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gmp-impl.h：源码内容

#endif
#ifndef mpn_decr_u
#define mpn_decr_u(p,incr)
do {
mp_limb_t __x;
mp_ptr __p = (p);
if (__builtin_constant_p (incr) && (incr) == 1)
{
while ((*(__p++))-- == 0)
;
}
else
{
__x = *__p;
*__p = __x - (incr);
if (__x < (incr))
while ((*(++__p))-- == 0)
;
}
} while (0)
#endif
#endif
#if GMP_NAIL_BITS >= 1
#ifndef mpn_incr_u
#define mpn_incr_u(p,incr)
do {
mp_limb_t __x;
mp_ptr __p = (p);
if (__builtin_constant_p (incr) && (incr) == 1)
{
do
{
__x = (*__p + 1) & GMP_NUMB_MASK;
*__p++ = __x;
}
while (__x == 0);
}
else
{
__x = (*__p + (incr));
*__p++ = __x & GMP_NUMB_MASK;
if (__x >> GMP_NUMB_BITS != 0)
{
do
{
__x = (*__p + 1) & GMP_NUMB_MASK;
*__p++ = __x;
}
while (__x == 0);
}
}
} while (0)
#endif
#ifndef mpn_decr_u
#define mpn_decr_u(p,incr)
do {
mp_limb_t __x;
mp_ptr __p = (p);
if (__builtin_constant_p (incr) && (incr) == 1)
{
do
{
__x = *__p;
*__p++ = (__x - 1) & GMP_NUMB_MASK;
}
while (__x == 0);
}
else
{
__x = *__p - (incr);
*__p++ = __x & GMP_NUMB_MASK;
if (__x >> GMP_NUMB_BITS != 0)
{
do
{
__x = *__p;
*__p++ = (__x - 1) & GMP_NUMB_MASK;
}
while (__x == 0);
}
}
} while (0)
#endif
#endif
#ifndef MPN_INCR_U
#if WANT_ASSERT
#define MPN_INCR_U(ptr, size, n)
do {
ASSERT ((size) >= 1);
ASSERT_NOCARRY (mpn_add_1 (ptr, ptr, size, n));
} while (0)
#else
#define MPN_INCR_U(ptr, size, n) mpn_incr_u (ptr, n)
#endif
#endif
#ifndef MPN_DECR_U
#if WANT_ASSERT
#define MPN_DECR_U(ptr, size, n)
do {
ASSERT ((size) >= 1);
ASSERT_NOCARRY (mpn_sub_1 (ptr, ptr, size, n));
} while (0)
#else
#define MPN_DECR_U(ptr, size, n) mpn_decr_u (ptr, n)
#endif
#endif
/* Structure for conversion between internal binary format and
strings in base 2..36. */
struct bases
{
/* Number of digits in the conversion base that always fits in an mp_limb_t.
For example, for base 10 on a machine where a mp_limb_t has 32 bits this
is 9, since 10**9 is the largest number that fits into a mp_limb_t. */
int chars_per_limb;
/* log(2)/log(conversion_base) */
double chars_per_bit_exactly;
/* base**chars_per_limb, i.e. the biggest number that fits a word, built by
factors of base. Exception: For 2, 4, 8, etc, big_base is log2(base),
i.e. the number of bits used to represent each digit in the base. */
mp_limb_t big_base;
/* A GMP_LIMB_BITS bit approximation to 1/big_base, represented as a
fixed-point number. Instead of dividing by big_base an application can
choose to multiply by big_base_inverted. */
mp_limb_t big_base_inverted;
};
#define mp_bases __MPN(bases)
__GMP_DECLSPEC extern const struct bases mp_bases[257];
/* For power of 2 bases this is exact. For other bases the result is either
exact or one too big.
To be exact always it'd be necessary to examine all the limbs of the
operand, since numbers like 100..000 and 99...999 generally differ only
in the lowest limb. It'd be possible to examine just a couple of high
limbs to increase the probability of being exact, but that doesn't seem
worth bothering with. */
#define MPN_SIZEINBASE(result, ptr, size, base)
do {
int __lb_base, __cnt;
size_t __totbits;
ASSERT ((size) >= 0);
ASSERT ((base) >= 2);
ASSERT ((base) < numberof (mp_bases));
/* Special case for X == 0. */
if ((size) == 0)
(result) = 1;
else
{
/* Calculate the total number of significant bits of X. */
count_leading_zeros (__cnt, (ptr)[(size)-1]);
__totbits = (size_t) (size) * GMP_NUMB_BITS - (__cnt - GMP_NAIL_BITS);
if (POW2_P (base))
{
__lb_base = mp_bases[base].big_base;
(result) = (__totbits + __lb_base - 1) / __lb_base;
}
else
(result) = (size_t)
(__totbits * mp_bases[base].chars_per_bit_exactly) + 1;
}
} while (0)
/* eliminate mp_bases lookups for base==16 */
#define MPN_SIZEINBASE_16(result, ptr, size)
do {
int __cnt;
mp_size_t __totbits;
ASSERT ((size) >= 0);
/* Special case for X == 0. */
if ((size) == 0)
(result) = 1;
else
{
/* Calculate the total number of significant bits of X. */
count_leading_zeros (__cnt, (ptr)[(size)-1]);
__totbits = (size_t) (size) * GMP_NUMB_BITS - (__cnt - GMP_NAIL_BITS);
(result) = (__totbits + 4 - 1) / 4;
}
} while (0)
/* bit count to limb count, rounding up */
#define BITS_TO_LIMBS(n) (((n) + (GMP_NUMB_BITS - 1)) / GMP_NUMB_BITS)
/* MPN_SET_UI sets an mpn (ptr, cnt) to given ui. MPZ_FAKE_UI creates fake
mpz_t from ui. The zp argument must have room for LIMBS_PER_ULONG limbs
in both cases (LIMBS_PER_ULONG is also defined here.) */
#if BITS_PER_ULONG <= GMP_NUMB_BITS /* need one limb per ulong */
#define LIMBS_PER_ULONG 1
#define MPN_SET_UI(zp, zn, u)
(zp)[0] = (u);
(zn) = ((zp)[0] != 0);
#define MPZ_FAKE_UI(z, zp, u)
(zp)[0] = (u);
PTR (z) = (zp);
SIZ (z) = ((zp)[0] != 0);
ASSERT_CODE (ALLOC (z) = 1);
#else /* need two limbs per ulong */
#define LIMBS_PER_ULONG 2
#define MPN_SET_UI(zp, zn, u)
(zp)[0] = (u) & GMP_NUMB_MASK;
(zp)[1] = (u) >> GMP_NUMB_BITS;
(zn) = ((zp)[1] != 0 ? 2 : (zp)[0] != 0 ? 1 : 0);
#define MPZ_FAKE_UI(z, zp, u)
(zp)[0] = (u) & GMP_NUMB_MASK;
(zp)[1] = (u) >> GMP_NUMB_BITS;
SIZ (z) = ((zp)[1] != 0 ? 2 : (zp)[0] != 0 ? 1 : 0);
PTR (z) = (zp);
ASSERT_CODE (ALLOC (z) = 2);
#endif
#if HAVE_HOST_CPU_FAMILY_x86
#define TARGET_REGISTER_STARVED 1
#else
#define TARGET_REGISTER_STARVED 0
#endif
/* LIMB_HIGHBIT_TO_MASK(n) examines the high bit of a limb value and turns 1
or 0 there into a limb 0xFF..FF or 0 respectively.
On most CPUs this is just an arithmetic right shift by GMP_LIMB_BITS-1,
but C99 doesn't guarantee signed right shifts are arithmetic, so we have
a little compile-time test and a fallback to a "? :" form. The latter is
necessary for instance on Cray vector systems.
Recent versions of gcc (eg. 3.3) will in fact optimize a "? :" like this
to an arithmetic right shift anyway, but it's good to get the desired
shift on past versions too (in particular since an important use of
LIMB_HIGHBIT_TO_MASK is in udiv_qrnnd_preinv). */
#define LIMB_HIGHBIT_TO_MASK(n)
(((mp_limb_signed_t) -1 >> 1) < 0
? (mp_limb_signed_t) (n) >> (GMP_LIMB_BITS - 1)
: (n) & GMP_LIMB_HIGHBIT ? MP_LIMB_T_MAX : CNST_LIMB(0))
/* Use a library function for invert_limb, if available. */
#define mpn_invert_limb __MPN(invert_limb)
__GMP_DECLSPEC mp_limb_t mpn_invert_limb __GMP_PROTO ((mp_limb_t)) ATTRIBUTE_CONST;
#if ! defined (invert_limb) && HAVE_NATIVE_mpn_invert_limb
#define invert_limb(invxl,xl)
do {
(invxl) = mpn_invert_limb (xl);
} while (0)
#endif
#ifndef invert_limb
#define invert_limb(invxl,xl)
do {
mp_limb_t dummy;
ASSERT ((xl) != 0);
udiv_qrnnd (invxl, dummy, ~(xl), ~CNST_LIMB(0), xl);
} while (0)
#endif
#define invert_pi1(dinv, d1, d0)
do {
mp_limb_t v, p, t1, t0, mask;
invert_limb (v, d1);
p = d1 * v;
p += d0;
if (p < d0)
{
v--;
mask = -(p >= d1);
p -= d1;
v += mask;
p -= mask & d1;
}
umul_ppmm (t1, t0, d0, v);
p += t1;
if (p < t1)
{
v--;
if (UNLIKELY (p >= d1))
{
if (p > d1 || t0 >= d0)
v--;
}
}
(dinv).inv32 = v;
} while (0)
#ifndef udiv_qrnnd_preinv
#define udiv_qrnnd_preinv udiv_qrnnd_preinv3
#endif
/* Divide the two-limb number in (NH,,NL) by D, with DI being the largest
limb not larger than (2**(2*GMP_LIMB_BITS))/D - (2**GMP_LIMB_BITS).
If this would yield overflow, DI should be the largest possible number
(i.e., only ones). For correct operation, the most significant bit of D
has to be set. Put the quotient in Q and the remainder in R. */
#define udiv_qrnnd_preinv1(q, r, nh, nl, d, di)
do {
mp_limb_t _q, _ql, _r;
mp_limb_t _xh, _xl;
ASSERT ((d) != 0);
umul_ppmm (_q, _ql, (nh), (di));
_q += (nh); /* Compensate, di is 2**GMP_LIMB_BITS too small */
umul_ppmm (_xh, _xl, _q, (d));
sub_ddmmss (_xh, _r, (nh), (nl), _xh, _xl);
if (_xh != 0)
{
sub_ddmmss (_xh, _r, _xh, _r, 0, (d));
_q += 1;
if (_xh != 0)
{
_r -= (d);
_q += 1;
}
}
if (_r >= (d))
{
_r -= (d);
_q += 1;
}
(r) = _r;
(q) = _q;
} while (0)
/* Like udiv_qrnnd_preinv, but branch-free. */
#define udiv_qrnnd_preinv2(q, r, nh, nl, d, di)
do {
mp_limb_t _n2, _n10, _nmask, _nadj, _q1;
mp_limb_t _xh, _xl;
_n2 = (nh);
_n10 = (nl);
_nmask = LIMB_HIGHBIT_TO_MASK (_n10);
_nadj = _n10 + (_nmask & (d));
umul_ppmm (_xh, _xl, di, _n2 - _nmask);
add_ssaaaa (_xh, _xl, _xh, _xl, _n2, _nadj);
_q1 = ~_xh;
umul_ppmm (_xh, _xl, _q1, d);
add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl);
_xh -= (d); /* xh = 0 or -1 */
(r) = _xl + ((d) & _xh);
(q) = _xh - _q1;
} while (0)
/* Like udiv_qrnnd_preinv2, but for for any value D. DNORM is D shifted left
so that its most significant bit is set. LGUP is ceil(log2(D)). */
#define udiv_qrnnd_preinv2gen(q, r, nh, nl, d, di, dnorm, lgup)
do {
mp_limb_t _n2, _n10, _nmask, _nadj, _q1;
mp_limb_t _xh, _xl;
_n2 = ((nh) << (GMP_LIMB_BITS - (lgup))) + ((nl) >> 1 >> (l - 1));
_n10 = (nl) << (GMP_LIMB_BITS - (lgup));
_nmask = LIMB_HIGHBIT_TO_MASK (_n10);
_nadj = _n10 + (_nmask & (dnorm));
umul_ppmm (_xh, _xl, di, _n2 - _nmask);
add_ssaaaa (_xh, _xl, _xh, _xl, _n2, _nadj);
_q1 = ~_xh;
umul_ppmm (_xh, _xl, _q1, d);
add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl);
_xh -= (d);
(r) = _xl + ((d) & _xh);
(q) = _xh - _q1;
} while (0)
/* udiv_qrnnd_preinv3 -- Based on work by Niels M鰈ler and Torbj鰎n Granlund.
