Contributed to the GNU project by Niels Möller
-Copyright 1991, 1992, 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2001,
-2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013
-Free Software Foundation, Inc.
+Copyright 1991-1997, 1999-2019 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
#include "mini-gmp.h"
-\f
+#if !defined(MINI_GMP_DONT_USE_FLOAT_H)
+#include <float.h>
+#endif
+
+
/* Macros */
#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
-#define GMP_LIMB_MAX (~ (mp_limb_t) 0)
+#define GMP_LIMB_MAX ((mp_limb_t) ~ (mp_limb_t) 0)
#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b))
#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b))
+#define GMP_CMP(a,b) (((a) > (b)) - ((a) < (b)))
+
+#if defined(DBL_MANT_DIG) && FLT_RADIX == 2
+#define GMP_DBL_MANT_BITS DBL_MANT_DIG
+#else
+#define GMP_DBL_MANT_BITS (53)
+#endif
+
+/* Return non-zero if xp,xsize and yp,ysize overlap.
+ If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no
+ overlap. If both these are false, there's an overlap. */
+#define GMP_MPN_OVERLAP_P(xp, xsize, yp, ysize) \
+ ((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp))
+
#define gmp_assert_nocarry(x) do { \
- mp_limb_t __cy = x; \
+ mp_limb_t __cy = (x); \
assert (__cy == 0); \
} while (0)
#define gmp_clz(count, x) do { \
mp_limb_t __clz_x = (x); \
- unsigned __clz_c; \
- for (__clz_c = 0; \
- (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \
- __clz_c += 8) \
- __clz_x <<= 8; \
+ unsigned __clz_c = 0; \
+ int LOCAL_SHIFT_BITS = 8; \
+ if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS) \
+ for (; \
+ (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \
+ __clz_c += 8) \
+ { __clz_x <<= LOCAL_SHIFT_BITS; } \
for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \
__clz_x <<= 1; \
(count) = __clz_c; \
#define gmp_umul_ppmm(w1, w0, u, v) \
do { \
- mp_limb_t __x0, __x1, __x2, __x3; \
- unsigned __ul, __vl, __uh, __vh; \
- mp_limb_t __u = (u), __v = (v); \
+ int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; \
+ if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS) \
+ { \
+ unsigned int __ww = (unsigned int) (u) * (v); \
+ w0 = (mp_limb_t) __ww; \
+ w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
+ } \
+ else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS) \
+ { \
+ unsigned long int __ww = (unsigned long int) (u) * (v); \
+ w0 = (mp_limb_t) __ww; \
+ w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
+ } \
+ else { \
+ mp_limb_t __x0, __x1, __x2, __x3; \
+ unsigned __ul, __vl, __uh, __vh; \
+ mp_limb_t __u = (u), __v = (v); \
\
- __ul = __u & GMP_LLIMB_MASK; \
- __uh = __u >> (GMP_LIMB_BITS / 2); \
- __vl = __v & GMP_LLIMB_MASK; \
- __vh = __v >> (GMP_LIMB_BITS / 2); \
+ __ul = __u & GMP_LLIMB_MASK; \
+ __uh = __u >> (GMP_LIMB_BITS / 2); \
+ __vl = __v & GMP_LLIMB_MASK; \
+ __vh = __v >> (GMP_LIMB_BITS / 2); \
\
- __x0 = (mp_limb_t) __ul * __vl; \
- __x1 = (mp_limb_t) __ul * __vh; \
- __x2 = (mp_limb_t) __uh * __vl; \
- __x3 = (mp_limb_t) __uh * __vh; \
+ __x0 = (mp_limb_t) __ul * __vl; \
+ __x1 = (mp_limb_t) __ul * __vh; \
+ __x2 = (mp_limb_t) __uh * __vl; \
+ __x3 = (mp_limb_t) __uh * __vh; \
\
- __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \
- __x1 += __x2; /* but this indeed can */ \
- if (__x1 < __x2) /* did we get it? */ \
- __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \
+ __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \
+ __x1 += __x2; /* but this indeed can */ \
+ if (__x1 < __x2) /* did we get it? */ \
+ __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \
\
- (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
- (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
+ (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
+ (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
+ } \
} while (0)
#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
} while (0)
#define MPZ_SRCPTR_SWAP(x, y) \
do { \
- mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
+ mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
(x) = (y); \
(y) = __mpz_srcptr_swap__tmp; \
} while (0)
+const int mp_bits_per_limb = GMP_LIMB_BITS;
+
\f
/* Memory allocation and other helper functions. */
static void
}
static void *
-gmp_default_realloc (void *old, size_t old_size, size_t new_size)
+gmp_default_realloc (void *old, size_t unused_old_size, size_t new_size)
{
- mp_ptr p;
+ void * p;
p = realloc (old, new_size);
if (!p)
- gmp_die("gmp_default_realoc: Virtual memory exhausted.");
+ gmp_die("gmp_default_realloc: Virtual memory exhausted.");
return p;
}
static void
-gmp_default_free (void *p, size_t size)
+gmp_default_free (void *p, size_t unused_size)
{
free (p);
}
static mp_ptr
gmp_xalloc_limbs (mp_size_t size)
{
- return gmp_xalloc (size * sizeof (mp_limb_t));
+ return (mp_ptr) gmp_xalloc (size * sizeof (mp_limb_t));
}
static mp_ptr
gmp_xrealloc_limbs (mp_ptr old, mp_size_t size)
{
assert (size > 0);
- return (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
+ return (mp_ptr) (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
}
\f
void
mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
{
- while (n-- > 0)
+ while (--n >= 0)
d[n] = s[n];
}
int
mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
{
- for (; n > 0; n--)
+ while (--n >= 0)
{
- if (ap[n-1] < bp[n-1])
- return -1;
- else if (ap[n-1] > bp[n-1])
- return 1;
+ if (ap[n] != bp[n])
+ return ap[n] > bp[n] ? 1 : -1;
}
return 0;
}
static int
mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
{
- if (an > bn)
- return 1;
- else if (an < bn)
- return -1;
+ if (an != bn)
+ return an < bn ? -1 : 1;
