void
mpq_set (mpq_ptr dest, mpq_srcptr src)
{
mp_size_t num_size, den_size;
mp_size_t abs_num_size;
mp_ptr dp;
num_size = SIZ(NUM(src));
SIZ(NUM(dest)) = num_size;
abs_num_size = ABS (num_size);
dp = MPZ_NEWALLOC (NUM(dest), abs_num_size);
MPN_COPY (dp, PTR(NUM(src)), abs_num_size);
den_size = SIZ(DEN(src));
SIZ(DEN(dest)) = den_size;
dp = MPZ_NEWALLOC (DEN(dest), den_size);
MPN_COPY (dp, PTR(DEN(src)), den_size);
}
void
mpq_abs (mpq_ptr dst, mpq_srcptr src)
{
mp_size_t num_abs_size = ABSIZ(NUM(src));
if (dst != src)
{
mp_size_t den_size = SIZ(DEN(src));
mp_ptr dp;
dp = MPZ_NEWALLOC (NUM(dst), num_abs_size);
MPN_COPY (dp, PTR(NUM(src)), num_abs_size);
dp = MPZ_NEWALLOC (DEN(dst), den_size);
SIZ(DEN(dst)) = den_size;
MPN_COPY (dp, PTR(DEN(src)), den_size);
}
SIZ(NUM(dst)) = num_abs_size;
}
void
mpq_set_num (mpq_ptr dest, mpz_srcptr num)
{
mp_size_t size = SIZ (num);
mp_size_t abs_size = ABS (size);
mp_ptr dp;
dp = MPZ_NEWALLOC (NUM(dest), abs_size);
SIZ(NUM(dest)) = size;
MPN_COPY (dp, PTR(num), abs_size);
}
void
mpq_set_den (mpq_ptr dest, mpz_srcptr den)
{
mp_size_t size = SIZ (den);
mp_size_t abs_size = ABS (size);
mp_ptr dp;
dp = MPZ_NEWALLOC (DEN(dest), abs_size);
SIZ(DEN(dest)) = size;
MPN_COPY (dp, PTR(den), abs_size);
}
void
mpq_inv (mpq_ptr dest, mpq_srcptr src)
{
mp_size_t num_size = SIZ(NUM(src));
mp_size_t den_size = SIZ(DEN(src));
if (num_size < 0)
{
num_size = -num_size;
den_size = -den_size;
}
else if (UNLIKELY (num_size == 0))
DIVIDE_BY_ZERO;
SIZ(DEN(dest)) = num_size;
SIZ(NUM(dest)) = den_size;
/* If dest == src we may just swap the numerator and denominator;
we ensured that the new denominator is positive. */
if (dest == src)
{
MP_PTR_SWAP (PTR(NUM(dest)), PTR(DEN(dest)));
MP_SIZE_T_SWAP (ALLOC(NUM(dest)), ALLOC(DEN(dest)));
}
else
{
mp_ptr dp;
den_size = ABS (den_size);
dp = MPZ_NEWALLOC (NUM(dest), den_size);
MPN_COPY (dp, PTR(DEN(src)), den_size);
dp = MPZ_NEWALLOC (DEN(dest), num_size);
MPN_COPY (dp, PTR(NUM(src)), num_size);
}
}
void
mpz_rrandomb (mpz_ptr x, gmp_randstate_t rstate, mp_bitcnt_t nbits)
{
mp_size_t nl;
mp_ptr xp;
nl = BITS_TO_LIMBS (nbits);
if (nbits != 0)
{
xp = MPZ_NEWALLOC (x, nl);
gmp_rrandomb (xp, rstate, nbits);
}
SIZ(x) = nl;
}
void
mpz_set_ui (mpz_ptr dest, unsigned long int val)
{
mp_size_t size;
MPZ_NEWALLOC (dest, 1)[0] = val & GMP_NUMB_MASK;
size = val != 0;
#if BITS_PER_ULONG > GMP_NUMB_BITS /* avoid warnings about shift amount */
if (val > GMP_NUMB_MAX)
{
MPZ_REALLOC (dest, 2);
PTR (dest)[1] = val >> GMP_NUMB_BITS;
size = 2;
}
void