We write things strangely below, to help gcc. A more straightforward
version:
_r = (nl) - _qh * (d);
_t = _r + (d);
if (_r >= _ql)
{
_qh--;
_r = _t;
}
For one operation shorter critical path, one may want to use this form:
_p = _qh * (d)
_s = (nl) + (d);
_r = (nl) - _p;
_t = _s - _p;
if (_r >= _ql)
{
_qh--;
_r = _t;
}
*/
#define udiv_qrnnd_preinv3(q, r, nh, nl, d, di)
do {
mp_limb_t _qh, _ql, _r;
umul_ppmm (_qh, _ql, (nh), (di));
if (__builtin_constant_p (nl) && (nl) == 0)
_qh += (nh) + 1;
else
add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl));
_r = (nl) - _qh * (d);
if (_r > _ql) /* both > and >= should be OK */
{
_r += (d);
_qh--;
}
if (UNLIKELY (_r >= (d)))
{
_r -= (d);
_qh++;
}
(r) = _r;
(q) = _qh;
} while (0)
/* Compute r = nh*B mod d, where di is the inverse of d. */
#define udiv_rnd_preinv(r, nh, d, di)
do {
mp_limb_t _qh, _ql, _r;
umul_ppmm (_qh, _ql, (nh), (di));
_qh += (nh) + 1;
_r = - _qh * (d);
if (_r > _ql)
_r += (d);
(r) = _r;
} while (0)
/* Compute quotient the quotient and remainder for n / d. Requires d
>= B^2 / 2 and n < d B. di is the inverse
floor ((B^3 - 1) / (d0 + d1 B)) - B.
NOTE: Output variables are updated multiple times. Only some inputs
and outputs may overlap.
*/
#define udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv)
do {
mp_limb_t _q0, _t1, _t0, _mask;
umul_ppmm ((q), _q0, (n2), (dinv));
add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1));
/* Compute the two most significant limbs of n - q'd */
(r1) = (n1) - (d1) * (q);
(r0) = (n0);
sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0));
umul_ppmm (_t1, _t0, (d0), (q));
sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0);
(q)++;
/* Conditionally adjust q and the remainders */
_mask = - (mp_limb_t) ((r1) >= _q0);
(q) += _mask;
add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0));
if (UNLIKELY ((r1) >= (d1)))
{
if ((r1) > (d1) || (r0) >= (d0))
{
(q)++;
sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0));
}
}
} while (0)
#ifndef mpn_preinv_divrem_1 /* if not done with cpuvec in a fat binary */
#define mpn_preinv_divrem_1 __MPN(preinv_divrem_1)
__GMP_DECLSPEC mp_limb_t mpn_preinv_divrem_1 __GMP_PROTO ((mp_ptr, mp_size_t, mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t, int));
#endif
/* USE_PREINV_DIVREM_1 is whether to use mpn_preinv_divrem_1, as opposed to the
plain mpn_divrem_1. The default is yes, since the few CISC chips where
preinv is not good have defines saying so. */
#ifndef USE_PREINV_DIVREM_1
#define USE_PREINV_DIVREM_1 1
#endif
#if USE_PREINV_DIVREM_1
#define MPN_DIVREM_OR_PREINV_DIVREM_1(qp,xsize,ap,size,d,dinv,shift)
mpn_preinv_divrem_1 (qp, xsize, ap, size, d, dinv, shift)
#else
#define MPN_DIVREM_OR_PREINV_DIVREM_1(qp,xsize,ap,size,d,dinv,shift)
mpn_divrem_1 (qp, xsize, ap, size, d)
#endif
#ifndef PREINV_MOD_1_TO_MOD_1_THRESHOLD
#define PREINV_MOD_1_TO_MOD_1_THRESHOLD 10
#endif
/* This selection may seem backwards. The reason mpn_mod_1 typically takes
over for larger sizes is that it uses the mod_1_1 function. */
#define MPN_MOD_OR_PREINV_MOD_1(src,size,divisor,inverse)
(BELOW_THRESHOLD (size, PREINV_MOD_1_TO_MOD_1_THRESHOLD)
? mpn_preinv_mod_1 (src, size, divisor, inverse)
: mpn_mod_1 (src, size, divisor))
#ifndef mpn_mod_34lsub1 /* if not done with cpuvec in a fat binary */
#define mpn_mod_34lsub1 __MPN(mod_34lsub1)
__GMP_DECLSPEC mp_limb_t mpn_mod_34lsub1 __GMP_PROTO ((mp_srcptr, mp_size_t)) __GMP_ATTRIBUTE_PURE;
#endif
/* DIVEXACT_1_THRESHOLD is at what size to use mpn_divexact_1, as opposed to
plain mpn_divrem_1. Likewise BMOD_1_TO_MOD_1_THRESHOLD for
mpn_modexact_1_odd against plain mpn_mod_1. On most CPUs divexact and
modexact are faster at all sizes, so the defaults are 0. Those CPUs
where this is not right have a tuned threshold. */
#ifndef DIVEXACT_1_THRESHOLD
#define DIVEXACT_1_THRESHOLD 0
#endif
#ifndef BMOD_1_TO_MOD_1_THRESHOLD
#define BMOD_1_TO_MOD_1_THRESHOLD 10
#endif
#ifndef mpn_divexact_1 /* if not done with cpuvec in a fat binary */
#define mpn_divexact_1 __MPN(divexact_1)
__GMP_DECLSPEC void mpn_divexact_1 __GMP_PROTO ((mp_ptr, mp_srcptr, mp_size_t, mp_limb_t));
#endif
#define MPN_DIVREM_OR_DIVEXACT_1(dst, src, size, divisor)
do {
if (BELOW_THRESHOLD (size, DIVEXACT_1_THRESHOLD))
ASSERT_NOCARRY (mpn_divrem_1 (dst, (mp_size_t) 0, src, size, divisor));
else
{
ASSERT (mpn_mod_1 (src, size, divisor) == 0);
mpn_divexact_1 (dst, src, size, divisor);
}
} while (0)
#ifndef mpn_modexact_1c_odd /* if not done with cpuvec in a fat binary */
#define mpn_modexact_1c_odd __MPN(modexact_1c_odd)
__GMP_DECLSPEC mp_limb_t mpn_modexact_1c_odd __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
#endif
#if HAVE_NATIVE_mpn_modexact_1_odd
#define mpn_modexact_1_odd __MPN(modexact_1_odd)
__GMP_DECLSPEC mp_limb_t mpn_modexact_1_odd __GMP_PROTO ((mp_srcptr, mp_size_t, mp_limb_t)) __GMP_ATTRIBUTE_PURE;
#else
#define mpn_modexact_1_odd(src,size,divisor)
mpn_modexact_1c_odd (src, size, divisor, CNST_LIMB(0))
#endif
#define MPN_MOD_OR_MODEXACT_1_ODD(src,size,divisor)
(BELOW_THRESHOLD (size, BMOD_1_TO_MOD_1_THRESHOLD)
? mpn_modexact_1_odd (src, size, divisor)
: mpn_mod_1 (src, size, divisor))
/* binvert_limb() sets inv to the multiplicative inverse of n modulo
2^GMP_NUMB_BITS, ie. satisfying inv*n == 1 mod 2^GMP_NUMB_BITS.
n must be odd (otherwise such an inverse doesn't exist).
This is not to be confused with invert_limb(), which is completely
different.
The table lookup gives an inverse with the low 8 bits valid, and each
multiply step doubles the number of bits. See Jebelean "An algorithm for
exact division" end of section 4 (reference in gmp.texi).
Possible enhancement: Could use UHWtype until the last step, if half-size
multiplies are faster (might help under _LONG_LONG_LIMB).
Alternative: As noted in Granlund and Montgomery "Division by Invariant
Integers using Multiplication" (reference in gmp.texi), n itself gives a
3-bit inverse immediately, and could be used instead of a table lookup.
A 4-bit inverse can be obtained effectively from xoring bits 1 and 2 into
bit 3, for instance with (((n + 2) & 4) << 1) ^ n. */
#define binvert_limb_table __gmp_binvert_limb_table
__GMP_DECLSPEC extern const unsigned char binvert_limb_table[128];
#define binvert_limb(inv,n)
do {
mp_limb_t __n = (n);
mp_limb_t __inv;
ASSERT ((__n & 1) == 1);
__inv = binvert_limb_table[(__n/2) & 0x7F]; /* 8 */
if (GMP_NUMB_BITS > 8) __inv = 2 * __inv - __inv * __inv * __n;
if (GMP_NUMB_BITS > 16) __inv = 2 * __inv - __inv * __inv * __n;
if (GMP_NUMB_BITS > 32) __inv = 2 * __inv - __inv * __inv * __n;
if (GMP_NUMB_BITS > 64)
{
int __invbits = 64;
do {
__inv = 2 * __inv - __inv * __inv * __n;
__invbits *= 2;
} while (__invbits < GMP_NUMB_BITS);
}
ASSERT ((__inv * __n & GMP_NUMB_MASK) == 1);
(inv) = __inv & GMP_NUMB_MASK;
} while (0)
#define modlimb_invert binvert_limb /* backward compatibility */
/* Multiplicative inverse of 3, modulo 2^GMP_NUMB_BITS.
Eg. 0xAAAAAAAB for 32 bits, 0xAAAAAAAAAAAAAAAB for 64 bits.
GMP_NUMB_MAX/3*2+1 is right when GMP_NUMB_BITS is even, but when it's odd
we need to start from GMP_NUMB_MAX>>1. */
#define MODLIMB_INVERSE_3 (((GMP_NUMB_MAX >> (GMP_NUMB_BITS % 2)) / 3) * 2 + 1)
/* ceil(GMP_NUMB_MAX/3) and ceil(2*GMP_NUMB_MAX/3).
These expressions work because GMP_NUMB_MAX%3 != 0 for all GMP_NUMB_BITS. */
#define GMP_NUMB_CEIL_MAX_DIV3 (GMP_NUMB_MAX / 3 + 1)
#define GMP_NUMB_CEIL_2MAX_DIV3 ((GMP_NUMB_MAX>>1) / 3 + 1 + GMP_NUMB_HIGHBIT)
/* Set r to -a mod d. a>=d is allowed. Can give r>d. All should be limbs.
It's not clear whether this is the best way to do this calculation.