else
return mpn_cmp (ap, bp, an);
}
static mp_size_t
mpn_normalized_size (mp_srcptr xp, mp_size_t n)
{
- for (; n > 0 && xp[n-1] == 0; n--)
- ;
+ while (n > 0 && xp[n-1] == 0)
+ --n;
return n;
}
-#define mpn_zero_p(xp, n) (mpn_normalized_size ((xp), (n)) == 0)
+int
+mpn_zero_p(mp_srcptr rp, mp_size_t n)
+{
+ return mpn_normalized_size (rp, n) == 0;
+}
+
+void
+mpn_zero (mp_ptr rp, mp_size_t n)
+{
+ while (--n >= 0)
+ rp[n] = 0;
+}
mp_limb_t
mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
mp_size_t i;
assert (n > 0);
-
- for (i = 0; i < n; i++)
+ i = 0;
+ do
{
mp_limb_t r = ap[i] + b;
/* Carry out */
b = (r < b);
rp[i] = r;
}
+ while (++i < n);
+
return b;
}
assert (n > 0);
- for (i = 0; i < n; i++)
+ i = 0;
+ do
{
mp_limb_t a = ap[i];
/* Carry out */
- mp_limb_t cy = a < b;;
+ mp_limb_t cy = a < b;
rp[i] = a - b;
b = cy;
}
+ while (++i < n);
+
return b;
}
{
assert (un >= vn);
assert (vn >= 1);
+ assert (!GMP_MPN_OVERLAP_P(rp, un + vn, up, un));
+ assert (!GMP_MPN_OVERLAP_P(rp, un + vn, vp, vn));
/* We first multiply by the low order limb. This result can be
stored, not added, to rp. We also avoid a loop for zeroing this
way. */
rp[un] = mpn_mul_1 (rp, up, un, vp[0]);
- rp += 1, vp += 1, vn -= 1;
/* Now accumulate the product of up[] and the next higher limb from
vp[]. */
- while (vn >= 1)
+ while (--vn >= 1)
{
+ rp += 1, vp += 1;
rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
- rp += 1, vp += 1, vn -= 1;
}
- return rp[un - 1];
+ return rp[un];
}
void
{
mp_limb_t high_limb, low_limb;
unsigned int tnc;
- mp_size_t i;
mp_limb_t retval;
assert (n >= 1);
retval = low_limb >> tnc;
high_limb = (low_limb << cnt);
- for (i = n - 1; i != 0; i--)
+ while (--n != 0)
{
low_limb = *--up;
*--rp = high_limb | (low_limb >> tnc);
{
mp_limb_t high_limb, low_limb;
unsigned int tnc;
- mp_size_t i;
mp_limb_t retval;
assert (n >= 1);
retval = (high_limb << tnc);
low_limb = high_limb >> cnt;
- for (i = n - 1; i != 0; i--)
+ while (--n != 0)
{
high_limb = *up++;
*rp++ = low_limb | (high_limb << tnc);
return retval;
}
+static mp_bitcnt_t
+mpn_common_scan (mp_limb_t limb, mp_size_t i, mp_srcptr up, mp_size_t un,
+ mp_limb_t ux)
+{
+ unsigned cnt;
+
+ assert (ux == 0 || ux == GMP_LIMB_MAX);
+ assert (0 <= i && i <= un );
+
+ while (limb == 0)
+ {
+ i++;
+ if (i == un)
+ return (ux == 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
+ limb = ux ^ up[i];
+ }
+ gmp_ctz (cnt, limb);
+ return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
+}
+
+mp_bitcnt_t
+mpn_scan1 (mp_srcptr ptr, mp_bitcnt_t bit)
+{
+ mp_size_t i;
+ i = bit / GMP_LIMB_BITS;
+
+ return mpn_common_scan ( ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
+ i, ptr, i, 0);
+}
+
+mp_bitcnt_t
+mpn_scan0 (mp_srcptr ptr, mp_bitcnt_t bit)
+{
+ mp_size_t i;
+ i = bit / GMP_LIMB_BITS;
+
+ return mpn_common_scan (~ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
+ i, ptr, i, GMP_LIMB_MAX);
+}
+
+void
+mpn_com (mp_ptr rp, mp_srcptr up, mp_size_t n)
+{
+ while (--n >= 0)
+ *rp++ = ~ *up++;
+}
+
+mp_limb_t
+mpn_neg (mp_ptr rp, mp_srcptr up, mp_size_t n)
+{
+ while (*up == 0)
+ {
+ *rp = 0;
+ if (!--n)
+ return 0;
+ ++up; ++rp;
+ }
+ *rp = - *up;
+ mpn_com (++rp, ++up, --n);
+ return 1;
+}
+
\f
/* MPN division interface. */
+
+/* The 3/2 inverse is defined as
+
+ m = floor( (B^3-1) / (B u1 + u0)) - B
+*/
mp_limb_t
mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
{
- mp_limb_t r, p, m;
- unsigned ul, uh;
- unsigned ql, qh;
+ mp_limb_t r, m;
- /* First, do a 2/1 inverse. */
- /* The inverse m is defined as floor( (B^2 - 1 - u1)/u1 ), so that 0 <
- * B^2 - (B + m) u1 <= u1 */
- assert (u1 >= GMP_LIMB_HIGHBIT);
+ {
+ mp_limb_t p, ql;
+ unsigned ul, uh, qh;
- ul = u1 & GMP_LLIMB_MASK;
- uh = u1 >> (GMP_LIMB_BITS / 2);
+ /* For notation, let b denote the half-limb base, so that B = b^2.
+ Split u1 = b uh + ul. */
+ ul = u1 & GMP_LLIMB_MASK;
+ uh = u1 >> (GMP_LIMB_BITS / 2);
- qh = ~u1 / uh;
- r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
+ /* Approximation of the high half of quotient. Differs from the 2/1
+ inverse of the half limb uh, since we have already subtracted
+ u0. */
+ qh = (u1 ^ GMP_LIMB_MAX) / uh;
- p = (mp_limb_t) qh * ul;
- /* Adjustment steps taken from udiv_qrnnd_c */
- if (r < p)
- {
- qh--;
- r += u1;
- if (r >= u1) /* i.e. we didn't get carry when adding to r */
- if (r < p)
- {
- qh--;
- r += u1;
- }
- }
- r -= p;
+ /* Adjust to get a half-limb 3/2 inverse, i.e., we want
- /* Do a 3/2 division (with half limb size) */
- p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
- ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
+ qh' = floor( (b^3 - 1) / u) - b = floor ((b^3 - b u - 1) / u
+ = floor( (b (~u) + b-1) / u),
- /* By the 3/2 method, we don't need the high half limb. */
- r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
+ and the remainder
- if (r >= (p << (GMP_LIMB_BITS / 2)))
- {
- ql--;
- r += u1;
- }
- m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
- if (r >= u1)
- {
- m++;
- r -= u1;
- }
+ r = b (~u) + b-1 - qh (b uh + ul)
+ = b (~u - qh uh) + b-1 - qh ul
+
+ Subtraction of qh ul may underflow, which implies adjustments.
+ But by normalization, 2 u >= B > qh ul, so we need to adjust by
+ at most 2.
+ */
+
+ r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
+
+ p = (mp_limb_t) qh * ul;
+ /* Adjustment steps taken from udiv_qrnnd_c */
+ if (r < p)
+ {
+ qh--;
+ r += u1;
+ if (r >= u1) /* i.e. we didn't get carry when adding to r */
+ if (r < p)
+ {
+ qh--;
+ r += u1;
+ }
+ }
+ r -= p;
+
+ /* Low half of the quotient is
+
+ ql = floor ( (b r + b-1) / u1).