mpz_fib2_ui (mpz_ptr fn, mpz_ptr fnsub1, unsigned long n)
{
mp_ptr fp, f1p;
mp_size_t size;
if (n <= FIB_TABLE_LIMIT)
{
MPZ_NEWALLOC (fn, 1)[0] = FIB_TABLE (n);
SIZ(fn) = (n != 0); /* F[0]==0, others are !=0 */
MPZ_NEWALLOC (fnsub1, 1)[0] = FIB_TABLE ((int) n - 1);
SIZ(fnsub1) = (n != 1); /* F[1-1]==0, others are !=0 */
return;
}
size = MPN_FIB2_SIZE (n);
fp = MPZ_NEWALLOC (fn, size);
f1p = MPZ_NEWALLOC (fnsub1, size);
size = mpn_fib2_ui (fp, f1p, n);
SIZ(fn) = size;
SIZ(fnsub1) = size - (f1p[size-1] == 0);
}
void
mpq_set_z (mpq_ptr dest, mpz_srcptr src)
{
mp_size_t num_size;
mp_size_t abs_num_size;
mp_ptr dp;
num_size = SIZ (src);
abs_num_size = ABS (num_size);
dp = MPZ_NEWALLOC (NUM(dest), abs_num_size);
SIZ(NUM(dest)) = num_size;
MPN_COPY (dp, PTR(src), abs_num_size);
PTR(DEN(dest))[0] = 1;
SIZ(DEN(dest)) = 1;
}
void
gmp_randinit_lc_2exp (gmp_randstate_t rstate,
mpz_srcptr a,
unsigned long int c,
mp_bitcnt_t m2exp)
{
gmp_rand_lc_struct *p;
mp_size_t seedn = BITS_TO_LIMBS (m2exp);
ASSERT_ALWAYS (m2exp != 0);
p = __GMP_ALLOCATE_FUNC_TYPE (1, gmp_rand_lc_struct);
RNG_STATE (rstate) = (mp_limb_t *) (void *) p;
RNG_FNPTR (rstate) = (void *) &Linear_Congruential_Generator;
/* allocate m2exp bits of space for p->_mp_seed, and initial seed "1" */
mpz_init2 (p->_mp_seed, m2exp);
MPN_ZERO (PTR (p->_mp_seed), seedn);
SIZ (p->_mp_seed) = seedn;
PTR (p->_mp_seed)[0] = 1;
/* "a", forced to 0 to 2^m2exp-1 */
mpz_init (p->_mp_a);
mpz_fdiv_r_2exp (p->_mp_a, a, m2exp);
/* Avoid SIZ(a) == 0 to avoid checking for special case in lc(). */
if (SIZ (p->_mp_a) == 0)
{
SIZ (p->_mp_a) = 1;
MPZ_NEWALLOC (p->_mp_a, 1)[0] = CNST_LIMB (0);
}
MPN_SET_UI (p->_cp, p->_cn, c);
/* Internally we may discard any bits of c above m2exp. The following
code ensures that __GMPN_ADD in lc() will always work. */
if (seedn < p->_cn)
p->_cn = (p->_cp[0] != 0);
p->_mp_m2exp = m2exp;
}
void
mpz_neg (mpz_ptr w, mpz_srcptr u)
{
mp_ptr wp;
mp_srcptr up;
mp_size_t usize, size;
usize = SIZ (u);
if (u != w)
{
size = ABS (usize);
wp = MPZ_NEWALLOC (w, size);
up = PTR (u);
MPN_COPY (wp, up, size);
}
SIZ (w) = -usize;
}
size_t
mpz_inp_raw (mpz_ptr x, FILE *fp)
{
unsigned char csize_bytes[4];
mp_size_t csize, abs_xsize, i;
size_t abs_csize;
char *cp;
mp_ptr xp, sp, ep;
mp_limb_t slimb, elimb;
if (fp == 0)
fp = stdin;
/* 4 bytes for size */
if (fread (csize_bytes, sizeof (csize_bytes), 1, fp) != 1)
return 0;
csize =
( (mp_size_t) csize_bytes[0] << 24)
+ ((mp_size_t) csize_bytes[1] << 16)
+ ((mp_size_t) csize_bytes[2] << 8)
+ ((mp_size_t) csize_bytes[3]);
/* Sign extend if necessary.