Anything congruent to -a would be fine for the one limb congruence
tests. */
#define NEG_MOD(r, a, d)
do {
ASSERT ((d) != 0);
ASSERT_LIMB (a);
ASSERT_LIMB (d);
if ((a) <= (d))
{
/* small a is reasonably likely */
(r) = (d) - (a);
}
else
{
unsigned __twos;
mp_limb_t __dnorm;
count_leading_zeros (__twos, d);
__twos -= GMP_NAIL_BITS;
__dnorm = (d) << __twos;
(r) = ((a) <= __dnorm ? __dnorm : 2*__dnorm) - (a);
}
ASSERT_LIMB (r);
} while (0)
/* A bit mask of all the least significant zero bits of n, or -1 if n==0. */
#define LOW_ZEROS_MASK(n) (((n) & -(n)) - 1)
/* ULONG_PARITY sets "p" to 1 if there's an odd number of 1 bits in "n", or
to 0 if there's an even number. "n" should be an unsigned long and "p"
an int. */
#if defined (__GNUC__) && ! defined (NO_ASM) && HAVE_HOST_CPU_alpha_CIX
#define ULONG_PARITY(p, n)
do {
int __p;
__asm__ ("ctpop %1, %0" : "=r" (__p) : "r" (n));
(p) = __p & 1;
} while (0)
#endif
/* Cray intrinsic _popcnt. */
#ifdef _CRAY
#define ULONG_PARITY(p, n)
do {
(p) = _popcnt (n) & 1;
} while (0)
#endif
#if defined (__GNUC__) && ! defined (__INTEL_COMPILER)
&& ! defined (NO_ASM) && defined (__ia64)
/* unsigned long is either 32 or 64 bits depending on the ABI, zero extend
to a 64 bit unsigned long long for popcnt */
#define ULONG_PARITY(p, n)
do {
unsigned long long __n = (unsigned long) (n);
int __p;
__asm__ ("popcnt %0 = %1" : "=r" (__p) : "r" (__n));
(p) = __p & 1;
} while (0)
#endif
#if defined (__GNUC__) && ! defined (__INTEL_COMPILER)
&& ! defined (NO_ASM) && HAVE_HOST_CPU_FAMILY_x86
#if __GMP_GNUC_PREREQ (3,1)
#define __GMP_qm "=Qm"
#define __GMP_q "=Q"
#else
#define __GMP_qm "=qm"
#define __GMP_q "=q"
#endif
#define ULONG_PARITY(p, n)
do {
char __p;
unsigned long __n = (n);
__n ^= (__n >> 16);
__asm__ ("xorb %h1, %b1nt"
"setpo %0"
: __GMP_qm (__p), __GMP_q (__n)
: "1" (__n));
(p) = __p;
} while (0)
#endif
#if ! defined (ULONG_PARITY)
#define ULONG_PARITY(p, n)
do {
unsigned long __n = (n);
int __p = 0;
do
{
__p ^= 0x96696996L >> (__n & 0x1F);
__n >>= 5;
}
while (__n != 0);
(p) = __p & 1;
} while (0)
#endif
/* 3 cycles on 604 or 750 since shifts and rlwimi's can pair. gcc (as of
version 3.1 at least) doesn't seem to know how to generate rlwimi for
anything other than bit-fields, so use "asm". */
#if defined (__GNUC__) && ! defined (NO_ASM)
&& HAVE_HOST_CPU_FAMILY_powerpc && GMP_LIMB_BITS == 32
#define BSWAP_LIMB(dst, src)
do {
mp_limb_t __bswapl_src = (src);
mp_limb_t __tmp1 = __bswapl_src >> 24; /* low byte */
mp_limb_t __tmp2 = __bswapl_src << 24; /* high byte */
__asm__ ("rlwimi %0, %2, 24, 16, 23" /* 2nd low */
: "=r" (__tmp1) : "0" (__tmp1), "r" (__bswapl_src));
__asm__ ("rlwimi %0, %2, 8, 8, 15" /* 3nd high */
: "=r" (__tmp2) : "0" (__tmp2), "r" (__bswapl_src));
(dst) = __tmp1 | __tmp2; /* whole */
} while (0)
#endif
/* bswap is available on i486 and up and is fast. A combination rorw $8 /
roll $16 / rorw $8 is used in glibc for plain i386 (and in the linux
kernel with xchgb instead of rorw), but this is not done here, because
i386 means generic x86 and mixing word and dword operations will cause
partial register stalls on P6 chips. */
#if defined (__GNUC__) && ! defined (NO_ASM)
&& HAVE_HOST_CPU_FAMILY_x86 && ! HAVE_HOST_CPU_i386
&& GMP_LIMB_BITS == 32
#define BSWAP_LIMB(dst, src)
do {
__asm__ ("bswap %0" : "=r" (dst) : "0" (src));
} while (0)
#endif
#if defined (__GNUC__) && ! defined (NO_ASM)
&& defined (__amd64__) && GMP_LIMB_BITS == 64
#define BSWAP_LIMB(dst, src)
do {
__asm__ ("bswap %q0" : "=r" (dst) : "0" (src));
} while (0)
#endif
#if defined (__GNUC__) && ! defined (__INTEL_COMPILER)
&& ! defined (NO_ASM) && defined (__ia64) && GMP_LIMB_BITS == 64
#define BSWAP_LIMB(dst, src)
do {
__asm__ ("mux1 %0 = %1, @rev" : "=r" (dst) : "r" (src));
} while (0)
#endif
/* As per glibc. */
#if defined (__GNUC__) && ! defined (NO_ASM)
&& HAVE_HOST_CPU_FAMILY_m68k && GMP_LIMB_BITS == 32
#define BSWAP_LIMB(dst, src)
do {
mp_limb_t __bswapl_src = (src);
__asm__ ("ror%.w %#8, %0nt"
"swap %0nt"
"ror%.w %#8, %0"
: "=d" (dst)
: "0" (__bswapl_src));
} while (0)
#endif
#if ! defined (BSWAP_LIMB)
#if GMP_LIMB_BITS == 8
#define BSWAP_LIMB(dst, src)
do { (dst) = (src); } while (0)
#endif
#if GMP_LIMB_BITS == 16
#define BSWAP_LIMB(dst, src)
do {
(dst) = ((src) << 8) + ((src) >> 8);
} while (0)
#endif
#if GMP_LIMB_BITS == 32
#define BSWAP_LIMB(dst, src)
do {
(dst) =
((src) << 24)
+ (((src) & 0xFF00) << 8)
+ (((src) >> 8) & 0xFF00)
+ ((src) >> 24);
} while (0)
#endif
#if GMP_LIMB_BITS == 64
#define BSWAP_LIMB(dst, src)
do {
(dst) =
((src) << 56)
+ (((src) & 0xFF00) << 40)
+ (((src) & 0xFF0000) << 24)
+ (((src) & 0xFF000000) << 8)
+ (((src) >> 8) & 0xFF000000)
+ (((src) >> 24) & 0xFF0000)
+ (((src) >> 40) & 0xFF00)
+ ((src) >> 56);
} while (0)
#endif
#endif
#if ! defined (BSWAP_LIMB)
#define BSWAP_LIMB(dst, src)
do {
mp_limb_t __bswapl_src = (src);
mp_limb_t __dst = 0;
int __i;
for (__i = 0; __i < BYTES_PER_MP_LIMB; __i++)
{
__dst = (__dst << 8) | (__bswapl_src & 0xFF);
__bswapl_src >>= 8;
}
(dst) = __dst;
} while (0)
#endif
/* Apparently lwbrx might be slow on some PowerPC chips, so restrict it to
those we know are fast. */
#if defined (__GNUC__) && ! defined (NO_ASM)
&& GMP_LIMB_BITS == 32 && HAVE_LIMB_BIG_ENDIAN
&& (HAVE_HOST_CPU_powerpc604
|| HAVE_HOST_CPU_powerpc604e
|| HAVE_HOST_CPU_powerpc750
|| HAVE_HOST_CPU_powerpc7400)
#define BSWAP_LIMB_FETCH(limb, src)
do {
mp_srcptr __blf_src = (src);
mp_limb_t __limb;
__asm__ ("lwbrx %0, 0, %1"
: "=r" (__limb)
: "r" (__blf_src),
"m" (*__blf_src));
(limb) = __limb;
} while (0)
#endif
#if ! defined (BSWAP_LIMB_FETCH)
#define BSWAP_LIMB_FETCH(limb, src) BSWAP_LIMB (limb, *(src))
#endif
/* On the same basis that lwbrx might be slow, restrict stwbrx to those we
know are fast. FIXME: Is this necessary? */
#if defined (__GNUC__) && ! defined (NO_ASM)
&& GMP_LIMB_BITS == 32 && HAVE_LIMB_BIG_ENDIAN
&& (HAVE_HOST_CPU_powerpc604
|| HAVE_HOST_CPU_powerpc604e
|| HAVE_HOST_CPU_powerpc750
|| HAVE_HOST_CPU_powerpc7400)
#define BSWAP_LIMB_STORE(dst, limb)
do {
mp_ptr __dst = (dst);
mp_limb_t __limb = (limb);
__asm__ ("stwbrx %1, 0, %2"
: "=m" (*__dst)
: "r" (__limb),
"r" (__dst));
} while (0)
#endif
#if ! defined (BSWAP_LIMB_STORE)
#define BSWAP_LIMB_STORE(dst, limb) BSWAP_LIMB (*(dst), limb)
#endif
/* Byte swap limbs from {src,size} and store at {dst,size}. */
#define MPN_BSWAP(dst, src, size)
do {
mp_ptr __dst = (dst);
mp_srcptr __src = (src);
mp_size_t __size = (size);
mp_size_t __i;
ASSERT ((size) >= 0);
ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, size));
CRAY_Pragma ("_CRI ivdep");
for (__i = 0; __i < __size; __i++)
{
BSWAP_LIMB_FETCH (*__dst, __src);
__dst++;
__src++;
}
} while (0)
/* Byte swap limbs from {dst,size} and store in reverse order at {src,size}. */
#define MPN_BSWAP_REVERSE(dst, src, size)
do {
mp_ptr __dst = (dst);
mp_size_t __size = (size);
mp_srcptr __src = (src) + __size - 1;
mp_size_t __i;
ASSERT ((size) >= 0);
ASSERT (! MPN_OVERLAP_P (dst, size, src, size));
CRAY_Pragma ("_CRI ivdep");
for (__i = 0; __i < __size; __i++)
{
BSWAP_LIMB_FETCH (*__dst, __src);
__dst++;
__src--;
}
} while (0)
/* No processor claiming to be SPARC v9 compliant seems to
implement the POPC instruction. Disable pattern for now. */
#if 0
#if defined __GNUC__ && defined __sparc_v9__ && GMP_LIMB_BITS == 64
#define popc_limb(result, input)
do {
DItype __res;
__asm__ ("popc %1,%0" : "=r" (result) : "rI" (input));
} while (0)
#endif
#endif
#if defined (__GNUC__) && ! defined (NO_ASM) && HAVE_HOST_CPU_alpha_CIX
#define popc_limb(result, input)
do {
__asm__ ("ctpop %1, %0" : "=r" (result) : "r" (input));
} while (0)
#endif
/* Cray intrinsic. */
#ifdef _CRAY
#define popc_limb(result, input)
do {
(result) = _popcnt (input);
} while (0)
#endif
#if defined (__GNUC__) && ! defined (__INTEL_COMPILER)
&& ! defined (NO_ASM) && defined (__ia64) && GMP_LIMB_BITS == 64
#define popc_limb(result, input)
do {
__asm__ ("popcnt %0 = %1" : "=r" (result) : "r" (input));
} while (0)
#endif
/* Cool population count of an mp_limb_t.
You have to figure out how this works, We won't tell you!