+
+ This is a 3/2 division (on half-limbs), for which qh is a
+ suitable inverse. */
+
+ p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
+ /* Unlike full-limb 3/2, we can add 1 without overflow. For this to
+ work, it is essential that ql is a full mp_limb_t. */
+ ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
+
+ /* By the 3/2 trick, we don't need the high half limb. */
+ r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
+
+ if (r >= (GMP_LIMB_MAX & (p << (GMP_LIMB_BITS / 2))))
+ {
+ ql--;
+ r += u1;
+ }
+ m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
+ if (r >= u1)
+ {
+ m++;
+ r -= u1;
+ }
+ }
+ /* Now m is the 2/1 inverse of u1. If u0 > 0, adjust it to become a
+ 3/2 inverse. */
if (u0 > 0)
{
mp_limb_t th, tl;
if (r < th)
{
m--;
- if (r > u1 || (r == u1 && tl > u0))
- m--;
+ m -= ((r > u1) | ((r == u1) & (tl > u0)));
}
}
if (inv->shift > 0)
{
- tp = gmp_xalloc_limbs (nn);
+ /* Shift, reusing qp area if possible. In-place shift if qp == np. */
+ tp = qp ? qp : gmp_xalloc_limbs (nn);
r = mpn_lshift (tp, np, nn, inv->shift);
np = tp;
}
d = inv->d1;
di = inv->di;
- while (nn-- > 0)
+ while (--nn >= 0)
{
mp_limb_t q;
if (qp)
qp[nn] = q;
}
- if (inv->shift > 0)
+ if ((inv->shift > 0) && (tp != qp))
gmp_free (tp);
return r >> inv->shift;
}
-static mp_limb_t
-mpn_div_qr_1 (mp_ptr qp, mp_srcptr np, mp_size_t nn, mp_limb_t d)
-{
- assert (d > 0);
-
- /* Special case for powers of two. */
- if (d > 1 && (d & (d-1)) == 0)
- {
- unsigned shift;
- mp_limb_t r = np[0] & (d-1);
- gmp_ctz (shift, d);
- if (qp)
- mpn_rshift (qp, np, nn, shift);
-
- return r;
- }
- else
- {
- struct gmp_div_inverse inv;
- mpn_div_qr_1_invert (&inv, d);
- return mpn_div_qr_1_preinv (qp, np, nn, &inv);
- }
-}
-
static void
-mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
+mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
const struct gmp_div_inverse *inv)
{
unsigned shift;
mp_size_t i;
mp_limb_t d1, d0, di, r1, r0;
- mp_ptr tp;
assert (nn >= 2);
shift = inv->shift;
di = inv->di;
if (shift > 0)
- {
- tp = gmp_xalloc_limbs (nn);
- r1 = mpn_lshift (tp, np, nn, shift);
- np = tp;
- }
+ r1 = mpn_lshift (np, np, nn, shift);
else
r1 = 0;
r0 = np[nn - 1];
- for (i = nn - 2; i >= 0; i--)
+ i = nn - 2;
+ do
{
mp_limb_t n0, q;
n0 = np[i];
if (qp)
qp[i] = q;
}
+ while (--i >= 0);
if (shift > 0)
{
- assert ((r0 << (GMP_LIMB_BITS - shift)) == 0);
+ assert ((r0 & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - shift))) == 0);
r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
r1 >>= shift;
-
- gmp_free (tp);
}
- rp[1] = r1;
- rp[0] = r0;
-}
-
-#if 0
-static void
-mpn_div_qr_2 (mp_ptr qp, mp_ptr rp, mp_srcptr np, mp_size_t nn,
- mp_limb_t d1, mp_limb_t d0)
-{
- struct gmp_div_inverse inv;
- assert (nn >= 2);
-
- mpn_div_qr_2_invert (&inv, d1, d0);
- mpn_div_qr_2_preinv (qp, rp, np, nn, &inv);
+ np[1] = r1;
+ np[0] = r0;
}
-#endif
static void
mpn_div_qr_pi1 (mp_ptr qp,
* by <d1, d0, dp[dn-3], ..., dp[0] >
*/
- for (i = nn - dn; i >= 0; i--)
+ i = nn - dn;
+ do
{
mp_limb_t n0 = np[dn-1+i];
if (qp)
qp[i] = q;
}
+ while (--i >= 0);
np[dn - 1] = n1;
}
if (dn == 1)
np[0] = mpn_div_qr_1_preinv (qp, np, nn, inv);
else if (dn == 2)
- mpn_div_qr_2_preinv (qp, np, np, nn, inv);
+ mpn_div_qr_2_preinv (qp, np, nn, inv);
else
{
mp_limb_t nh;
unsigned char mask;
size_t sn, j;
mp_size_t i;
- int shift;
+ unsigned shift;
sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1])
+ bits - 1) / bits;
l = w << binv->shift;
gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
- assert ( (r << (GMP_LIMB_BITS - binv->shift)) == 0);
+ assert ((r & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - binv->shift))) == 0);
r >>= binv->shift;
sp[i] = r;
return rn;
}
+/* Result is usually normalized, except for all-zero input, in which
+ case a single zero limb is written at *RP, and 1 is returned. */
static mp_size_t
mpn_set_str_other (mp_ptr rp, const unsigned char *sp, size_t sn,
mp_limb_t b, const struct mpn_base_info *info)
{
mp_size_t rn;
mp_limb_t w;
- unsigned first;
unsigned k;
size_t j;
- first = 1 + (sn - 1) % info->exp;
+ assert (sn > 0);
+
+ k = 1 + (sn - 1) % info->exp;
j = 0;
w = sp[j++];
- for (k = 1; k < first; k++)
+ while (--k != 0)
w = w * b + sp[j++];
rp[0] = w;
- for (rn = (w > 0); j < sn;)
+ for (rn = 1; j < sn;)
{
mp_limb_t cy;
void
mpz_init (mpz_t r)
{
- r->_mp_alloc = 1;
+ static const mp_limb_t dummy_limb = GMP_LIMB_MAX & 0xc1a0;
+
+ r->_mp_alloc = 0;
r->_mp_size = 0;
- r->_mp_d = gmp_xalloc_limbs (1);
+ r->_mp_d = (mp_ptr) &dummy_limb;
}
/* The utility of this function is a bit limited, since many functions
- assings the result variable using mpz_swap. */
+ assigns the result variable using mpz_swap. */
void
mpz_init2 (mpz_t r, mp_bitcnt_t bits)