Could write "csize -= ((csize & 0x80000000L) << 1)", but that tickles a
bug in gcc 3.0 for powerpc64 on AIX. */
if (sizeof (csize) > 4 && csize & 0x80000000L)
csize -= 0x80000000L << 1;
abs_csize = ABS (csize);
/* round up to a multiple of limbs */
abs_xsize = BITS_TO_LIMBS (abs_csize*8);
if (abs_xsize != 0)
{
xp = MPZ_NEWALLOC (x, abs_xsize);
/* Get limb boundaries right in the read, for the benefit of the
non-nails case. */
xp[0] = 0;
cp = (char *) (xp + abs_xsize) - abs_csize;
if (fread (cp, abs_csize, 1, fp) != 1)
return 0;
if (GMP_NAIL_BITS == 0)
{
/* Reverse limbs to least significant first, and byte swap. If
abs_xsize is odd then on the last iteration elimb and slimb are
the same. It doesn't seem extra code to handle that case
separately, to save an NTOH. */
sp = xp;
ep = xp + abs_xsize-1;
for (i = 0; i < (abs_xsize+1)/2; i++)
{
NTOH_LIMB_FETCH (elimb, ep);
NTOH_LIMB_FETCH (slimb, sp);
*sp++ = elimb;
*ep-- = slimb;
}
}
else
{
/* It ought to be possible to do the transformation in-place, but
for now it's easier to use an extra temporary area. */
mp_limb_t byte, limb;
int bits;
mp_size_t tpos;
mp_ptr tp;
TMP_DECL;
TMP_MARK;
tp = TMP_ALLOC_LIMBS (abs_xsize);
limb = 0;
bits = 0;
tpos = 0;
for (i = abs_csize-1; i >= 0; i--)
{
byte = (unsigned char) cp[i];
limb |= (byte << bits);
bits += 8;
if (bits >= GMP_NUMB_BITS)
{
ASSERT (tpos < abs_xsize);
tp[tpos++] = limb & GMP_NUMB_MASK;
bits -= GMP_NUMB_BITS;
ASSERT (bits < 8);
limb = byte >> (8 - bits);
}
}
if (bits != 0)
{
ASSERT (tpos < abs_xsize);
tp[tpos++] = limb;
}
ASSERT (tpos == abs_xsize);
MPN_COPY (xp, tp, abs_xsize);
TMP_FREE;
}
void
mpq_set_f (mpq_ptr q, mpf_srcptr f)
{
mp_size_t fexp = EXP(f);
mp_ptr fptr = PTR(f);
mp_size_t fsize = SIZ(f);
mp_size_t abs_fsize = ABS(fsize);
mp_limb_t flow;
if (fsize == 0)
{
/* set q=0 */
SIZ(NUM(q)) = 0;
SIZ(DEN(q)) = 1;
PTR(DEN(q))[0] = 1;
return;
}
/* strip low zero limbs from f */
flow = *fptr;
MPN_STRIP_LOW_ZEROS_NOT_ZERO (fptr, abs_fsize, flow);
if (fexp >= abs_fsize)
{
/* radix point is to the right of the limbs, no denominator */
mp_ptr num_ptr;
num_ptr = MPZ_NEWALLOC (mpq_numref (q), fexp);
MPN_ZERO (num_ptr, fexp - abs_fsize);
MPN_COPY (num_ptr + fexp - abs_fsize, fptr, abs_fsize);
SIZ(NUM(q)) = fsize >= 0 ? fexp : -fexp;
SIZ(DEN(q)) = 1;
PTR(DEN(q))[0] = 1;
}
else
{
/* radix point is within or to the left of the limbs, use denominator */
mp_ptr num_ptr, den_ptr;
mp_size_t den_size;
den_size = abs_fsize - fexp;
num_ptr = MPZ_NEWALLOC (mpq_numref (q), abs_fsize);
den_ptr = MPZ_NEWALLOC (mpq_denref (q), den_size+1);
if (flow & 1)
{