The constants could also be expressed as:
0x55... = [2^N / 3] = [(2^N-1)/3]
0x33... = [2^N / 5] = [(2^N-1)/5]
0x0f... = [2^N / 17] = [(2^N-1)/17]
(N is GMP_LIMB_BITS, [] denotes truncation.) */
#if ! defined (popc_limb) && GMP_LIMB_BITS == 8
#define popc_limb(result, input)
do {
mp_limb_t __x = (input);
__x -= (__x >> 1) & MP_LIMB_T_MAX/3;
__x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5);
__x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17;
(result) = __x & 0xff;
} while (0)
#endif
#if ! defined (popc_limb) && GMP_LIMB_BITS == 16
#define popc_limb(result, input)
do {
mp_limb_t __x = (input);
__x -= (__x >> 1) & MP_LIMB_T_MAX/3;
__x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5);
__x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17;
__x = ((__x >> 8) + __x);
(result) = __x & 0xff;
} while (0)
#endif
#if ! defined (popc_limb) && GMP_LIMB_BITS == 32
#define popc_limb(result, input)
do {
mp_limb_t __x = (input);
__x -= (__x >> 1) & MP_LIMB_T_MAX/3;
__x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5);
__x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17;
__x = ((__x >> 8) + __x);
__x = ((__x >> 16) + __x);
(result) = __x & 0xff;
} while (0)
#endif
#if ! defined (popc_limb) && GMP_LIMB_BITS == 64
#define popc_limb(result, input)
do {
mp_limb_t __x = (input);
__x -= (__x >> 1) & MP_LIMB_T_MAX/3;
__x = ((__x >> 2) & MP_LIMB_T_MAX/5) + (__x & MP_LIMB_T_MAX/5);
__x = ((__x >> 4) + __x) & MP_LIMB_T_MAX/17;
__x = ((__x >> 8) + __x);
__x = ((__x >> 16) + __x);
__x = ((__x >> 32) + __x);
(result) = __x & 0xff;
} while (0)
#endif
/* Define stuff for longlong.h. */
#if HAVE_ATTRIBUTE_MODE
typedef unsigned int UQItype __attribute__ ((mode (QI)));
typedef int SItype __attribute__ ((mode (SI)));
typedef unsigned int USItype __attribute__ ((mode (SI)));
typedef int DItype __attribute__ ((mode (DI)));
typedef unsigned int UDItype __attribute__ ((mode (DI)));
#else
typedef unsigned char UQItype;
typedef long SItype;
typedef unsigned long USItype;
#if HAVE_LONG_LONG
typedef long long int DItype;
typedef unsigned long long int UDItype;
#else /* Assume `long' gives us a wide enough type. Needed for hppa2.0w. */
typedef long int DItype;
typedef unsigned long int UDItype;
#endif
#endif
typedef mp_limb_t UWtype;
typedef unsigned int UHWtype;
#define W_TYPE_SIZE GMP_LIMB_BITS
/* Define ieee_double_extract and _GMP_IEEE_FLOATS.
Bit field packing is "implementation defined" according to C99, which
leaves us at the compiler's mercy here. For some systems packing is
defined in the ABI (eg. x86). In any case so far it seems universal that
little endian systems pack from low to high, and big endian from high to
low within the given type.
Within the fields we rely on the integer endianness being the same as the
float endianness, this is true everywhere we know of and it'd be a fairly
strange system that did anything else. */
#if HAVE_DOUBLE_IEEE_LITTLE_SWAPPED
#define _GMP_IEEE_FLOATS 1
union ieee_double_extract
{
struct
{
gmp_uint_least32_t manh:20;
gmp_uint_least32_t exp:11;
gmp_uint_least32_t sig:1;
gmp_uint_least32_t manl:32;
} s;
double d;
};
#endif
#if HAVE_DOUBLE_IEEE_LITTLE_ENDIAN
#define _GMP_IEEE_FLOATS 1
union ieee_double_extract
{
struct
{
gmp_uint_least32_t manl:32;
gmp_uint_least32_t manh:20;
gmp_uint_least32_t exp:11;
gmp_uint_least32_t sig:1;
} s;
double d;
};
#endif
#if HAVE_DOUBLE_IEEE_BIG_ENDIAN
#define _GMP_IEEE_FLOATS 1
union ieee_double_extract
{
struct
{
gmp_uint_least32_t sig:1;
gmp_uint_least32_t exp:11;
gmp_uint_least32_t manh:20;
gmp_uint_least32_t manl:32;
} s;
double d;
};
#endif
/* Use (4.0 * ...) instead of (2.0 * ...) to work around buggy compilers
that don't convert ulong->double correctly (eg. SunOS 4 native cc). */
#define MP_BASE_AS_DOUBLE (4.0 * ((mp_limb_t) 1 << (GMP_NUMB_BITS - 2)))
/* Maximum number of limbs it will take to store any `double'.
We assume doubles have 53 mantissa bits. */
#define LIMBS_PER_DOUBLE ((53 + GMP_NUMB_BITS - 2) / GMP_NUMB_BITS + 1)
__GMP_DECLSPEC int __gmp_extract_double __GMP_PROTO ((mp_ptr, double));
#define mpn_get_d __gmpn_get_d
__GMP_DECLSPEC double mpn_get_d __GMP_PROTO ((mp_srcptr, mp_size_t, mp_size_t, long)) __GMP_ATTRIBUTE_PURE;
/* DOUBLE_NAN_INF_ACTION executes code a_nan if x is a NaN, or executes
a_inf if x is an infinity. Both are considered unlikely values, for
branch prediction. */
#if _GMP_IEEE_FLOATS
#define DOUBLE_NAN_INF_ACTION(x, a_nan, a_inf)
do {
union ieee_double_extract u;
u.d = (x);
if (UNLIKELY (u.s.exp == 0x7FF))
{
if (u.s.manl == 0 && u.s.manh == 0)
{ a_inf; }
else
{ a_nan; }
}
} while (0)
#endif
#if HAVE_DOUBLE_VAX_D || HAVE_DOUBLE_VAX_G || HAVE_DOUBLE_CRAY_CFP
/* no nans or infs in these formats */
#define DOUBLE_NAN_INF_ACTION(x, a_nan, a_inf)
do { } while (0)
#endif
#ifndef DOUBLE_NAN_INF_ACTION
/* Unknown format, try something generic.
NaN should be "unordered", so x!=x.
Inf should be bigger than DBL_MAX. */
#define DOUBLE_NAN_INF_ACTION(x, a_nan, a_inf)
do {
{
if (UNLIKELY ((x) != (x)))
{ a_nan; }
else if (UNLIKELY ((x) > DBL_MAX || (x) < -DBL_MAX))
{ a_inf; }
}
} while (0)
#endif
/* On m68k, x86 and amd64, gcc (and maybe other compilers) can hold doubles
in the coprocessor, which means a bigger exponent range than normal, and
depending on the rounding mode, a bigger mantissa than normal. (See
"Disappointments" in the gcc manual.) FORCE_DOUBLE stores and fetches
"d" through memory to force any rounding and overflows to occur.
On amd64, and on x86s with SSE2, gcc (depending on options) uses the xmm
registers, where there's no such extra precision and no need for the
FORCE_DOUBLE. We don't bother to detect this since the present uses for
FORCE_DOUBLE are only in test programs and default generic C code.
Not quite sure that an "automatic volatile" will use memory, but it does
in gcc. An asm("":"=m"(d):"0"(d)) can't be used to trick gcc, since
apparently matching operands like "0" are only allowed on a register
output. gcc 3.4 warns about this, though in fact it and past versions
seem to put the operand through memory as hoped. */
#if (HAVE_HOST_CPU_FAMILY_m68k || HAVE_HOST_CPU_FAMILY_x86
|| defined (__amd64__))
#define FORCE_DOUBLE(d)
do { volatile double __gmp_force = (d); (d) = __gmp_force; } while (0)
#else
#define FORCE_DOUBLE(d) do { } while (0)
#endif
__GMP_DECLSPEC extern int __gmp_junk;
__GMP_DECLSPEC extern const int __gmp_0;
__GMP_DECLSPEC void __gmp_exception __GMP_PROTO ((int)) ATTRIBUTE_NORETURN;
__GMP_DECLSPEC void __gmp_divide_by_zero __GMP_PROTO ((void)) ATTRIBUTE_NORETURN;
__GMP_DECLSPEC void __gmp_sqrt_of_negative __GMP_PROTO ((void)) ATTRIBUTE_NORETURN;
__GMP_DECLSPEC void __gmp_invalid_operation __GMP_PROTO ((void)) ATTRIBUTE_NORETURN;
#define GMP_ERROR(code) __gmp_exception (code)
#define DIVIDE_BY_ZERO __gmp_divide_by_zero ()
#define SQRT_OF_NEGATIVE __gmp_sqrt_of_negative ()
#if defined _LONG_LONG_LIMB
#if __GMP_HAVE_TOKEN_PASTE
#define CNST_LIMB(C) ((mp_limb_t) C##LL)
#else
#define CNST_LIMB(C) ((mp_limb_t) C/**/LL)
#endif
#else /* not _LONG_LONG_LIMB */
#if __GMP_HAVE_TOKEN_PASTE
#define CNST_LIMB(C) ((mp_limb_t) C##L)
#else
#define CNST_LIMB(C) ((mp_limb_t) C/**/L)
#endif
#endif /* _LONG_LONG_LIMB */
/* Stuff used by mpn/generic/perfsqr.c and mpz/prime_p.c */
#if GMP_NUMB_BITS == 2
#define PP 0x3 /* 3 */
#define PP_FIRST_OMITTED 5
#endif
#if GMP_NUMB_BITS == 4
#define PP 0xF /* 3 x 5 */
#define PP_FIRST_OMITTED 7
#endif
#if GMP_NUMB_BITS == 8
#define PP 0x69 /* 3 x 5 x 7 */
#define PP_FIRST_OMITTED 11
#endif
#if GMP_NUMB_BITS == 16
#define PP 0x3AA7 /* 3 x 5 x 7 x 11 x 13 */
#define PP_FIRST_OMITTED 17
#endif
#if GMP_NUMB_BITS == 32
#define PP 0xC0CFD797L /* 3 x 5 x 7 x 11 x ... x 29 */
#define PP_INVERTED 0x53E5645CL
#define PP_FIRST_OMITTED 31
#endif
#if GMP_NUMB_BITS == 64
#define PP CNST_LIMB(0xE221F97C30E94E1D) /* 3 x 5 x 7 x 11 x ... x 53 */
#define PP_INVERTED CNST_LIMB(0x21CFE6CFC938B36B)
#define PP_FIRST_OMITTED 59
#endif
#ifndef PP_FIRST_OMITTED
#define PP_FIRST_OMITTED 3
#endif
/* BIT1 means a result value in bit 1 (second least significant bit), with a
zero bit representing +1 and a one bit representing -1. Bits other than
bit 1 are garbage. These are meant to be kept in "int"s, and casts are
used to ensure the expressions are "int"s even if a and/or b might be
other types.
