(input[0]), x);
if (mslimb)
{
output[FLINT_ABS(input[0])+1] = mslimb;
if ((long) output[0] > 0) output[0]++;
else output[0]--;
}
}
}
mp_size_t mpn_prod_limbs_direct(mp_limb_t * result, const mp_limb_t * factors,
mp_size_t n)
{
mp_size_t k, len;
mp_limb_t top;
if (n < 1)
{
result[0] = 1UL;
return 1;
}
result[0] = factors[0];
len = 1;
for (k=1; k<n; k++)
{
top = mpn_mul_1(result, result, len, factors[k]);
if (top)
{
result[len] = top;
len++;
}
}
return len;
}
// Montgomery multiplication.
// See Blake, Seroussi and Smart.
static inline void mont_mul(mp_limb_t *c, mp_limb_t *a, mp_limb_t *b,
fptr p) {
// Instead of right shifting every iteration
// I allocate more room for the z array.
size_t i, t = p->limbs;
#ifdef _MSC_VER // for VC++ compatibility
mp_limb_t z[2 * MAX_LIMBS + 1];
#else
mp_limb_t z[2 * t + 1];
#endif
mp_limb_t u = (a[0] * b[0]) * p->negpinv;
mp_limb_t v = z[t] = mpn_mul_1(z, b, t, a[0]);
z[t] += mpn_addmul_1(z, p->primelimbs, t, u);
z[t + 1] = z[t] < v; // Handle overflow.
for (i = 1; i < t; i++) {
u = (z[i] + a[i] * b[0]) * p->negpinv;
v = z[t + i] += mpn_addmul_1(z + i, b, t, a[i]);
z[t + i] += mpn_addmul_1(z + i, p->primelimbs, t, u);
z[t + i + 1] = z[t + i] < v;
}
if (z[t * 2] || mpn_cmp(z + t, p->primelimbs, t) >= 0) {
mpn_sub_n(c, z + t, p->primelimbs, t);
}
else {
memcpy(c, z + t, t * sizeof(mp_limb_t));
// Doesn't seem to make a difference:
/*
mpz_t z1, z2;
z1->_mp_d = c;
z2->_mp_d = z + t;
z1->_mp_size = z1->_mp_alloc = z2->_mp_size = z2->_mp_alloc = t;
mpz_set(z1, z2);
*/
}
}
void _nmod_poly_divrem_q1(mp_ptr Q, mp_ptr R,
mp_srcptr A, long lenA, mp_srcptr B, long lenB,
nmod_t mod)
{
const mp_limb_t invL = (B[lenB-1] == 1) ? 1 : n_invmod(B[lenB-1], mod.n);
if (lenB == 1)
{
_nmod_vec_scalar_mul_nmod(Q, A, lenA, invL, mod);
}
else
{
mp_limb_t t;
Q[1] = n_mulmod2_preinv(A[lenA-1], invL, mod.n, mod.ninv);
t = n_mulmod2_preinv(Q[1], B[lenB-2], mod.n, mod.ninv);
t = n_submod(A[lenA-2], t, mod.n);
Q[0] = n_mulmod2_preinv(t, invL, mod.n, mod.ninv);
if (FLINT_BITS + 2 <= 2 * mod.norm)
{
mpn_mul_1(R, B, lenB - 1, Q[0]);
if (lenB > 2)
mpn_addmul_1(R + 1, B, lenB - 2, Q[1]);
_nmod_vec_reduce(R, R, lenB - 1, mod);
}
else
{
_nmod_vec_scalar_mul_nmod(R, B, lenB - 1, Q[0], mod);
if (lenB > 2)
_nmod_vec_scalar_addmul_nmod(R + 1, B, lenB - 2, Q[1], mod);
}
_nmod_vec_sub(R, A, R, lenB - 1, mod);
}
}
dig_t fp_mul1_low(dig_t *c, const dig_t *a, dig_t digit) {
return mpn_mul_1(c, a, FP_DIGS, digit);
}
void tc4_addmul_1(mp_ptr wp, mp_size_t * wn, mp_srcptr xp, mp_size_t xn, mp_limb_t y)