{
void
mpz_clear (mpz_t r)
{
- gmp_free (r->_mp_d);
+ if (r->_mp_alloc)
+ gmp_free (r->_mp_d);
}
-static void *
+static mp_ptr
mpz_realloc (mpz_t r, mp_size_t size)
{
size = GMP_MAX (size, 1);
- r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size);
+ if (r->_mp_alloc)
+ r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size);
+ else
+ r->_mp_d = gmp_xalloc_limbs (size);
r->_mp_alloc = size;
if (GMP_ABS (r->_mp_size) > size)
if (x >= 0)
mpz_set_ui (r, x);
else /* (x < 0) */
+ if (GMP_LIMB_BITS < GMP_ULONG_BITS)
+ {
+ mpz_set_ui (r, GMP_NEG_CAST (unsigned long int, x));
+ mpz_neg (r, r);
+ }
+ else
{
r->_mp_size = -1;
- r->_mp_d[0] = GMP_NEG_CAST (unsigned long int, x);
+ MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (unsigned long int, x);
}
}
if (x > 0)
{
r->_mp_size = 1;
- r->_mp_d[0] = x;
+ MPZ_REALLOC (r, 1)[0] = x;
+ if (GMP_LIMB_BITS < GMP_ULONG_BITS)
+ {
+ int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
+ while (x >>= LOCAL_GMP_LIMB_BITS)
+ {
+ ++ r->_mp_size;
+ MPZ_REALLOC (r, r->_mp_size)[r->_mp_size - 1] = x;
+ }
+ }
}
else
r->_mp_size = 0;
int
mpz_fits_slong_p (const mpz_t u)
{
- mp_size_t us = u->_mp_size;
+ return (LONG_MAX + LONG_MIN == 0 || mpz_cmp_ui (u, LONG_MAX) <= 0) &&
+ mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, LONG_MIN)) <= 0;
+}
- if (us == 0)
- return 1;
- else if (us == 1)
- return u->_mp_d[0] < GMP_LIMB_HIGHBIT;
- else if (us == -1)
- return u->_mp_d[0] <= GMP_LIMB_HIGHBIT;
- else
- return 0;
+static int
+mpn_absfits_ulong_p (mp_srcptr up, mp_size_t un)
+{
+ int ulongsize = GMP_ULONG_BITS / GMP_LIMB_BITS;
+ mp_limb_t ulongrem = 0;
+
+ if (GMP_ULONG_BITS % GMP_LIMB_BITS != 0)
+ ulongrem = (mp_limb_t) (ULONG_MAX >> GMP_LIMB_BITS * ulongsize) + 1;
+
+ return un <= ulongsize || (up[ulongsize] < ulongrem && un == ulongsize + 1);
}
int
{
mp_size_t us = u->_mp_size;
- return us == 0 || us == 1;
+ return us >= 0 && mpn_absfits_ulong_p (u->_mp_d, us);
}
long int
mpz_get_si (const mpz_t u)
{
- mp_size_t us = u->_mp_size;
+ unsigned long r = mpz_get_ui (u);
+ unsigned long c = -LONG_MAX - LONG_MIN;
- if (us > 0)
- return (long) (u->_mp_d[0] & ~GMP_LIMB_HIGHBIT);
- else if (us < 0)
- return (long) (- u->_mp_d[0] | GMP_LIMB_HIGHBIT);
+ if (u->_mp_size < 0)
+ /* This expression is necessary to properly handle -LONG_MIN */
+ return -(long) c - (long) ((r - c) & LONG_MAX);
else
- return 0;
+ return (long) (r & LONG_MAX);
}
unsigned long int
mpz_get_ui (const mpz_t u)
{
+ if (GMP_LIMB_BITS < GMP_ULONG_BITS)
+ {
+ int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
+ unsigned long r = 0;
+ mp_size_t n = GMP_ABS (u->_mp_size);
+ n = GMP_MIN (n, 1 + (mp_size_t) (GMP_ULONG_BITS - 1) / GMP_LIMB_BITS);
+ while (--n >= 0)
+ r = (r << LOCAL_GMP_LIMB_BITS) + u->_mp_d[n];
+ return r;
+ }
+
return u->_mp_size == 0 ? 0 : u->_mp_d[0];
}
return 0;
}
+void
+mpz_realloc2 (mpz_t x, mp_bitcnt_t n)
+{
+ mpz_realloc (x, 1 + (n - (n != 0)) / GMP_LIMB_BITS);
+}
+
+mp_srcptr
+mpz_limbs_read (mpz_srcptr x)
+{
+ return x->_mp_d;
+}
+
+mp_ptr
+mpz_limbs_modify (mpz_t x, mp_size_t n)
+{
+ assert (n > 0);
+ return MPZ_REALLOC (x, n);
+}
+
+mp_ptr
+mpz_limbs_write (mpz_t x, mp_size_t n)
+{
+ return mpz_limbs_modify (x, n);
+}
+
+void
+mpz_limbs_finish (mpz_t x, mp_size_t xs)
+{
+ mp_size_t xn;
+ xn = mpn_normalized_size (x->_mp_d, GMP_ABS (xs));
+ x->_mp_size = xs < 0 ? -xn : xn;
+}
+
+static mpz_srcptr
+mpz_roinit_normal_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
+{
+ x->_mp_alloc = 0;
+ x->_mp_d = (mp_ptr) xp;
+ x->_mp_size = xs;
+ return x;
+}
+
+mpz_srcptr
+mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
+{
+ mpz_roinit_normal_n (x, xp, xs);
+ mpz_limbs_finish (x, xs);
+ return x;
+}
+
\f
/* Conversions and comparison to double. */
void
/* x != x is true when x is a NaN, and x == x * 0.5 is true when x is
zero or infinity. */
- if (x == 0.0 || x != x || x == x * 0.5)
+ if (x != x || x == x * 0.5)
{
r->_mp_size = 0;
return;
}
- if (x < 0.0)
- {
- x = - x;
- sign = 1;
- }
- else
- sign = 0;
+ sign = x < 0.0 ;
+ if (sign)
+ x = - x;
if (x < 1.0)
{
r->_mp_size = 0;
return;
}
- B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+ B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
Bi = 1.0 / B;
for (rn = 1; x >= B; rn++)
x *= Bi;
f = (mp_limb_t) x;
x -= f;
assert (x < 1.0);
- rp[rn-1] = f;
- for (i = rn-1; i-- > 0; )
+ i = rn-1;
+ rp[i] = f;
+ while (--i >= 0)
{
x = B * x;
f = (mp_limb_t) x;
double
mpz_get_d (const mpz_t u)
{
+ int m;
+ mp_limb_t l;
mp_size_t un;
double x;
- double B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+ double B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
un = GMP_ABS (u->_mp_size);
if (un == 0)
return 0.0;
- x = u->_mp_d[--un];
- while (un > 0)