JACOBI_TWOS_U_BIT1 and JACOBI_RECIP_UU_BIT1 are used in mpn_jacobi_base
and their speed is important. Expressions are used rather than
conditionals to accumulate sign changes, which effectively means XORs
instead of conditional JUMPs. */
/* (a/0), with a signed; is 1 if a=+/-1, 0 otherwise */
#define JACOBI_S0(a) (((a) == 1) | ((a) == -1))
/* (a/0), with a unsigned; is 1 if a=+/-1, 0 otherwise */
#define JACOBI_U0(a) ((a) == 1)
/* (a/0), with a given by low and size;
is 1 if a=+/-1, 0 otherwise */
#define JACOBI_LS0(alow,asize)
(((asize) == 1 || (asize) == -1) && (alow) == 1)
/* (a/0), with a an mpz_t;
fetch of low limb always valid, even if size is zero */
#define JACOBI_Z0(a) JACOBI_LS0 (PTR(a)[0], SIZ(a))
/* (0/b), with b unsigned; is 1 if b=1, 0 otherwise */
#define JACOBI_0U(b) ((b) == 1)
/* (0/b), with b unsigned; is 1 if b=+/-1, 0 otherwise */
#define JACOBI_0S(b) ((b) == 1 || (b) == -1)
/* (0/b), with b given by low and size; is 1 if b=+/-1, 0 otherwise */
#define JACOBI_0LS(blow,bsize)
(((bsize) == 1 || (bsize) == -1) && (blow) == 1)
/* Convert a bit1 to +1 or -1. */
#define JACOBI_BIT1_TO_PN(result_bit1)
(1 - ((int) (result_bit1) & 2))
/* (2/b), with b unsigned and odd;
is (-1)^((b^2-1)/8) which is 1 if b==1,7mod8 or -1 if b==3,5mod8 and
hence obtained from (b>>1)^b */
#define JACOBI_TWO_U_BIT1(b)
((int) (((b) >> 1) ^ (b)))
/* (2/b)^twos, with b unsigned and odd */
#define JACOBI_TWOS_U_BIT1(twos, b)
((int) ((twos) << 1) & JACOBI_TWO_U_BIT1 (b))
/* (2/b)^twos, with b unsigned and odd */
#define JACOBI_TWOS_U(twos, b)
(JACOBI_BIT1_TO_PN (JACOBI_TWOS_U_BIT1 (twos, b)))
/* (-1/b), with b odd (signed or unsigned);
is (-1)^((b-1)/2) */
#define JACOBI_N1B_BIT1(b)
((int) (b))
/* (a/b) effect due to sign of a: signed/unsigned, b odd;
is (-1/b) if a<0, or +1 if a>=0 */
#define JACOBI_ASGN_SU_BIT1(a, b)
((((a) < 0) << 1) & JACOBI_N1B_BIT1(b))
/* (a/b) effect due to sign of b: signed/signed;
is -1 if a and b both negative, +1 otherwise */
#define JACOBI_BSGN_SS_BIT1(a, b)
((((a)<0) & ((b)<0)) << 1)
/* (a/b) effect due to sign of b: signed/mpz;
is -1 if a and b both negative, +1 otherwise */
#define JACOBI_BSGN_SZ_BIT1(a, b)
JACOBI_BSGN_SS_BIT1 (a, SIZ(b))
/* (a/b) effect due to sign of b: mpz/signed;
is -1 if a and b both negative, +1 otherwise */
#define JACOBI_BSGN_ZS_BIT1(a, b)
JACOBI_BSGN_SZ_BIT1 (b, a)
/* (a/b) reciprocity to switch to (b/a), a,b both unsigned and odd;
is (-1)^((a-1)*(b-1)/4), which means +1 if either a,b==1mod4, or -1 if
both a,b==3mod4, achieved in bit 1 by a&b. No ASSERT()s about a,b odd
because this is used in a couple of places with only bit 1 of a or b
valid. */
#define JACOBI_RECIP_UU_BIT1(a, b)
((int) ((a) & (b)))
/* Strip low zero limbs from {b_ptr,b_size} by incrementing b_ptr and
decrementing b_size. b_low should be b_ptr[0] on entry, and will be
updated for the new b_ptr. result_bit1 is updated according to the
factors of 2 stripped, as per (a/2). */
#define JACOBI_STRIP_LOW_ZEROS(result_bit1, a, b_ptr, b_size, b_low)
do {
ASSERT ((b_size) >= 1);
ASSERT ((b_low) == (b_ptr)[0]);
while (UNLIKELY ((b_low) == 0))
{
(b_size)--;
ASSERT ((b_size) >= 1);
(b_ptr)++;
(b_low) = *(b_ptr);
ASSERT (((a) & 1) != 0);
if ((GMP_NUMB_BITS % 2) == 1)
(result_bit1) ^= JACOBI_TWO_U_BIT1(a);
}
} while (0)
/* Set a_rem to {a_ptr,a_size} reduced modulo b, either using mod_1 or
modexact_1_odd, but in either case leaving a_rem<b. b must be odd and
unsigned. modexact_1_odd effectively calculates -a mod b, and
result_bit1 is adjusted for the factor of -1.
The way mpn_modexact_1_odd sometimes bases its remainder on a_size and
sometimes on a_size-1 means if GMP_NUMB_BITS is odd we can't know what
factor to introduce into result_bit1, so for that case use mpn_mod_1
unconditionally.
FIXME: mpn_modexact_1_odd is more efficient, so some way to get it used
for odd GMP_NUMB_BITS would be good. Perhaps it could mung its result,
or not skip a divide step, or something. */
#define JACOBI_MOD_OR_MODEXACT_1_ODD(result_bit1, a_rem, a_ptr, a_size, b)
do {
mp_srcptr __a_ptr = (a_ptr);
mp_size_t __a_size = (a_size);
mp_limb_t __b = (b);
ASSERT (__a_size >= 1);
ASSERT (__b & 1);
if ((GMP_NUMB_BITS % 2) != 0
|| ABOVE_THRESHOLD (__a_size, BMOD_1_TO_MOD_1_THRESHOLD))
{
(a_rem) = mpn_mod_1 (__a_ptr, __a_size, __b);
}
else
{
(result_bit1) ^= JACOBI_N1B_BIT1 (__b);
(a_rem) = mpn_modexact_1_odd (__a_ptr, __a_size, __b);
}
} while (0)
/* Matrix multiplication */
#define mpn_matrix22_mul __MPN(matrix22_mul)
__GMP_DECLSPEC void mpn_matrix22_mul __GMP_PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_srcptr, mp_srcptr, mp_srcptr, mp_size_t, mp_ptr));
#define mpn_matrix22_mul_strassen __MPN(matrix22_mul_strassen)
__GMP_DECLSPEC void mpn_matrix22_mul_strassen __GMP_PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_srcptr, mp_srcptr, mp_srcptr, mp_size_t, mp_ptr));
#define mpn_matrix22_mul_itch __MPN(matrix22_mul_itch)
__GMP_DECLSPEC mp_size_t mpn_matrix22_mul_itch __GMP_PROTO ((mp_size_t, mp_size_t));
#ifndef MATRIX22_STRASSEN_THRESHOLD
#define MATRIX22_STRASSEN_THRESHOLD 30
#endif
/* HGCD definitions */
/* Extract one numb, shifting count bits left
________ ________
|___xh___||___xl___|
|____r____|
>count <
The count includes any nail bits, so it should work fine if count
is computed using count_leading_zeros. If GMP_NAIL_BITS > 0, all of
xh, xl and r include nail bits. Must have 0 < count < GMP_LIMB_BITS.
FIXME: Omit masking with GMP_NUMB_MASK, and let callers do that for
those calls where the count high bits of xh may be non-zero.
*/
#define MPN_EXTRACT_NUMB(count, xh, xl)
((((xh) << ((count) - GMP_NAIL_BITS)) & GMP_NUMB_MASK) |
((xl) >> (GMP_LIMB_BITS - (count))))
/* The matrix non-negative M = (u, u'; v,v') keeps track of the
reduction (a;b) = M (alpha; beta) where alpha, beta are smaller
than a, b. The determinant must always be one, so that M has an
inverse (v', -u'; -v, u). Elements always fit in GMP_NUMB_BITS - 1
bits. */
struct hgcd_matrix1
{
mp_limb_t u[2][2];
};
#define mpn_hgcd2 __MPN (hgcd2)
__GMP_DECLSPEC int mpn_hgcd2 __GMP_PROTO ((mp_limb_t, mp_limb_t, mp_limb_t, mp_limb_t, struct hgcd_matrix1 *));
#define mpn_hgcd_mul_matrix1_vector __MPN (hgcd_mul_matrix1_vector)
__GMP_DECLSPEC mp_size_t mpn_hgcd_mul_matrix1_vector __GMP_PROTO ((const struct hgcd_matrix1 *, mp_ptr, mp_srcptr, mp_ptr, mp_size_t));
#define mpn_hgcd_mul_matrix1_inverse_vector __MPN (hgcd_mul_matrix1_inverse_vector)
__GMP_DECLSPEC mp_size_t mpn_hgcd_mul_matrix1_inverse_vector __GMP_PROTO ((const struct hgcd_matrix1 *, mp_ptr, mp_srcptr, mp_ptr, mp_size_t));
struct hgcd_matrix
{
mp_size_t alloc; /* for sanity checking only */
mp_size_t n;
mp_ptr p[2][2];
};
#define MPN_HGCD_MATRIX_INIT_ITCH(n) (4 * ((n+1)/2 + 1))
#define mpn_hgcd_matrix_init __MPN (hgcd_matrix_init)
__GMP_DECLSPEC void mpn_hgcd_matrix_init __GMP_PROTO ((struct hgcd_matrix *, mp_size_t, mp_ptr));
#define mpn_hgcd_matrix_mul __MPN (hgcd_matrix_mul)
__GMP_DECLSPEC void mpn_hgcd_matrix_mul __GMP_PROTO ((struct hgcd_matrix *, const struct hgcd_matrix *, mp_ptr));
#define mpn_hgcd_matrix_adjust __MPN (hgcd_matrix_adjust)
__GMP_DECLSPEC mp_size_t mpn_hgcd_matrix_adjust __GMP_PROTO ((struct hgcd_matrix *, mp_size_t, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
#define mpn_hgcd_itch __MPN (hgcd_itch)
__GMP_DECLSPEC mp_size_t mpn_hgcd_itch __GMP_PROTO ((mp_size_t));
#define mpn_hgcd __MPN (hgcd)
__GMP_DECLSPEC mp_size_t mpn_hgcd __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, struct hgcd_matrix *, mp_ptr));
#define MPN_HGCD_LEHMER_ITCH(n) (n)
#define mpn_hgcd_lehmer __MPN (hgcd_lehmer)
__GMP_DECLSPEC mp_size_t mpn_hgcd_lehmer __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t, struct hgcd_matrix *, mp_ptr));
/* Needs storage for the quotient */
#define MPN_GCD_SUBDIV_STEP_ITCH(n) (n)
#define mpn_gcd_subdiv_step __MPN(gcd_subdiv_step)
__GMP_DECLSPEC mp_size_t mpn_gcd_subdiv_step __GMP_PROTO ((mp_ptr, mp_size_t *, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
#define MPN_GCD_LEHMER_N_ITCH(n) (n)
#define mpn_gcd_lehmer_n __MPN(gcd_lehmer_n)
__GMP_DECLSPEC mp_size_t mpn_gcd_lehmer_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
#define mpn_gcdext_subdiv_step __MPN(gcdext_subdiv_step)
__GMP_DECLSPEC mp_size_t mpn_gcdext_subdiv_step __GMP_PROTO ((mp_ptr, mp_size_t *, mp_ptr, mp_size_t *, mp_ptr, mp_ptr, mp_size_t, mp_ptr, mp_ptr, mp_size_t *, mp_ptr, mp_ptr));
#define MPN_GCDEXT_LEHMER_N_ITCH(n) (4*(n) + 3)
#define mpn_gcdext_lehmer_n __MPN(gcdext_lehmer_n)
__GMP_DECLSPEC mp_size_t mpn_gcdext_lehmer_n __GMP_PROTO ((mp_ptr, mp_ptr, mp_size_t *, mp_ptr, mp_ptr, mp_size_t, mp_ptr));
/* 4*(an + 1) + 4*(bn + 1) + an */
#define MPN_GCDEXT_LEHMER_ITCH(an, bn) (5*(an) + 4*(bn) + 8)
#ifndef HGCD_THRESHOLD
#define HGCD_THRESHOLD 400
#endif
#ifndef GCD_DC_THRESHOLD
#define GCD_DC_THRESHOLD 1000
#endif
#ifndef GCDEXT_DC_THRESHOLD
#define GCDEXT_DC_THRESHOLD 600
#endif
/* Definitions for mpn_set_str and mpn_get_str */
struct powers
{
mp_ptr p; /* actual power value */
mp_size_t n; /* # of limbs at p */
mp_size_t shift; /* weight of lowest limb, in limb base B */
size_t digits_in_base; /* number of corresponding digits */
int base;
};
typedef struct powers powers_t;
#define mpn_dc_set_str_powtab_alloc(n) ((n) + GMP_LIMB_BITS)
#define mpn_dc_set_str_itch(n) ((n) + GMP_LIMB_BITS)
#define mpn_dc_get_str_powtab_alloc(n) ((n) + 2 * GMP_LIMB_BITS)
#define mpn_dc_get_str_itch(n) ((n) + GMP_LIMB_BITS)
#define mpn_dc_set_str __MPN(dc_set_str)
__GMP_DECLSPEC mp_size_t mpn_dc_set_str __GMP_PROTO ((mp_ptr, const unsigned char *, size_t, const powers_t *, mp_ptr));
#define mpn_bc_set_str __MPN(bc_set_str)
__GMP_DECLSPEC mp_size_t mpn_bc_set_str __GMP_PROTO ((mp_ptr, const unsigned char *, size_t, int));
#define mpn_set_str_compute_powtab __MPN(set_str_compute_powtab)
__GMP_DECLSPEC void mpn_set_str_compute_powtab __GMP_PROTO ((powers_t *, mp_ptr, mp_size_t, int));
/* __GMPF_BITS_TO_PREC applies a minimum 53 bits, rounds upwards to a whole
limb and adds an extra limb. __GMPF_PREC_TO_BITS drops that extra limb,
hence giving back the user's size in bits rounded up. Notice that
converting prec->bits->prec gives an unchanged value. */
#define __GMPF_BITS_TO_PREC(n)
((mp_size_t) ((__GMP_MAX (53, n) + 2 * GMP_NUMB_BITS - 1) / GMP_NUMB_BITS))
#define __GMPF_PREC_TO_BITS(n)
((mp_bitcnt_t) (n) * GMP_NUMB_BITS - GMP_NUMB_BITS)
__GMP_DECLSPEC extern mp_size_t __gmp_default_fp_limb_precision;
/* Set n to the number of significant digits an mpf of the given _mp_prec
field, in the given base. This is a rounded up value, designed to ensure
there's enough digits to reproduce all the guaranteed part of the value.