{
mp_size_t sign, wu, xu, ws, new_wn, min_size, dsize;
mp_limb_t cy;
/* w unaffected if x==0 or y==0 */
if (xn == 0 || y == 0)
return;
sign = xn;
xu = ABS (xn);
ws = *wn;
if (*wn == 0)
{
/* nothing to add to, just set x*y, "sign" gives the sign */
cy = mpn_mul_1 (wp, xp, xu, y);
if (cy)
{
wp[xu] = cy;
xu = xu + 1;
}
*wn = (sign >= 0 ? xu : -xu);
return;
}
sign ^= *wn;
wu = ABS (*wn);
new_wn = MAX (wu, xu);
min_size = MIN (wu, xu);
if (sign >= 0)
{
/* addmul of absolute values */
cy = mpn_addmul_1 (wp, xp, min_size, y);
dsize = xu - wu;
#if HAVE_NATIVE_mpn_mul_1c
if (dsize > 0)
cy = mpn_mul_1c (wp + min_size, xp + min_size, dsize, y, cy);
else if (dsize < 0)
{
dsize = -dsize;
cy = mpn_add_1 (wp + min_size, wp + min_size, dsize, cy);
}
#else
if (dsize != 0)
{
mp_limb_t cy2;
if (dsize > 0)
cy2 = mpn_mul_1 (wp + min_size, xp + min_size, dsize, y);
else
{
dsize = -dsize;
cy2 = 0;
}
cy = cy2 + mpn_add_1 (wp + min_size, wp + min_size, dsize, cy);
}
#endif
if (cy)
{
wp[dsize + min_size] = cy;
new_wn ++;
}
} else
{
/* submul of absolute values */
cy = mpn_submul_1 (wp, xp, min_size, y);
if (wu >= xu)
{
/* if w bigger than x, then propagate borrow through it */
if (wu != xu)
cy = mpn_sub_1 (wp + xu, wp + xu, wu - xu, cy);
if (cy != 0)
{
/* Borrow out of w, take twos complement negative to get
absolute value, flip sign of w. */
wp[new_wn] = ~-cy; /* extra limb is 0-cy */
mpn_not (wp, new_wn);
new_wn++;
MPN_INCR_U (wp, new_wn, CNST_LIMB(1));
ws = -*wn;
}
} else /* wu < xu */
{
/* x bigger than w, so want x*y-w. Submul has given w-x*y, so
take twos complement and use an mpn_mul_1 for the rest. */
mp_limb_t cy2;
/* -(-cy*b^n + w-x*y) = (cy-1)*b^n + ~(w-x*y) + 1 */
mpn_not (wp, wu);
cy += mpn_add_1 (wp, wp, wu, CNST_LIMB(1));
cy -= 1;
/* If cy-1 == -1 then hold that -1 for latter. mpn_submul_1 never
returns cy==MP_LIMB_T_MAX so that value always indicates a -1. */
cy2 = (cy == MP_LIMB_T_MAX);
cy += cy2;
MPN_MUL_1C (cy, wp + wu, xp + wu, xu - wu, y, cy);
wp[new_wn] = cy;
new_wn += (cy != 0);
/* Apply any -1 from above. The value at wp+wsize is non-zero
because y!=0 and the high limb of x will be non-zero. */
if (cy2)
MPN_DECR_U (wp+wu, new_wn - wu, CNST_LIMB(1));
ws = -*wn;
}
/* submul can produce high zero limbs due to cancellation, both when w
has more limbs or x has more */
MPN_NORMALIZE (wp, new_wn);
}
*wn = (ws >= 0 ? new_wn : -new_wn);
ASSERT (new_wn == 0 || wp[new_wn - 1] != 0);
}
int
mpfr_mul_ui (mpfr_ptr y, mpfr_srcptr x, unsigned long int u, mpfr_rnd_t rnd_mode)
{
mp_limb_t *yp;