- x = B*x + u->_mp_d[--un];
+ l = u->_mp_d[--un];
+ gmp_clz (m, l);
+ m = m + GMP_DBL_MANT_BITS - GMP_LIMB_BITS;
+ if (m < 0)
+ l &= GMP_LIMB_MAX << -m;
+
+ for (x = l; --un >= 0;)
+ {
+ x = B*x;
+ if (m > 0) {
+ l = u->_mp_d[un];
+ m -= GMP_LIMB_BITS;
+ if (m < 0)
+ l &= GMP_LIMB_MAX << -m;
+ x += l;
+ }
+ }
if (u->_mp_size < 0)
x = -x;
{
xn = GMP_ABS (xn);
- B = 2.0 * (double) GMP_LIMB_HIGHBIT;
+ B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
Bi = 1.0 / B;
/* Scale d so it can be compared with the top limb. */
int
mpz_sgn (const mpz_t u)
{
- mp_size_t usize = u->_mp_size;
-
- if (usize > 0)
- return 1;
- else if (usize < 0)
- return -1;
- else
- return 0;
+ return GMP_CMP (u->_mp_size, 0);
}
int
{
mp_size_t usize = u->_mp_size;
- if (usize < -1)
- return -1;
- else if (v >= 0)
+ if (v >= 0)
return mpz_cmp_ui (u, v);
else if (usize >= 0)
return 1;
- else /* usize == -1 */
- {
- mp_limb_t ul = u->_mp_d[0];
- if ((mp_limb_t)GMP_NEG_CAST (unsigned long int, v) < ul)
- return -1;
- else if ( (mp_limb_t)GMP_NEG_CAST (unsigned long int, v) > ul)
- return 1;
- }
- return 0;
+ else
+ return - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, v));
}
int
{
mp_size_t usize = u->_mp_size;
- if (usize > 1)
- return 1;
- else if (usize < 0)
+ if (usize < 0)
return -1;
else
- {
- mp_limb_t ul = (usize > 0) ? u->_mp_d[0] : 0;
- if (ul > v)
- return 1;
- else if (ul < v)
- return -1;
- }
- return 0;
+ return mpz_cmpabs_ui (u, v);
}
int
mp_size_t asize = a->_mp_size;
mp_size_t bsize = b->_mp_size;
- if (asize > bsize)
- return 1;
- else if (asize < bsize)
- return -1;
- else if (asize > 0)
+ if (asize != bsize)
+ return (asize < bsize) ? -1 : 1;
+ else if (asize >= 0)
return mpn_cmp (a->_mp_d, b->_mp_d, asize);
- else if (asize < 0)
- return -mpn_cmp (a->_mp_d, b->_mp_d, -asize);
else
- return 0;
+ return mpn_cmp (b->_mp_d, a->_mp_d, -asize);
}
int
mpz_cmpabs_ui (const mpz_t u, unsigned long v)
{
mp_size_t un = GMP_ABS (u->_mp_size);
- mp_limb_t ul;
-
- if (un > 1)
- return 1;
- ul = (un == 1) ? u->_mp_d[0] : 0;
-
- if (ul > v)
+ if (! mpn_absfits_ulong_p (u->_mp_d, un))
return 1;
- else if (ul < v)
- return -1;
else
- return 0;
+ {
+ unsigned long uu = mpz_get_ui (u);
+ return GMP_CMP(uu, v);
+ }
}
int
void
mpz_abs (mpz_t r, const mpz_t u)
{
- if (r != u)
- mpz_set (r, u);
-
+ mpz_set (r, u);
r->_mp_size = GMP_ABS (r->_mp_size);
}
void
mpz_neg (mpz_t r, const mpz_t u)
{
- if (r != u)
- mpz_set (r, u);
-
+ mpz_set (r, u);
r->_mp_size = -r->_mp_size;
}
\f
/* MPZ addition and subtraction */
-/* Adds to the absolute value. Returns new size, but doesn't store it. */
-static mp_size_t
-mpz_abs_add_ui (mpz_t r, const mpz_t a, unsigned long b)
-{
- mp_size_t an;
- mp_ptr rp;
- mp_limb_t cy;
-
- an = GMP_ABS (a->_mp_size);
- if (an == 0)
- {
- r->_mp_d[0] = b;
- return b > 0;
- }
-
- rp = MPZ_REALLOC (r, an + 1);
-
- cy = mpn_add_1 (rp, a->_mp_d, an, b);
- rp[an] = cy;
- an += (cy > 0);
-
- return an;
-}
-
-/* Subtract from the absolute value. Returns new size, (or -1 on underflow),
- but doesn't store it. */
-static mp_size_t
-mpz_abs_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
-{
- mp_size_t an = GMP_ABS (a->_mp_size);
- mp_ptr rp = MPZ_REALLOC (r, an);
-
- if (an == 0)
- {
- rp[0] = b;
- return -(b > 0);
- }
- else if (an == 1 && a->_mp_d[0] < b)
- {
- rp[0] = b - a->_mp_d[0];
- return -1;
- }
- else
- {
- gmp_assert_nocarry (mpn_sub_1 (rp, a->_mp_d, an, b));
- return mpn_normalized_size (rp, an);
- }
-}
void
mpz_add_ui (mpz_t r, const mpz_t a, unsigned long b)
{
- if (a->_mp_size >= 0)
- r->_mp_size = mpz_abs_add_ui (r, a, b);
- else
- r->_mp_size = -mpz_abs_sub_ui (r, a, b);
+ mpz_t bb;
+ mpz_init_set_ui (bb, b);
+ mpz_add (r, a, bb);
+ mpz_clear (bb);
}
void
mpz_sub_ui (mpz_t r, const mpz_t a, unsigned long b)
{
- if (a->_mp_size < 0)
- r->_mp_size = -mpz_abs_add_ui (r, a, b);
- else
- r->_mp_size = mpz_abs_sub_ui (r, a, b);
+ mpz_ui_sub (r, b, a);
+ mpz_neg (r, r);
}
void
mpz_ui_sub (mpz_t r, unsigned long a, const mpz_t b)
{
- if (b->_mp_size < 0)
- r->_mp_size = mpz_abs_add_ui (r, b, a);
- else
- r->_mp_size = -mpz_abs_sub_ui (r, b, a);
+ mpz_neg (r, b);
+ mpz_add_ui (r, r, a);
}
static mp_size_t
{
mp_size_t an = GMP_ABS (a->_mp_size);
mp_size_t bn = GMP_ABS (b->_mp_size);
- mp_size_t rn;
mp_ptr rp;
mp_limb_t cy;
- rn = GMP_MAX (an, bn);
- rp = MPZ_REALLOC (r, rn + 1);
- if (an >= bn)
- cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
- else
- cy = mpn_add (rp, b->_mp_d, bn, a->_mp_d, an);
+ if (an < bn)
+ {
+ MPZ_SRCPTR_SWAP (a, b);
+ MP_SIZE_T_SWAP (an, bn);
+ }
+
+ rp = MPZ_REALLOC (r, an + 1);
+ cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
- rp[rn] = cy;
+ rp[an] = cy;
- return rn + (cy > 0);
+ return an + cy;