There are prec many limbs, but the high might be only "1" so forget it
and just count prec-1 limbs into chars. +1 rounds that upwards, and a
further +1 is because the limbs usually won't fall on digit boundaries.
FIXME: If base is a power of 2 and the bits per digit divides
GMP_LIMB_BITS then the +2 is unnecessary. This happens always for
base==2, and in base==16 with the current 32 or 64 bit limb sizes. */
#define MPF_SIGNIFICANT_DIGITS(n, base, prec)
do {
ASSERT (base >= 2 && base < numberof (mp_bases));
(n) = 2 + (size_t) ((((size_t) (prec) - 1) * GMP_NUMB_BITS)
* mp_bases[(base)].chars_per_bit_exactly);
} while (0)
/* Decimal point string, from the current C locale. Needs <langinfo.h> for
nl_langinfo and constants, preferably with _GNU_SOURCE defined to get
DECIMAL_POINT from glibc, and needs <locale.h> for localeconv, each under
their respective #if HAVE_FOO_H.
GLIBC recommends nl_langinfo because getting only one facet can be
faster, apparently. */
/* DECIMAL_POINT seems to need _GNU_SOURCE defined to get it from glibc. */
#if HAVE_NL_LANGINFO && defined (DECIMAL_POINT)
#define GMP_DECIMAL_POINT (nl_langinfo (DECIMAL_POINT))
#endif
/* RADIXCHAR is deprecated, still in unix98 or some such. */
#if HAVE_NL_LANGINFO && defined (RADIXCHAR) && ! defined (GMP_DECIMAL_POINT)
#define GMP_DECIMAL_POINT (nl_langinfo (RADIXCHAR))
#endif
/* localeconv is slower since it returns all locale stuff */
#if HAVE_LOCALECONV && ! defined (GMP_DECIMAL_POINT)
#define GMP_DECIMAL_POINT (localeconv()->decimal_point)
#endif
#if ! defined (GMP_DECIMAL_POINT)
#define GMP_DECIMAL_POINT (".")
#endif
#define DOPRNT_CONV_FIXED 1
#define DOPRNT_CONV_SCIENTIFIC 2
#define DOPRNT_CONV_GENERAL 3
#define DOPRNT_JUSTIFY_NONE 0
#define DOPRNT_JUSTIFY_LEFT 1
#define DOPRNT_JUSTIFY_RIGHT 2
#define DOPRNT_JUSTIFY_INTERNAL 3
#define DOPRNT_SHOWBASE_YES 1
#define DOPRNT_SHOWBASE_NO 2
#define DOPRNT_SHOWBASE_NONZERO 3
struct doprnt_params_t {
int base; /* negative for upper case */
int conv; /* choices above */
const char *expfmt; /* exponent format */
int exptimes4; /* exponent multiply by 4 */
char fill; /* character */
int justify; /* choices above */
int prec; /* prec field, or -1 for all digits */
int showbase; /* choices above */
int showpoint; /* if radix point always shown */
int showtrailing; /* if trailing zeros wanted */
char sign; /* '+', ' ', or '' */
int width; /* width field */
};
#if _GMP_H_HAVE_VA_LIST
__GMP_DECLSPEC typedef int (*doprnt_format_t) __GMP_PROTO ((void *, const char *, va_list));
__GMP_DECLSPEC typedef int (*doprnt_memory_t) __GMP_PROTO ((void *, const char *, size_t));
__GMP_DECLSPEC typedef int (*doprnt_reps_t) __GMP_PROTO ((void *, int, int));
__GMP_DECLSPEC typedef int (*doprnt_final_t) __GMP_PROTO ((void *));
struct doprnt_funs_t {
doprnt_format_t format;
doprnt_memory_t memory;
doprnt_reps_t reps;
doprnt_final_t final; /* NULL if not required */
};
extern const struct doprnt_funs_t __gmp_fprintf_funs;
extern const struct doprnt_funs_t __gmp_sprintf_funs;
extern const struct doprnt_funs_t __gmp_snprintf_funs;
extern const struct doprnt_funs_t __gmp_obstack_printf_funs;
extern const struct doprnt_funs_t __gmp_ostream_funs;
/* "buf" is a __gmp_allocate_func block of "alloc" many bytes. The first
"size" of these have been written. "alloc > size" is maintained, so
there's room to store a '' at the end. "result" is where the
application wants the final block pointer. */
struct gmp_asprintf_t {
char **result;
char *buf;
size_t size;
size_t alloc;
};
#define GMP_ASPRINTF_T_INIT(d, output)
do {
(d).result = (output);
(d).alloc = 256;
(d).buf = (char *) (*__gmp_allocate_func) ((d).alloc);
(d).size = 0;
} while (0)
/* If a realloc is necessary, use twice the size actually required, so as to
avoid repeated small reallocs. */
#define GMP_ASPRINTF_T_NEED(d, n)
do {
size_t alloc, newsize, newalloc;
ASSERT ((d)->alloc >= (d)->size + 1);
alloc = (d)->alloc;
newsize = (d)->size + (n);
if (alloc <= newsize)
{
newalloc = 2*newsize;
(d)->alloc = newalloc;
(d)->buf = __GMP_REALLOCATE_FUNC_TYPE ((d)->buf,
alloc, newalloc, char);
}
} while (0)
__GMP_DECLSPEC int __gmp_asprintf_memory __GMP_PROTO ((struct gmp_asprintf_t *, const char *, size_t));
__GMP_DECLSPEC int __gmp_asprintf_reps __GMP_PROTO ((struct gmp_asprintf_t *, int, int));
__GMP_DECLSPEC int __gmp_asprintf_final __GMP_PROTO ((struct gmp_asprintf_t *));
/* buf is where to write the next output, and size is how much space is left
there. If the application passed size==0 then that's what we'll have
here, and nothing at all should be written. */
struct gmp_snprintf_t {
char *buf;
size_t size;
};
/* Add the bytes printed by the call to the total retval, or bail out on an
error. */
#define DOPRNT_ACCUMULATE(call)
do {
int __ret;
__ret = call;
if (__ret == -1)
goto error;
retval += __ret;
} while (0)
#define DOPRNT_ACCUMULATE_FUN(fun, params)
do {
ASSERT ((fun) != NULL);
DOPRNT_ACCUMULATE ((*(fun)) params);
} while (0)
#define DOPRNT_FORMAT(fmt, ap)
DOPRNT_ACCUMULATE_FUN (funs->format, (data, fmt, ap))
#define DOPRNT_MEMORY(ptr, len)
DOPRNT_ACCUMULATE_FUN (funs->memory, (data, ptr, len))
#define DOPRNT_REPS(c, n)
DOPRNT_ACCUMULATE_FUN (funs->reps, (data, c, n))
#define DOPRNT_STRING(str) DOPRNT_MEMORY (str, strlen (str))
#define DOPRNT_REPS_MAYBE(c, n)
do {
if ((n) != 0)
DOPRNT_REPS (c, n);
} while (0)
#define DOPRNT_MEMORY_MAYBE(ptr, len)
do {
if ((len) != 0)
DOPRNT_MEMORY (ptr, len);
} while (0)
__GMP_DECLSPEC int __gmp_doprnt __GMP_PROTO ((const struct doprnt_funs_t *, void *, const char *, va_list));
__GMP_DECLSPEC int __gmp_doprnt_integer __GMP_PROTO ((const struct doprnt_funs_t *, void *, const struct doprnt_params_t *, const char *));
#define __gmp_doprnt_mpf __gmp_doprnt_mpf2
__GMP_DECLSPEC int __gmp_doprnt_mpf __GMP_PROTO ((const struct doprnt_funs_t *, void *, const struct doprnt_params_t *, const char *, mpf_srcptr));
__GMP_DECLSPEC int __gmp_replacement_vsnprintf __GMP_PROTO ((char *, size_t, const char *, va_list));
#endif /* _GMP_H_HAVE_VA_LIST */
typedef int (*gmp_doscan_scan_t) __GMP_PROTO ((void *, const char *, ...));
typedef void *(*gmp_doscan_step_t) __GMP_PROTO ((void *, int));
typedef int (*gmp_doscan_get_t) __GMP_PROTO ((void *));
typedef int (*gmp_doscan_unget_t) __GMP_PROTO ((int, void *));
struct gmp_doscan_funs_t {
gmp_doscan_scan_t scan;
gmp_doscan_step_t step;
gmp_doscan_get_t get;
gmp_doscan_unget_t unget;
};
extern const struct gmp_doscan_funs_t __gmp_fscanf_funs;
extern const struct gmp_doscan_funs_t __gmp_sscanf_funs;
#if _GMP_H_HAVE_VA_LIST
__GMP_DECLSPEC int __gmp_doscan __GMP_PROTO ((const struct gmp_doscan_funs_t *, void *, const char *, va_list));
#endif
/* For testing and debugging. */
#define MPZ_CHECK_FORMAT(z)
do {
ASSERT_ALWAYS (SIZ(z) == 0 || PTR(z)[ABSIZ(z) - 1] != 0);
ASSERT_ALWAYS (ALLOC(z) >= ABSIZ(z));
ASSERT_ALWAYS_MPN (PTR(z), ABSIZ(z));
} while (0)
#define MPQ_CHECK_FORMAT(q)
do {
MPZ_CHECK_FORMAT (mpq_numref (q));
MPZ_CHECK_FORMAT (mpq_denref (q));
ASSERT_ALWAYS (SIZ(mpq_denref(q)) >= 1);
if (SIZ(mpq_numref(q)) == 0)
{
/* should have zero as 0/1 */
ASSERT_ALWAYS (SIZ(mpq_denref(q)) == 1
&& PTR(mpq_denref(q))[0] == 1);
}
else
{
/* should have no common factors */
mpz_t g;
mpz_init (g);
mpz_gcd (g, mpq_numref(q), mpq_denref(q));
ASSERT_ALWAYS (mpz_cmp_ui (g, 1) == 0);
mpz_clear (g);
}
} while (0)
#define MPF_CHECK_FORMAT(f)
do {
ASSERT_ALWAYS (PREC(f) >= __GMPF_BITS_TO_PREC(53));
ASSERT_ALWAYS (ABSIZ(f) <= PREC(f)+1);
if (SIZ(f) == 0)
ASSERT_ALWAYS (EXP(f) == 0);
if (SIZ(f) != 0)
ASSERT_ALWAYS (PTR(f)[ABSIZ(f) - 1] != 0);
} while (0)
#define MPZ_PROVOKE_REALLOC(z)
do { ALLOC(z) = ABSIZ(z); } while (0)
/* Enhancement: The "mod" and "gcd_1" functions below could have
__GMP_ATTRIBUTE_PURE, but currently (gcc 3.3) that's not supported on
function pointers, only actual functions. It probably doesn't make much
difference to the gmp code, since hopefully we arrange calls so there's
no great need for the compiler to move things around. */
#if WANT_FAT_BINARY && (HAVE_HOST_CPU_FAMILY_x86 || HAVE_HOST_CPU_FAMILY_x86_64)
/* NOTE: The function pointers in this struct are also in CPUVEC_FUNCS_LIST
in mpn/x86/x86-defs.m4. Be sure to update that when changing here. */
struct cpuvec_t {
DECL_add_n ((*add_n));
DECL_addmul_1 ((*addmul_1));
DECL_copyd ((*copyd));
DECL_copyi ((*copyi));
DECL_divexact_1 ((*divexact_1));
DECL_divexact_by3c ((*divexact_by3c));
DECL_divrem_1 ((*divrem_1));
DECL_gcd_1 ((*gcd_1));
DECL_lshift ((*lshift));
DECL_mod_1 ((*mod_1));
DECL_mod_34lsub1 ((*mod_34lsub1));
DECL_modexact_1c_odd ((*modexact_1c_odd));
DECL_mul_1 ((*mul_1));
DECL_mul_basecase ((*mul_basecase));
DECL_preinv_divrem_1 ((*preinv_divrem_1));
DECL_preinv_mod_1 ((*preinv_mod_1));
DECL_rshift ((*rshift));
DECL_sqr_basecase ((*sqr_basecase));
DECL_sub_n ((*sub_n));
DECL_submul_1 ((*submul_1));
int initialized;
mp_size_t mul_toom22_threshold;
mp_size_t mul_toom33_threshold;
mp_size_t sqr_toom2_threshold;
mp_size_t sqr_toom3_threshold;
};
__GMP_DECLSPEC extern struct cpuvec_t __gmpn_cpuvec;
#endif /* x86 fat binary */
__GMP_DECLSPEC void __gmpn_cpuvec_init __GMP_PROTO ((void));
/* Get a threshold "field" from __gmpn_cpuvec, running __gmpn_cpuvec_init()
if that hasn't yet been done (to establish the right values). */
#define CPUVEC_THRESHOLD(field)
((LIKELY (__gmpn_cpuvec.initialized) ? 0 : (__gmpn_cpuvec_init (), 0)),
__gmpn_cpuvec.field)
#if HAVE_NATIVE_mpn_add_nc
#define mpn_add_nc __MPN(add_nc)
__GMP_DECLSPEC mp_limb_t mpn_add_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
#else
static inline
mp_limb_t
mpn_add_nc (mp_ptr rp, mp_srcptr up, mp_srcptr vp, mp_size_t n, mp_limb_t ci)
{
mp_limb_t co;
co = mpn_add_n (rp, up, vp, n);
co += mpn_add_1 (rp, rp, n, ci);
return co;
}
#endif
#if HAVE_NATIVE_mpn_sub_nc
#define mpn_sub_nc __MPN(sub_nc)
__GMP_DECLSPEC mp_limb_t mpn_sub_nc __GMP_PROTO ((mp_ptr, mp_srcptr, mp_srcptr, mp_size_t, mp_limb_t));
#else
static inline mp_limb_t
mpn_sub_nc (mp_ptr rp, mp_srcptr up, mp_srcptr vp, mp_size_t n, mp_limb_t ci)
{
mp_limb_t co;
co = mpn_sub_n (rp, up, vp, n);
co += mpn_sub_1 (rp, rp, n, ci);
return co;
}
#endif
static inline int
mpn_zero_p (mp_srcptr ap, mp_size_t n)
{
mp_size_t i;
for (i = n - 1; i >= 0; i--)
{
if (ap[i] != 0)
return 0;
}
return 1;
}
#if TUNE_PROGRAM_BUILD
/* Some extras wanted when recompiling some .c files for use by the tune
program. Not part of a normal build.