mp_size_t xn;
int cnt, inexact;
MPFR_TMP_DECL (marker);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
{
if (MPFR_IS_NAN (x))
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
else if (MPFR_IS_INF (x))
{
if (u != 0)
{
MPFR_SET_INF (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0); /* infinity is exact */
}
else /* 0 * infinity */
{
MPFR_SET_NAN (y);
MPFR_RET_NAN;
}
}
else /* x is zero */
{
MPFR_ASSERTD (MPFR_IS_ZERO (x));
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0); /* zero is exact */
}
}
else if (MPFR_UNLIKELY (u <= 1))
{
if (u < 1)
{
MPFR_SET_ZERO (y);
MPFR_SET_SAME_SIGN (y, x);
MPFR_RET (0); /* zero is exact */
}
else
return mpfr_set (y, x, rnd_mode);
}
else if (MPFR_UNLIKELY (IS_POW2 (u)))
return mpfr_mul_2si (y, x, MPFR_INT_CEIL_LOG2 (u), rnd_mode);
yp = MPFR_MANT (y);
xn = MPFR_LIMB_SIZE (x);
MPFR_ASSERTD (xn < MP_SIZE_T_MAX);
MPFR_TMP_MARK(marker);
yp = MPFR_TMP_LIMBS_ALLOC (xn + 1);
MPFR_ASSERTN (u == (mp_limb_t) u);
yp[xn] = mpn_mul_1 (yp, MPFR_MANT (x), xn, u);
/* x * u is stored in yp[xn], ..., yp[0] */
/* since the case u=1 was treated above, we have u >= 2, thus
yp[xn] >= 1 since x was msb-normalized */
MPFR_ASSERTD (yp[xn] != 0);
if (MPFR_LIKELY (MPFR_LIMB_MSB (yp[xn]) == 0))
{
count_leading_zeros (cnt, yp[xn]);
mpn_lshift (yp, yp, xn + 1, cnt);
}
else
{
cnt = 0;
}
/* now yp[xn], ..., yp[0] is msb-normalized too, and has at most
PREC(x) + (GMP_NUMB_BITS - cnt) non-zero bits */
MPFR_RNDRAW (inexact, y, yp, (mpfr_prec_t) (xn + 1) * GMP_NUMB_BITS,
rnd_mode, MPFR_SIGN (x), cnt -- );
MPFR_TMP_FREE (marker);
cnt = GMP_NUMB_BITS - cnt;
if (MPFR_UNLIKELY (__gmpfr_emax < MPFR_EMAX_MIN + cnt
|| MPFR_GET_EXP (x) > __gmpfr_emax - cnt))
return mpfr_overflow (y, rnd_mode, MPFR_SIGN(x));
MPFR_SET_EXP (y, MPFR_GET_EXP (x) + cnt);
MPFR_SET_SAME_SIGN (y, x);
return inexact;
}
void compute_B_terms(QS_t * qs_inf, poly_t * poly_inf)
{
unsigned long s = poly_inf->s;
unsigned long * A_ind = poly_inf->A_ind;
unsigned long * A_modp = poly_inf->A_modp;
unsigned long * B_terms = poly_inf->B_terms;
prime_t * factor_base = qs_inf->factor_base;
unsigned long limbs = qs_inf->prec+1;
unsigned long limbs2;
unsigned long * A = poly_inf->A;
unsigned long * B = poly_inf->B;
unsigned long p, i;
unsigned long * temp1 = (unsigned long *) flint_stack_alloc(limbs);
unsigned long temp;
mp_limb_t msl;
double pinv;
for (i = 0; i < s; i++)
{
p = factor_base[A_ind[i]].p;
pinv = z_precompute_inverse(p);
mpn_divmod_1(temp1 + 1, A + 1, A[0], p);
temp1[0] = A[0] - (temp1[A[0]] == 0);