}
static mp_size_t
mpz_neg (r, r);
}
else
- mpz_mul_ui (r, u, (unsigned long int) v);
+ mpz_mul_ui (r, u, v);
}
void
mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int v)
{
- mp_size_t un;
- mpz_t t;
- mp_ptr tp;
- mp_limb_t cy;
-
- un = GMP_ABS (u->_mp_size);
-
- if (un == 0 || v == 0)
- {
- r->_mp_size = 0;
- return;
- }
-
- mpz_init2 (t, (un + 1) * GMP_LIMB_BITS);
-
- tp = t->_mp_d;
- cy = mpn_mul_1 (tp, u->_mp_d, un, v);
- tp[un] = cy;
-
- t->_mp_size = un + (cy > 0);
- if (u->_mp_size < 0)
- t->_mp_size = - t->_mp_size;
-
- mpz_swap (r, t);
- mpz_clear (t);
+ mpz_t vv;
+ mpz_init_set_ui (vv, v);
+ mpz_mul (r, u, vv);
+ mpz_clear (vv);
+ return;
}
void
mpz_t t;
mp_ptr tp;
- un = GMP_ABS (u->_mp_size);
- vn = GMP_ABS (v->_mp_size);
+ un = u->_mp_size;
+ vn = v->_mp_size;
if (un == 0 || vn == 0)
{
return;
}
- sign = (u->_mp_size ^ v->_mp_size) < 0;
+ sign = (un ^ vn) < 0;
+
+ un = GMP_ABS (un);
+ vn = GMP_ABS (vn);
mpz_init2 (t, (un + vn) * GMP_LIMB_BITS);
else
mpn_copyd (rp + limbs, u->_mp_d, un);
- while (limbs > 0)
- rp[--limbs] = 0;
+ mpn_zero (rp, limbs);
r->_mp_size = (u->_mp_size < 0) ? - rn : rn;
}
+void
+mpz_addmul_ui (mpz_t r, const mpz_t u, unsigned long int v)
+{
+ mpz_t t;
+ mpz_init_set_ui (t, v);
+ mpz_mul (t, u, t);
+ mpz_add (r, r, t);
+ mpz_clear (t);
+}
+
+void
+mpz_submul_ui (mpz_t r, const mpz_t u, unsigned long int v)
+{
+ mpz_t t;
+ mpz_init_set_ui (t, v);
+ mpz_mul (t, u, t);
+ mpz_sub (r, r, t);
+ mpz_clear (t);
+}
+
+void
+mpz_addmul (mpz_t r, const mpz_t u, const mpz_t v)
+{
+ mpz_t t;
+ mpz_init (t);
+ mpz_mul (t, u, v);
+ mpz_add (r, r, t);
+ mpz_clear (t);
+}
+
+void
+mpz_submul (mpz_t r, const mpz_t u, const mpz_t v)
+{
+ mpz_t t;
+ mpz_init (t);
+ mpz_mul (t, u, v);
+ mpz_sub (r, r, t);
+ mpz_clear (t);
+}
+
\f
/* MPZ division */
enum mpz_div_round_mode { GMP_DIV_FLOOR, GMP_DIV_CEIL, GMP_DIV_TRUNC };
mp_size_t qn, rn;
mpz_t tq, tr;
- mpz_init (tr);
- mpz_set (tr, n);
+ mpz_init_set (tr, n);
np = tr->_mp_d;
qn = nn - dn + 1;
void
mpz_mod (mpz_t r, const mpz_t n, const mpz_t d)
{
- if (d->_mp_size >= 0)
- mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR);
- else
- mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL);
+ mpz_div_qr (NULL, r, n, d, d->_mp_size >= 0 ? GMP_DIV_FLOOR : GMP_DIV_CEIL);
}
static void
mp_size_t un, qn;
mp_size_t limb_cnt;
mp_ptr qp;
- mp_limb_t adjust;
+ int adjust;
un = u->_mp_size;
if (un == 0)
if (qn <= 0)
qn = 0;
-
else
{
qp = MPZ_REALLOC (q, qn);
q->_mp_size = qn;
- mpz_add_ui (q, q, adjust);
+ if (adjust)
+ mpz_add_ui (q, q, 1);
if (un < 0)
mpz_neg (q, q);
}
{
/* Have to negate and sign extend. */
mp_size_t i;
- mp_limb_t cy;
- for (cy = 1, i = 0; i < un; i++)
- {
- mp_limb_t s = ~u->_mp_d[i] + cy;
- cy = s < cy;
- rp[i] = s;
- }
- assert (cy == 0);
- for (; i < rn - 1; i++)
+ gmp_assert_nocarry (! mpn_neg (rp, u->_mp_d, un));
+ for (i = un; i < rn - 1; i++)
rp[i] = GMP_LIMB_MAX;
rp[rn-1] = mask;
if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
{
/* If r != 0, compute 2^{bit_count} - r. */
- mp_size_t i;
-
- for (i = 0; i < rn && rp[i] == 0; i++)
- ;
- if (i < rn)
- {
- /* r > 0, need to flip sign. */
- rp[i] = ~rp[i] + 1;
- for (i++; i < rn; i++)
- rp[i] = ~rp[i];
+ mpn_neg (rp, rp, rn);
- rp[rn-1] &= mask;
+ rp[rn-1] &= mask;
- /* us is not used for anything else, so we can modify it
- here to indicate flipped sign. */
- us = -us;
- }
+ /* us is not used for anything else, so we can modify it
+ here to indicate flipped sign. */
+ us = -us;
}
}
rn = mpn_normalized_size (rp, rn);
return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
}
-static unsigned long
-mpz_div_qr_ui (mpz_t q, mpz_t r,
- const mpz_t n, unsigned long d, enum mpz_div_round_mode mode)
+int
+mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m)
{
- mp_size_t ns, qn;
- mp_ptr qp;
- mp_limb_t rl;
- mp_size_t rs;
+ mpz_t t;
+ int res;
- ns = n->_mp_size;
- if (ns == 0)
- {
- if (q)
- q->_mp_size = 0;
- if (r)
- r->_mp_size = 0;
- return 0;
- }
+ /* a == b (mod 0) iff a == b */
+ if (mpz_sgn (m) == 0)
+ return (mpz_cmp (a, b) == 0);
- qn = GMP_ABS (ns);
- if (q)
- qp = MPZ_REALLOC (q, qn);
- else
- qp = NULL;
+ mpz_init (t);
+ mpz_sub (t, a, b);
+ res = mpz_divisible_p (t, m);
+ mpz_clear (t);
- rl = mpn_div_qr_1 (qp, n->_mp_d, qn, d);
- assert (rl < d);
+ return res;
+}
- rs = rl > 0;
- rs = (ns < 0) ? -rs : rs;
+static unsigned long
+mpz_div_qr_ui (mpz_t q, mpz_t r,
+ const mpz_t n, unsigned long d, enum mpz_div_round_mode mode)
+{
+ unsigned long ret;
+ mpz_t rr, dd;
- if (rl > 0 && ( (mode == GMP_DIV_FLOOR && ns < 0)
- || (mode == GMP_DIV_CEIL && ns >= 0)))
- {
- if (q)
- gmp_assert_nocarry (mpn_add_1 (qp, qp, qn, 1));
- rl = d - rl;
- rs = -rs;
- }
+ mpz_init (rr);