/* no powers of two to strip from numerator */
MPN_COPY (num_ptr, fptr, abs_fsize);
MPN_ZERO (den_ptr, den_size);
den_ptr[den_size] = 1;
}
else
{
/* right shift numerator, adjust denominator accordingly */
int shift;
den_size--;
count_trailing_zeros (shift, flow);
mpn_rshift (num_ptr, fptr, abs_fsize, shift);
abs_fsize -= (num_ptr[abs_fsize-1] == 0);
MPN_ZERO (den_ptr, den_size);
den_ptr[den_size] = GMP_LIMB_HIGHBIT >> (shift-1);
}
SIZ(NUM(q)) = fsize >= 0 ? abs_fsize : -abs_fsize;
SIZ(DEN(q)) = den_size + 1;
}
}
/* Get a limb pointer for writing, previous contents may be
destroyed. */
mp_limb_t *
mpz_limbs_write (mpz_ptr x, mp_size_t n)
{
assert (n > 0);
return MPZ_NEWALLOC (x, n);
}
choke me
#endif
void
mpq_set_d (mpq_ptr dest, double d)
{
int negative;
mp_exp_t exp;
mp_limb_t tp[LIMBS_PER_DOUBLE];
mp_ptr np, dp;
mp_size_t nn, dn;
int c;
DOUBLE_NAN_INF_ACTION (d,
__gmp_invalid_operation (),
__gmp_invalid_operation ());
negative = d < 0;
d = ABS (d);
exp = __gmp_extract_double (tp, d);
/* There are two main version of the conversion. The `then' arm handles
numbers with a fractional part, while the `else' arm handles integers. */
#if LIMBS_PER_DOUBLE == 4
if (exp <= 1 || (exp == 2 && (tp[0] | tp[1]) != 0))
#endif
#if LIMBS_PER_DOUBLE == 3
if (exp <= 1 || (exp == 2 && tp[0] != 0))
#endif
#if LIMBS_PER_DOUBLE == 2
if (exp <= 1)
#endif
{
if (d == 0.0)
{
SIZ(NUM(dest)) = 0;
SIZ(DEN(dest)) = 1;
PTR(DEN(dest))[0] = 1;
return;
}
#if LIMBS_PER_DOUBLE == 4
np = MPZ_NEWALLOC (NUM(dest), 4);
if ((tp[0] | tp[1] | tp[2]) == 0)
np[0] = tp[3], nn = 1;
else if ((tp[0] | tp[1]) == 0)
np[1] = tp[3], np[0] = tp[2], nn = 2;
else if (tp[0] == 0)
np[2] = tp[3], np[1] = tp[2], np[0] = tp[1], nn = 3;
else
np[3] = tp[3], np[2] = tp[2], np[1] = tp[1], np[0] = tp[0], nn = 4;
#endif
#if LIMBS_PER_DOUBLE == 3
np = MPZ_NEWALLOC (NUM(dest), 3);
if ((tp[0] | tp[1]) == 0)
np[0] = tp[2], nn = 1;
else if (tp[0] == 0)
np[1] = tp[2], np[0] = tp[1], nn = 2;
else
np[2] = tp[2], np[1] = tp[1], np[0] = tp[0], nn = 3;
#endif
#if LIMBS_PER_DOUBLE == 2
np = MPZ_NEWALLOC (NUM(dest), 2);
if (tp[0] == 0)
np[0] = tp[1], nn = 1;
else
np[1] = tp[1], np[0] = tp[0], nn = 2;
#endif
dn = nn + 1 - exp;
ASSERT (dn > 0); /* -exp >= -1; nn >= 1*/
dp = MPZ_NEWALLOC (DEN(dest), dn);
MPN_ZERO (dp, dn - 1);
dp[dn - 1] = 1;
count_trailing_zeros (c, np[0] | dp[0]);
if (c != 0)
{
mpn_rshift (np, np, nn, c);
nn -= np[nn - 1] == 0;
--dn;
dp[dn - 1] = CNST_LIMB(1) << (GMP_LIMB_BITS - c);
}
SIZ(DEN(dest)) = dn;
}
else
{
nn = exp;
np = MPZ_NEWALLOC (NUM(dest), nn);
switch (nn)
{
default:
MPN_ZERO (np, nn - LIMBS_PER_DOUBLE);
np += nn - LIMBS_PER_DOUBLE;
/* fall through */
#if LIMBS_PER_DOUBLE == 2
case 2:
np[1] = tp[1], np[0] = tp[0];
break;
#endif
#if LIMBS_PER_DOUBLE == 3
case 3:
np[2] = tp[2], np[1] = tp[1], np[0] = tp[0];
break;
case 2:
np[1] = tp[2], np[0] = tp[1];
break;
#endif
#if LIMBS_PER_DOUBLE == 4
case 4:
np[3] = tp[3], np[2] = tp[2], np[1] = tp[1], np[0] = tp[0];
break;
case 3:
np[2] = tp[3], np[1] = tp[2], np[0] = tp[1];
break;
case 2:
np[1] = tp[3], np[0] = tp[2];
break;
#endif
}
*PTR(DEN(dest)) = 1;
SIZ(DEN(dest)) = 1;
}
SIZ(NUM(dest)) = negative ? -nn : nn;
}
void
mpz_gcdext (mpz_ptr g, mpz_ptr s, mpz_ptr t, mpz_srcptr a, mpz_srcptr b)
{
mp_size_t asize, bsize;
mp_ptr tmp_ap, tmp_bp;
mp_size_t gsize, ssize, tmp_ssize;
mp_ptr gp, tmp_gp, tmp_sp;
TMP_DECL;
/* mpn_gcdext requires that Usize >= Vsize. Therefore, we often
have to swap U and V. The computed cofactor will be the
"smallest" one, which is faster to produce. The wanted one will
be computed here; this is needed anyway when both are requested. */
asize = ABSIZ (a);
bsize = ABSIZ (b);
if (asize < bsize)
{
MPZ_SRCPTR_SWAP (a, b);
MP_SIZE_T_SWAP (asize, bsize);
MPZ_PTR_SWAP (s, t);
}
if (bsize == 0)
{
/* g = |a|, s = sgn(a), t = 0. */
ssize = SIZ (a) >= 0 ? (asize != 0) : -1;
gp = MPZ_REALLOC (g, asize);
MPN_COPY (gp, PTR (a), asize);
SIZ (g) = asize;
if (t != NULL)
SIZ (t) = 0;
if (s != NULL)
{
SIZ (s) = ssize;
MPZ_NEWALLOC (s, 1)[0] = 1;
}
return;
}
TMP_MARK;
TMP_ALLOC_LIMBS_2 (tmp_ap, asize, tmp_bp, bsize);
MPN_COPY (tmp_ap, PTR (a), asize);
MPN_COPY (tmp_bp, PTR (b), bsize);
TMP_ALLOC_LIMBS_2 (tmp_gp, bsize, tmp_sp, bsize + 1);
gsize = mpn_gcdext (tmp_gp, tmp_sp, &tmp_ssize, tmp_ap, asize, tmp_bp, bsize);
ssize = ABS (tmp_ssize);
tmp_ssize = SIZ (a) >= 0 ? tmp_ssize : -tmp_ssize;
if (t != NULL)
{
mpz_t x;
__mpz_struct gtmp, stmp;
PTR (>mp) = tmp_gp;
SIZ (>mp) = gsize;
PTR (&stmp) = tmp_sp;
SIZ (&stmp) = tmp_ssize;
MPZ_TMP_INIT (x, ssize + asize + 1);
mpz_mul (x, &stmp, a);
mpz_sub (x, >mp, x);
mpz_divexact (t, x, b);
}
if (s != NULL)
{
mp_ptr sp;
sp = MPZ_REALLOC (s, ssize);
MPN_COPY (sp, tmp_sp, ssize);
SIZ (s) = tmp_ssize;
}
gp = MPZ_REALLOC (g, gsize);
MPN_COPY (gp, tmp_gp, gsize);
SIZ (g) = gsize;
TMP_FREE;
}
void
mpz_powm_sec (mpz_ptr r, mpz_srcptr b, mpz_srcptr e, mpz_srcptr m)
{
mp_size_t n;
mp_ptr rp, tp;
mp_srcptr bp, ep, mp;
mp_size_t rn, bn, es, en;
TMP_DECL;
n = ABSIZ(m);
mp = PTR(m);
if (UNLIKELY ((n == 0) || (mp[0] % 2 == 0)))
DIVIDE_BY_ZERO;
es = SIZ(e);
if (UNLIKELY (es <= 0))
{
if (es == 0)
{
/* b^0 mod m, b is anything and m is non-zero.