It's necessary to keep these thresholds as #defines (just to an
identically named variable), since various defaults are established based
on #ifdef in the .c files. For some this is not so (the defaults are
instead established above), but all are done this way for consistency. */
#undef MUL_TOOM22_THRESHOLD
#define MUL_TOOM22_THRESHOLD mul_toom22_threshold
extern mp_size_t mul_toom22_threshold;
#undef MUL_TOOM33_THRESHOLD
#define MUL_TOOM33_THRESHOLD mul_toom33_threshold
extern mp_size_t mul_toom33_threshold;
#undef MUL_TOOM44_THRESHOLD
#define MUL_TOOM44_THRESHOLD mul_toom44_threshold
extern mp_size_t mul_toom44_threshold;
#undef MUL_TOOM6H_THRESHOLD
#define MUL_TOOM6H_THRESHOLD mul_toom6h_threshold
extern mp_size_t mul_toom6h_threshold;
#undef MUL_TOOM8H_THRESHOLD
#define MUL_TOOM8H_THRESHOLD mul_toom8h_threshold
extern mp_size_t mul_toom8h_threshold;
#undef MUL_TOOM32_TO_TOOM43_THRESHOLD
#define MUL_TOOM32_TO_TOOM43_THRESHOLD mul_toom32_to_toom43_threshold
extern mp_size_t mul_toom32_to_toom43_threshold;
#undef MUL_TOOM32_TO_TOOM53_THRESHOLD
#define MUL_TOOM32_TO_TOOM53_THRESHOLD mul_toom32_to_toom53_threshold
extern mp_size_t mul_toom32_to_toom53_threshold;
#undef MUL_TOOM42_TO_TOOM53_THRESHOLD
#define MUL_TOOM42_TO_TOOM53_THRESHOLD mul_toom42_to_toom53_threshold
extern mp_size_t mul_toom42_to_toom53_threshold;
#undef MUL_TOOM42_TO_TOOM63_THRESHOLD
#define MUL_TOOM42_TO_TOOM63_THRESHOLD mul_toom42_to_toom63_threshold
extern mp_size_t mul_toom42_to_toom63_threshold;
#undef MUL_FFT_THRESHOLD
#define MUL_FFT_THRESHOLD mul_fft_threshold
extern mp_size_t mul_fft_threshold;
#undef MUL_FFT_MODF_THRESHOLD
#define MUL_FFT_MODF_THRESHOLD mul_fft_modf_threshold
extern mp_size_t mul_fft_modf_threshold;
#undef MUL_FFT_TABLE
#define MUL_FFT_TABLE { 0 }
#undef MUL_FFT_TABLE3
#define MUL_FFT_TABLE3 { {0,0} }
/* A native mpn_sqr_basecase is not tuned and SQR_BASECASE_THRESHOLD should
remain as zero (always use it). */
#if ! HAVE_NATIVE_mpn_sqr_basecase
#undef SQR_BASECASE_THRESHOLD
#define SQR_BASECASE_THRESHOLD sqr_basecase_threshold
extern mp_size_t sqr_basecase_threshold;
#endif
#if TUNE_PROGRAM_BUILD_SQR
#undef SQR_TOOM2_THRESHOLD
#define SQR_TOOM2_THRESHOLD SQR_TOOM2_MAX_GENERIC
#else
#undef SQR_TOOM2_THRESHOLD
#define SQR_TOOM2_THRESHOLD sqr_toom2_threshold
extern mp_size_t sqr_toom2_threshold;
#endif
#undef SQR_TOOM3_THRESHOLD
#define SQR_TOOM3_THRESHOLD sqr_toom3_threshold
extern mp_size_t sqr_toom3_threshold;
#undef SQR_TOOM4_THRESHOLD
#define SQR_TOOM4_THRESHOLD sqr_toom4_threshold
extern mp_size_t sqr_toom4_threshold;
#undef SQR_TOOM6_THRESHOLD
#define SQR_TOOM6_THRESHOLD sqr_toom6_threshold
extern mp_size_t sqr_toom6_threshold;
#undef SQR_TOOM8_THRESHOLD
#define SQR_TOOM8_THRESHOLD sqr_toom8_threshold
extern mp_size_t sqr_toom8_threshold;
#undef SQR_FFT_THRESHOLD
#define SQR_FFT_THRESHOLD sqr_fft_threshold
extern mp_size_t sqr_fft_threshold;
#undef SQR_FFT_MODF_THRESHOLD
#define SQR_FFT_MODF_THRESHOLD sqr_fft_modf_threshold
extern mp_size_t sqr_fft_modf_threshold;
#undef SQR_FFT_TABLE
#define SQR_FFT_TABLE { 0 }
#undef SQR_FFT_TABLE3
#define SQR_FFT_TABLE3 { {0,0} }
#undef MULLO_BASECASE_THRESHOLD
#define MULLO_BASECASE_THRESHOLD mullo_basecase_threshold
extern mp_size_t mullo_basecase_threshold;
#undef MULLO_DC_THRESHOLD
#define MULLO_DC_THRESHOLD mullo_dc_threshold
extern mp_size_t mullo_dc_threshold;
#undef MULLO_MUL_N_THRESHOLD
#define MULLO_MUL_N_THRESHOLD mullo_mul_n_threshold
extern mp_size_t mullo_mul_n_threshold;
#undef DC_DIV_QR_THRESHOLD
#define DC_DIV_QR_THRESHOLD dc_div_qr_threshold
extern mp_size_t dc_div_qr_threshold;
#undef DC_DIVAPPR_Q_THRESHOLD
#define DC_DIVAPPR_Q_THRESHOLD dc_divappr_q_threshold
extern mp_size_t dc_divappr_q_threshold;
#undef DC_BDIV_Q_THRESHOLD
#define DC_BDIV_Q_THRESHOLD dc_bdiv_q_threshold
extern mp_size_t dc_bdiv_q_threshold;
#undef DC_BDIV_QR_THRESHOLD
#define DC_BDIV_QR_THRESHOLD dc_bdiv_qr_threshold
extern mp_size_t dc_bdiv_qr_threshold;
#undef MU_DIV_QR_THRESHOLD
#define MU_DIV_QR_THRESHOLD mu_div_qr_threshold
extern mp_size_t mu_div_qr_threshold;
#undef MU_DIVAPPR_Q_THRESHOLD
#define MU_DIVAPPR_Q_THRESHOLD mu_divappr_q_threshold
extern mp_size_t mu_divappr_q_threshold;
#undef MUPI_DIV_QR_THRESHOLD
#define MUPI_DIV_QR_THRESHOLD mupi_div_qr_threshold
extern mp_size_t mupi_div_qr_threshold;
#undef MU_BDIV_QR_THRESHOLD
#define MU_BDIV_QR_THRESHOLD mu_bdiv_qr_threshold
extern mp_size_t mu_bdiv_qr_threshold;
#undef MU_BDIV_Q_THRESHOLD
#define MU_BDIV_Q_THRESHOLD mu_bdiv_q_threshold
extern mp_size_t mu_bdiv_q_threshold;
#undef INV_MULMOD_BNM1_THRESHOLD
#define INV_MULMOD_BNM1_THRESHOLD inv_mulmod_bnm1_threshold
extern mp_size_t inv_mulmod_bnm1_threshold;
#undef INV_NEWTON_THRESHOLD
#define INV_NEWTON_THRESHOLD inv_newton_threshold
extern mp_size_t inv_newton_threshold;
#undef INV_APPR_THRESHOLD
#define INV_APPR_THRESHOLD inv_appr_threshold
extern mp_size_t inv_appr_threshold;
#undef BINV_NEWTON_THRESHOLD
#define BINV_NEWTON_THRESHOLD binv_newton_threshold
extern mp_size_t binv_newton_threshold;
#undef REDC_1_TO_REDC_2_THRESHOLD
#define REDC_1_TO_REDC_2_THRESHOLD redc_1_to_redc_2_threshold
extern mp_size_t redc_1_to_redc_2_threshold;
#undef REDC_2_TO_REDC_N_THRESHOLD
#define REDC_2_TO_REDC_N_THRESHOLD redc_2_to_redc_n_threshold
extern mp_size_t redc_2_to_redc_n_threshold;
#undef REDC_1_TO_REDC_N_THRESHOLD
#define REDC_1_TO_REDC_N_THRESHOLD redc_1_to_redc_n_threshold
extern mp_size_t redc_1_to_redc_n_threshold;
#undef MATRIX22_STRASSEN_THRESHOLD
#define MATRIX22_STRASSEN_THRESHOLD matrix22_strassen_threshold
extern mp_size_t matrix22_strassen_threshold;
#undef HGCD_THRESHOLD
#define HGCD_THRESHOLD hgcd_threshold
extern mp_size_t hgcd_threshold;
#undef GCD_DC_THRESHOLD
#define GCD_DC_THRESHOLD gcd_dc_threshold
extern mp_size_t gcd_dc_threshold;
#undef GCDEXT_DC_THRESHOLD
#define GCDEXT_DC_THRESHOLD gcdext_dc_threshold
extern mp_size_t gcdext_dc_threshold;
#undef DIVREM_1_NORM_THRESHOLD
#define DIVREM_1_NORM_THRESHOLD divrem_1_norm_threshold
extern mp_size_t divrem_1_norm_threshold;
#undef DIVREM_1_UNNORM_THRESHOLD
#define DIVREM_1_UNNORM_THRESHOLD divrem_1_unnorm_threshold
extern mp_size_t divrem_1_unnorm_threshold;
#undef MOD_1_NORM_THRESHOLD
#define MOD_1_NORM_THRESHOLD mod_1_norm_threshold
extern mp_size_t mod_1_norm_threshold;
#undef MOD_1_UNNORM_THRESHOLD
#define MOD_1_UNNORM_THRESHOLD mod_1_unnorm_threshold
extern mp_size_t mod_1_unnorm_threshold;
#undef MOD_1N_TO_MOD_1_1_THRESHOLD
#define MOD_1N_TO_MOD_1_1_THRESHOLD mod_1n_to_mod_1_1_threshold
extern mp_size_t mod_1n_to_mod_1_1_threshold;
#undef MOD_1U_TO_MOD_1_1_THRESHOLD
#define MOD_1U_TO_MOD_1_1_THRESHOLD mod_1u_to_mod_1_1_threshold
extern mp_size_t mod_1u_to_mod_1_1_threshold;
#undef MOD_1_1_TO_MOD_1_2_THRESHOLD