+ mpz_init_set_ui (dd, d);
+ mpz_div_qr (q, rr, n, dd, mode);
+ mpz_clear (dd);
+ ret = mpz_get_ui (rr);
if (r)
- {
- r->_mp_d[0] = rl;
- r->_mp_size = rs;
- }
- if (q)
- {
- qn -= (qp[qn-1] == 0);
- assert (qn == 0 || qp[qn-1] > 0);
-
- q->_mp_size = (ns < 0) ? - qn : qn;
- }
+ mpz_swap (r, rr);
+ mpz_clear (rr);
- return rl;
+ return ret;
}
unsigned long
unsigned long
mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long v)
{
- mp_size_t un;
+ mpz_t t;
+ mpz_init_set_ui(t, v);
+ mpz_gcd (t, u, t);
+ if (v > 0)
+ v = mpz_get_ui (t);
- if (v == 0)
- {
- if (g)
- mpz_abs (g, u);
- }
- else
- {
- un = GMP_ABS (u->_mp_size);
- if (un != 0)
- v = mpn_gcd_11 (mpn_div_qr_1 (NULL, u->_mp_d, un, v), v);
+ if (g)
+ mpz_swap (t, g);
- if (g)
- mpz_set_ui (g, v);
- }
+ mpz_clear (t);
return v;
}
static mp_bitcnt_t
-mpz_make_odd (mpz_t r, const mpz_t u)
+mpz_make_odd (mpz_t r)
{
- mp_size_t un, rn, i;
- mp_ptr rp;
- unsigned shift;
+ mp_bitcnt_t shift;
- un = GMP_ABS (u->_mp_size);
- assert (un > 0);
-
- for (i = 0; u->_mp_d[i] == 0; i++)
- ;
-
- gmp_ctz (shift, u->_mp_d[i]);
-
- rn = un - i;
- rp = MPZ_REALLOC (r, rn);
- if (shift > 0)
- {
- mpn_rshift (rp, u->_mp_d + i, rn, shift);
- rn -= (rp[rn-1] == 0);
- }
- else
- mpn_copyi (rp, u->_mp_d + i, rn);
+ assert (r->_mp_size > 0);
+ /* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */
+ shift = mpn_common_scan (r->_mp_d[0], 0, r->_mp_d, 0, 0);
+ mpz_tdiv_q_2exp (r, r, shift);
- r->_mp_size = rn;
- return i * GMP_LIMB_BITS + shift;
+ return shift;
}
void
mpz_init (tu);
mpz_init (tv);
- uz = mpz_make_odd (tu, u);
- vz = mpz_make_odd (tv, v);
+ mpz_abs (tu, u);
+ uz = mpz_make_odd (tu);
+ mpz_abs (tv, v);
+ vz = mpz_make_odd (tv);
gz = GMP_MIN (uz, vz);
if (tu->_mp_size < tv->_mp_size)
{
int c;
- mpz_make_odd (tu, tu);
+ mpz_make_odd (tu);
c = mpz_cmp (tu, tv);
if (c == 0)
{
signed long sign = mpz_sgn (v);
mpz_abs (g, v);
if (s)
- mpz_set_ui (s, 0);
+ s->_mp_size = 0;
if (t)
mpz_set_si (t, sign);
return;
if (s)
mpz_set_si (s, sign);
if (t)
- mpz_set_ui (t, 0);
+ t->_mp_size = 0;
return;
}
mpz_init (t0);
mpz_init (t1);
- uz = mpz_make_odd (tu, u);
- vz = mpz_make_odd (tv, v);
+ mpz_abs (tu, u);
+ uz = mpz_make_odd (tu);
+ mpz_abs (tv, v);
+ vz = mpz_make_odd (tv);
gz = GMP_MIN (uz, vz);
uz -= gz;
if (tu->_mp_size > 0)
{
mp_bitcnt_t shift;
- shift = mpz_make_odd (tu, tu);
+ shift = mpz_make_odd (tu);
mpz_mul_2exp (t0, t0, shift);
mpz_mul_2exp (s0, s0, shift);
power += shift;
mpz_add (t0, t0, t1);
mpz_add (s0, s0, s1);
- shift = mpz_make_odd (tv, tv);
+ shift = mpz_make_odd (tv);
mpz_mul_2exp (t1, t1, shift);
mpz_mul_2exp (s1, s1, shift);
}
mpz_add (t1, t0, t1);
mpz_add (s1, s0, s1);
- shift = mpz_make_odd (tu, tu);
+ shift = mpz_make_odd (tu);
mpz_mul_2exp (t0, t0, shift);
mpz_mul_2exp (s0, s0, shift);
}
mpz_sub (s0, s0, s1);
mpz_add (t0, t0, t1);
}
- mpz_divexact_ui (s0, s0, 2);
- mpz_divexact_ui (t0, t0, 2);
+ assert (mpz_even_p (t0) && mpz_even_p (s0));
+ mpz_tdiv_q_2exp (s0, s0, 1);
+ mpz_tdiv_q_2exp (t0, t0, 1);
}
/* Arrange so that |s| < |u| / 2g */
mpz_t tr;
mpz_init_set_ui (tr, 1);
- for (bit = GMP_ULONG_HIGHBIT; bit > 0; bit >>= 1)
+ bit = GMP_ULONG_HIGHBIT;
+ do
{
mpz_mul (tr, tr, tr);
if (e & bit)
mpz_mul (tr, tr, b);
+ bit >>= 1;
}
+ while (bit > 0);
+
mpz_swap (r, tr);
mpz_clear (tr);
}
mpz_ui_pow_ui (mpz_t r, unsigned long blimb, unsigned long e)
{
mpz_t b;
+
mpz_init_set_ui (b, blimb);
mpz_pow_ui (r, b, e);
mpz_clear (b);
if (e->_mp_size < 0)
{
if (!mpz_invert (base, b, m))
- gmp_die ("mpz_powm: Negative exponent and non-invertibe base.");
+ gmp_die ("mpz_powm: Negative exponent and non-invertible base.");
}
else
{
}
mpz_init_set_ui (tr, 1);
- while (en-- > 0)
+ while (--en >= 0)
{
mp_limb_t w = e->_mp_d[en];
mp_limb_t bit;
- for (bit = GMP_LIMB_HIGHBIT; bit > 0; bit >>= 1)
+ bit = GMP_LIMB_HIGHBIT;
+ do
{
mpz_mul (tr, tr, tr);
if (w & bit)
mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
}
+ bit >>= 1;
}
+ while (bit > 0);
}
/* Final reduction */
mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long elimb, const mpz_t m)
{
mpz_t e;
+
mpz_init_set_ui (e, elimb);
mpz_powm (r, b, e, m);
mpz_clear (e);
mpz_t t, u;
sgn = y->_mp_size < 0;
- if (sgn && (z & 1) == 0)
+ if ((~z & sgn) != 0)
gmp_die ("mpz_rootrem: Negative argument, with even root.");
if (z == 0)
gmp_die ("mpz_rootrem: Zeroth root.");
if (mpz_cmpabs_ui (y, 1) <= 0) {
- mpz_set (x, y);
+ if (x)
+ mpz_set (x, y);
if (r)
r->_mp_size = 0;
return;
}
- mpz_init (t);
mpz_init (u);
+ mpz_init (t);
mpz_setbit (t, mpz_sizeinbase (y, 2) / z + 1);
if (z == 2) /* simplify sqrt loop: z-1 == 1 */
mpz_pow_ui (t, u, z);
mpz_sub (r, y, t);
}
- mpz_swap (x, u);
+ if (x)
+ mpz_swap (x, u);
mpz_clear (u);
mpz_clear (t);
}