A_modp[i] = (temp = mpn_mod_1(temp1 + 1, temp1[0], p));
temp = z_invert(temp, p);
temp = z_mulmod_precomp(temp, qs_inf->sqrts[A_ind[i]], p, pinv);
if (temp > p/2) temp = p - temp;
msl = mpn_mul_1(B_terms + i*limbs + 1, temp1 + 1, temp1[0], temp);
if (msl)
{
B_terms[i*limbs + temp1[0] + 1] = msl;
B_terms[i*limbs] = temp1[0] + 1;
}
else B_terms[i*limbs] = temp1[0];
#if B_TERMS
mpz_t temp;
mpz_init(temp);
fmpz_to_mpz(temp, B_terms + i*limbs);
gmp_printf("B_%ld = %Zd\n", i, temp);
mpz_clear(temp);
#endif
}
F_mpn_copy(B, B_terms, B_terms[0]+1); // Set B to the sum of the B terms
if (limbs > B_terms[0] + 1) F_mpn_clear(B + B_terms[0] + 1, limbs - B_terms[0] - 1);
for (i = 1; i < s; i++)
{
limbs2 = B_terms[i*limbs];
msl = mpn_add_n(B+1, B+1, B_terms + i*limbs + 1, limbs2);
if (msl) mpn_add_1(B + limbs2 + 1, B + limbs2 + 1, limbs - limbs2 - 1, msl);
}
B[0] = limbs - 1;
while (!B[B[0]] && B[0]) B[0]--;
#if B_TERMS
mpz_t temp2;
mpz_init(temp2);
fmpz_to_mpz(temp2, B);
gmp_printf("B = %Zd\n", temp2);
mpz_clear(temp2);
#endif
flint_stack_release(); // release temp1
}
mp_limb_t
mpn_mul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
{
mp_limb_t cy[n];
mp_limb_t a, b, r, s0, s1, c0, c1;
mp_size_t i;
int more_carries;
if (up == rp)
{
/* The algorithm used below cannot handle overlap. Handle it here by
making a temporary copy of the source vector, then call ourselves. */
mp_limb_t xp[n];
MPN_COPY (xp, up, n);
return mpn_mul_1 (rp, xp, n, vl);
}
a = up[0] * vl;
rp[0] = a;
cy[0] = 0;
/* Main multiply loop. Generate a raw accumulated output product in rp[]
and a carry vector in cy[]. */
#pragma _CRI ivdep
for (i = 1; i < n; i++)
{
a = up[i] * vl;
b = _int_mult_upper (up[i - 1], vl);
s0 = a + b;
c0 = ((a & b) | ((a | b) & ~s0)) >> 63;
rp[i] = s0;
cy[i] = c0;
}
/* Carry add loop. Add the carry vector cy[] to the raw sum rp[] and
store the new sum back to rp[0]. */
more_carries = 0;
#pragma _CRI ivdep
for (i = 2; i < n; i++)
{
r = rp[i];
c0 = cy[i - 1];
s0 = r + c0;
rp[i] = s0;
c0 = (r & ~s0) >> 63;
more_carries += c0;
}
/* If that second loop generated carry, handle that in scalar loop. */
if (more_carries)
{
mp_limb_t cyrec = 0;
/* Look for places where rp[k] is zero and cy[k-1] is non-zero.
These are where we got a recurrency carry. */
for (i = 2; i < n; i++)
{
r = rp[i];
c0 = (r == 0 && cy[i - 1] != 0);
s0 = r + cyrec;
rp[i] = s0;
c1 = (r & ~s0) >> 63;
cyrec = c0 | c1;
}
return _int_mult_upper (up[n - 1], vl) + cyrec + cy[n - 1];
}
return _int_mult_upper (up[n - 1], vl) + cy[n - 1];
}