#define MOD_1_1_TO_MOD_1_2_THRESHOLD mod_1_1_to_mod_1_2_threshold
extern mp_size_t mod_1_1_to_mod_1_2_threshold;
#undef MOD_1_2_TO_MOD_1_4_THRESHOLD
#define MOD_1_2_TO_MOD_1_4_THRESHOLD mod_1_2_to_mod_1_4_threshold
extern mp_size_t mod_1_2_to_mod_1_4_threshold;
#undef PREINV_MOD_1_TO_MOD_1_THRESHOLD
#define PREINV_MOD_1_TO_MOD_1_THRESHOLD preinv_mod_1_to_mod_1_threshold
extern mp_size_t preinv_mod_1_to_mod_1_threshold;
#if ! UDIV_PREINV_ALWAYS
#undef DIVREM_2_THRESHOLD
#define DIVREM_2_THRESHOLD divrem_2_threshold
extern mp_size_t divrem_2_threshold;
#endif
#undef MULMOD_BNM1_THRESHOLD
#define MULMOD_BNM1_THRESHOLD mulmod_bnm1_threshold
extern mp_size_t mulmod_bnm1_threshold;
#undef SQRMOD_BNM1_THRESHOLD
#define SQRMOD_BNM1_THRESHOLD sqrmod_bnm1_threshold
extern mp_size_t sqrmod_bnm1_threshold;
#undef GET_STR_DC_THRESHOLD
#define GET_STR_DC_THRESHOLD get_str_dc_threshold
extern mp_size_t get_str_dc_threshold;
#undef GET_STR_PRECOMPUTE_THRESHOLD
#define GET_STR_PRECOMPUTE_THRESHOLD get_str_precompute_threshold
extern mp_size_t get_str_precompute_threshold;
#undef SET_STR_DC_THRESHOLD
#define SET_STR_DC_THRESHOLD set_str_dc_threshold
extern mp_size_t set_str_dc_threshold;
#undef SET_STR_PRECOMPUTE_THRESHOLD
#define SET_STR_PRECOMPUTE_THRESHOLD set_str_precompute_threshold
extern mp_size_t set_str_precompute_threshold;
#undef FFT_TABLE_ATTRS
#define FFT_TABLE_ATTRS
extern mp_size_t mpn_fft_table[2][MPN_FFT_TABLE_SIZE];
#define FFT_TABLE3_SIZE 2000 /* generous space for tuning */
extern struct fft_table_nk mpn_fft_table3[2][FFT_TABLE3_SIZE];
/* Sizes the tune program tests up to, used in a couple of recompilations. */
#undef MUL_TOOM22_THRESHOLD_LIMIT
#undef MUL_TOOM33_THRESHOLD_LIMIT
#undef MULLO_BASECASE_THRESHOLD_LIMIT
#undef SQR_TOOM3_THRESHOLD_LIMIT
#define SQR_TOOM2_MAX_GENERIC 200
#define MUL_TOOM22_THRESHOLD_LIMIT 700
#define MUL_TOOM33_THRESHOLD_LIMIT 700
#define SQR_TOOM3_THRESHOLD_LIMIT 400
#define MUL_TOOM44_THRESHOLD_LIMIT 1000
#define SQR_TOOM4_THRESHOLD_LIMIT 1000
#define MUL_TOOM6H_THRESHOLD_LIMIT 1100
#define SQR_TOOM6_THRESHOLD_LIMIT 1100
#define MUL_TOOM8H_THRESHOLD_LIMIT 1200
#define SQR_TOOM8_THRESHOLD_LIMIT 1200
#define MULLO_BASECASE_THRESHOLD_LIMIT 200
#define GET_STR_THRESHOLD_LIMIT 150
#endif /* TUNE_PROGRAM_BUILD */
#if defined (__cplusplus)
}
#endif
/* FIXME: Make these itch functions less conservative. Also consider making
them dependent on just 'an', and compute the allocation directly from 'an'
instead of via n. */
/* toom22/toom2: Scratch need is 2*(an + k), k is the recursion depth.
k is ths smallest k such that
ceil(an/2^k) < MUL_TOOM22_THRESHOLD.
which implies that
k = bitsize of floor ((an-1)/(MUL_TOOM22_THRESHOLD-1))
= 1 + floor (log_2 (floor ((an-1)/(MUL_TOOM22_THRESHOLD-1))))
*/
#define mpn_toom22_mul_itch(an, bn)
(2 * ((an) + GMP_NUMB_BITS))
#define mpn_toom2_sqr_itch(an)
(2 * ((an) + GMP_NUMB_BITS))
/* Can probably be trimmed to 2 an + O(log an). */
#define mpn_toom33_mul_itch(an, bn)
((5 * (an) >> 1) + GMP_NUMB_BITS)
#define mpn_toom3_sqr_itch(an)
((5 * (an) >> 1) + GMP_NUMB_BITS)
#define mpn_toom44_mul_itch(an, bn)
(3 * (an) + GMP_NUMB_BITS)
#define mpn_toom4_sqr_itch(an)
(3 * (an) + GMP_NUMB_BITS)
#define mpn_toom6_sqr_itch(n)
( ((n) - SQR_TOOM6_THRESHOLD)*2 +
MAX(SQR_TOOM6_THRESHOLD*2 + GMP_NUMB_BITS*6,
mpn_toom4_sqr_itch(SQR_TOOM6_THRESHOLD)) )
#define mpn_toom6_mul_n_itch(n)
( ((n) - MUL_TOOM6H_THRESHOLD)*2 +
MAX(MUL_TOOM6H_THRESHOLD*2 + GMP_NUMB_BITS*6,
mpn_toom44_mul_itch(MUL_TOOM6H_THRESHOLD,MUL_TOOM6H_THRESHOLD)) )
static inline mp_size_t
mpn_toom6h_mul_itch (mp_size_t an, mp_size_t bn) {
mp_size_t estimatedN;
estimatedN = (an + bn) / (size_t) 10 + 1;
return mpn_toom6_mul_n_itch (estimatedN * 6);
}
#define mpn_toom8_sqr_itch(n)
( (((n)*15)>>3) - ((SQR_TOOM8_THRESHOLD*15)>>3) +
MAX(((SQR_TOOM8_THRESHOLD*15)>>3) + GMP_NUMB_BITS*6,
mpn_toom6_sqr_itch(SQR_TOOM8_THRESHOLD)) )
#define mpn_toom8_mul_n_itch(n)
( (((n)*15)>>3) - ((MUL_TOOM8H_THRESHOLD*15)>>3) +
MAX(((MUL_TOOM8H_THRESHOLD*15)>>3) + GMP_NUMB_BITS*6,
mpn_toom6_mul_n_itch(MUL_TOOM8H_THRESHOLD)) )
static inline mp_size_t
mpn_toom8h_mul_itch (mp_size_t an, mp_size_t bn) {
mp_size_t estimatedN;
estimatedN = (an + bn) / (size_t) 14 + 1;
return mpn_toom8_mul_n_itch (estimatedN * 8);
}
static inline mp_size_t
mpn_toom32_mul_itch (mp_size_t an, mp_size_t bn)
{
mp_size_t n = 1 + (2 * an >= 3 * bn ? (an - 1) / (size_t) 3 : (bn - 1) >> 1);
mp_size_t itch = 2 * n + 1;
return itch;
}
static inline mp_size_t
mpn_toom42_mul_itch (mp_size_t an, mp_size_t bn)
{
mp_size_t n = an >= 2 * bn ? (an + 3) >> 2 : (bn + 1) >> 1;
return 6 * n + 3;
}
static inline mp_size_t
mpn_toom43_mul_itch (mp_size_t an, mp_size_t bn)
{
mp_size_t n = 1 + (3 * an >= 4 * bn ? (an - 1) >> 2 : (bn - 1) / (size_t) 3);
return 6*n + 4;
}
static inline mp_size_t
mpn_toom52_mul_itch (mp_size_t an, mp_size_t bn)
{
mp_size_t n = 1 + (2 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) >> 1);
return 6*n + 4;
}
static inline mp_size_t
mpn_toom53_mul_itch (mp_size_t an, mp_size_t bn)
{
mp_size_t n = 1 + (3 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 3);
return 10 * n + 10;
}
static inline mp_size_t
mpn_toom62_mul_itch (mp_size_t an, mp_size_t bn)
{
mp_size_t n = 1 + (an >= 3 * bn ? (an - 1) / (size_t) 6 : (bn - 1) >> 1);
return 10 * n + 10;
}
static inline mp_size_t
mpn_toom63_mul_itch (mp_size_t an, mp_size_t bn)
{
mp_size_t n = 1 + (an >= 2 * bn ? (an - 1) / (size_t) 6 : (bn - 1) / (size_t) 3);
return 9 * n + 3;
}
#if 0
#define mpn_fft_mul mpn_mul_fft_full
#else
#define mpn_fft_mul mpn_nussbaumer_mul
#endif
#ifdef __cplusplus
/* A little helper for a null-terminated __gmp_allocate_func string.
The destructor ensures it's freed even if an exception is thrown.
The len field is needed by the destructor, and can be used by anyone else
to avoid a second strlen pass over the data.
Since our input is a C string, using strlen is correct. Perhaps it'd be
more C++-ish style to use std::char_traits<char>::length, but char_traits
isn't available in gcc 2.95.4. */
class gmp_allocated_string {
public:
char *str;
size_t len;
gmp_allocated_string(char *arg)
{
str = arg;
len = std::strlen (str);
}
~gmp_allocated_string()
{
(*__gmp_free_func) (str, len+1);
}
};
std::istream &__gmpz_operator_in_nowhite (std::istream &, mpz_ptr, char);
int __gmp_istream_set_base (std::istream &, char &, bool &, bool &);
void __gmp_istream_set_digits (std::string &, std::istream &, char &, bool &, int);
void __gmp_doprnt_params_from_ios (struct doprnt_params_t *p, std::ios &o);
std::ostream& __gmp_doprnt_integer_ostream (std::ostream &o, struct doprnt_params_t *p, char *s);
extern const struct doprnt_funs_t __gmp_asprintf_funs_noformat;
#endif /* __cplusplus */
#endif /* __GMP_IMPL_H__ */