Result is 1 mod m, i.e., 1 or 0 depending on if m = 1. */
SIZ(r) = n != 1 || mp[0] != 1;
MPZ_NEWALLOC (r, 1)[0] = 1;
return;
}
DIVIDE_BY_ZERO;
}
en = es;
bn = ABSIZ(b);
if (UNLIKELY (bn == 0))
{
SIZ(r) = 0;
return;
}
TMP_MARK;
tp = TMP_ALLOC_LIMBS (n + mpn_sec_powm_itch (bn, en * GMP_NUMB_BITS, n));
rp = tp; tp += n;
bp = PTR(b);
ep = PTR(e);
mpn_sec_powm (rp, bp, bn, ep, en * GMP_NUMB_BITS, mp, n, tp);
rn = n;
MPN_NORMALIZE (rp, rn);
if ((ep[0] & 1) && SIZ(b) < 0 && rn != 0)
{
mpn_sub (rp, PTR(m), n, rp, rn);
rn = n;
MPN_NORMALIZE (rp, rn);
}
MPZ_REALLOC (r, rn);
SIZ(r) = rn;
MPN_COPY (PTR(r), rp, rn);
TMP_FREE;
}
void
mpz_mfac_uiui (mpz_ptr x, unsigned long n, unsigned long m)
{
ASSERT (n <= GMP_NUMB_MAX);
ASSERT (m != 0);
if ((n < 3) | (n - 3 < m - 1)) { /* (n < 3 || n - 1 <= m || m == 0) */
PTR (x)[0] = n + (n == 0);
SIZ (x) = 1;
} else { /* m < n - 1 < GMP_NUMB_MAX */
mp_limb_t g, sn;
mpz_t t;
sn = n;
g = mpn_gcd_1 (&sn, 1, m);
if (g > 1) { n/=g; m/=g; }
if (m <= 2) { /* fac or 2fac */
if (m == 1) {
if (g > 2) {
mpz_init (t);
mpz_fac_ui (t, n);
sn = n;
} else {
if (g == 2)
mpz_2fac_ui (x, n << 1);
else
mpz_fac_ui (x, n);
return;
}
} else { /* m == 2 */
if (g > 1) {
mpz_init (t);
mpz_2fac_ui (t, n);
sn = n / 2 + 1;
} else {
mpz_2fac_ui (x, n);
return;
}
}
} else { /* m >= 3, gcd(n,m) = 1 */
mp_limb_t *factors;
mp_limb_t prod, max_prod, j;
TMP_DECL;
sn = n / m + 1;
j = 0;
prod = n;
n -= m;
max_prod = GMP_NUMB_MAX / n;
if (g > 1)
factors = MPZ_NEWALLOC (x, sn / log_n_max (n) + 2);
else {
TMP_MARK;
factors = TMP_ALLOC_LIMBS (sn / log_n_max (n) + 2);
}
for (; n > m; n -= m)
FACTOR_LIST_STORE (n, prod, max_prod, factors, j);
factors[j++] = n;
factors[j++] = prod;
if (g > 1) {
mpz_init (t);
mpz_prodlimbs (t, factors, j);
} else {
mpz_prodlimbs (x, factors, j);
TMP_FREE;
return;
}
}
{
mpz_t p;
mpz_init (p);
mpz_ui_pow_ui (p, g, sn); /* g^sn */
mpz_mul (x, p, t);
mpz_clear (p);
mpz_clear (t);
}
}
}