mpz_rootrem (s, NULL, u, 2);
}
+int
+mpz_perfect_square_p (const mpz_t u)
+{
+ if (u->_mp_size <= 0)
+ return (u->_mp_size == 0);
+ else
+ return mpz_root (NULL, u, 2);
+}
+
+int
+mpn_perfect_square_p (mp_srcptr p, mp_size_t n)
+{
+ mpz_t t;
+
+ assert (n > 0);
+ assert (p [n-1] != 0);
+ return mpz_root (NULL, mpz_roinit_normal_n (t, p, n), 2);
+}
+
+mp_size_t
+mpn_sqrtrem (mp_ptr sp, mp_ptr rp, mp_srcptr p, mp_size_t n)
+{
+ mpz_t s, r, u;
+ mp_size_t res;
+
+ assert (n > 0);
+ assert (p [n-1] != 0);
+
+ mpz_init (r);
+ mpz_init (s);
+ mpz_rootrem (s, r, mpz_roinit_normal_n (u, p, n), 2);
+
+ assert (s->_mp_size == (n+1)/2);
+ mpn_copyd (sp, s->_mp_d, s->_mp_size);
+ mpz_clear (s);
+ res = r->_mp_size;
+ if (rp)
+ mpn_copyd (rp, r->_mp_d, res);
+ mpz_clear (r);
+ return res;
+}
\f
/* Combinatorics */
+void
+mpz_mfac_uiui (mpz_t x, unsigned long n, unsigned long m)
+{
+ mpz_set_ui (x, n + (n == 0));
+ if (m + 1 < 2) return;
+ while (n > m + 1)
+ mpz_mul_ui (x, x, n -= m);
+}
+
+void
+mpz_2fac_ui (mpz_t x, unsigned long n)
+{
+ mpz_mfac_uiui (x, n, 2);
+}
+
void
mpz_fac_ui (mpz_t x, unsigned long n)
{
- if (n < 2) {
- mpz_set_ui (x, 1);
- return;
- }
- mpz_set_ui (x, n);
- for (;--n > 1;)
- mpz_mul_ui (x, x, n);
+ mpz_mfac_uiui (x, n, 1);
}
void
{
mpz_t t;
- if (k > n) {
- r->_mp_size = 0;
- return;
- }
- mpz_fac_ui (r, n);
+ mpz_set_ui (r, k <= n);
+
+ if (k > (n >> 1))
+ k = (k <= n) ? n - k : 0;
+
mpz_init (t);
mpz_fac_ui (t, k);
- mpz_divexact (r, r, t);
- mpz_fac_ui (t, n - k);
+
+ for (; k > 0; --k)
+ mpz_mul_ui (r, r, n--);
+
mpz_divexact (r, r, t);
mpz_clear (t);
}
+\f
+/* Primality testing */
+
+/* Computes Kronecker (a/b) with odd b, a!=0 and GCD(a,b) = 1 */
+/* Adapted from JACOBI_BASE_METHOD==4 in mpn/generic/jacbase.c */
+static int
+gmp_jacobi_coprime (mp_limb_t a, mp_limb_t b)
+{
+ int c, bit = 0;
+
+ assert (b & 1);
+ assert (a != 0);
+ /* assert (mpn_gcd_11 (a, b) == 1); */
+
+ /* Below, we represent a and b shifted right so that the least
+ significant one bit is implicit. */
+ b >>= 1;
+
+ gmp_ctz(c, a);
+ a >>= 1;
+
+ do
+ {
+ a >>= c;
+ /* (2/b) = -1 if b = 3 or 5 mod 8 */
+ bit ^= c & (b ^ (b >> 1));
+ if (a < b)
+ {
+ bit ^= a & b;
+ a = b - a;
+ b -= a;
+ }
+ else
+ {
+ a -= b;
+ assert (a != 0);
+ }
+
+ gmp_ctz(c, a);
+ ++c;
+ }
+ while (b > 0);
+
+ return bit & 1 ? -1 : 1;
+}
+
+static void
+gmp_lucas_step_k_2k (mpz_t V, mpz_t Qk, const mpz_t n)
+{
+ mpz_mod (Qk, Qk, n);
+ /* V_{2k} <- V_k ^ 2 - 2Q^k */
+ mpz_mul (V, V, V);
+ mpz_submul_ui (V, Qk, 2);
+ mpz_tdiv_r (V, V, n);
+ /* Q^{2k} = (Q^k)^2 */
+ mpz_mul (Qk, Qk, Qk);
+}
+
+/* Computes V_k, Q^k (mod n) for the Lucas' sequence */
+/* with P=1, Q=Q; k = (n>>b0)|1. */
+/* Requires an odd n > 4; b0 > 0; -2*Q must not overflow a long */
+/* Returns (U_k == 0) and sets V=V_k and Qk=Q^k. */
+static int
+gmp_lucas_mod (mpz_t V, mpz_t Qk, long Q,
+ mp_bitcnt_t b0, const mpz_t n)
+{
+ mp_bitcnt_t bs;
+ mpz_t U;
+ int res;
+
+ assert (b0 > 0);
+ assert (Q <= - (LONG_MIN / 2));
+ assert (Q >= - (LONG_MAX / 2));
+ assert (mpz_cmp_ui (n, 4) > 0);
+ assert (mpz_odd_p (n));
+
+ mpz_init_set_ui (U, 1); /* U1 = 1 */
+ mpz_set_ui (V, 1); /* V1 = 1 */
+ mpz_set_si (Qk, Q);
+
+ for (bs = mpz_sizeinbase (n, 2) - 1; --bs >= b0;)
+ {
+ /* U_{2k} <- U_k * V_k */
+ mpz_mul (U, U, V);
+ /* V_{2k} <- V_k ^ 2 - 2Q^k */
+ /* Q^{2k} = (Q^k)^2 */
+ gmp_lucas_step_k_2k (V, Qk, n);
+
+ /* A step k->k+1 is performed if the bit in $n$ is 1 */
+ /* mpz_tstbit(n,bs) or the the bit is 0 in $n$ but */
+ /* should be 1 in $n+1$ (bs == b0) */
+ if (b0 == bs || mpz_tstbit (n, bs))
+ {
+ /* Q^{k+1} <- Q^k * Q */
+ mpz_mul_si (Qk, Qk, Q);
+ /* U_{k+1} <- (U_k + V_k) / 2 */
+ mpz_swap (U, V); /* Keep in V the old value of U_k */
+ mpz_add (U, U, V);
+ /* We have to compute U/2, so we need an even value, */
+ /* equivalent (mod n) */
+ if (mpz_odd_p (U))
+ mpz_add (U, U, n);
+ mpz_tdiv_q_2exp (U, U, 1);
+ /* V_{k+1} <-(D*U_k + V_k) / 2 =
+ U_{k+1} + (D-1)/2*U_k = U_{k+1} - 2Q*U_k */
+ mpz_mul_si (V, V, -2*Q);
+ mpz_add (V, U, V);
+ mpz_tdiv_r (V, V, n);
+ }
+ mpz_tdiv_r (U, U, n);
+ }
+
+ res = U->_mp_size == 0;
+ mpz_clear (U);
+ return res;
+}
+
+/* Performs strong Lucas' test on x, with parameters suggested */
+/* for the BPSW test. Qk is only passed to recycle a variable. */
+/* Requires GCD (x,6) = 1.*/
+static int
+gmp_stronglucas (const mpz_t x, mpz_t Qk)
+{
+ mp_bitcnt_t b0;
+ mpz_t V, n;
+ mp_limb_t maxD, D; /* The absolute value is stored. */
+ long Q;
+ mp_limb_t tl;
+
+ /* Test on the absolute value. */
+ mpz_roinit_normal_n (n, x->_mp_d, GMP_ABS (x->_mp_size));
+
+ assert (mpz_odd_p (n));
+ /* assert (mpz_gcd_ui (NULL, n, 6) == 1); */
+ if (mpz_root (Qk, n, 2))
+ return 0; /* A square is composite. */
+
+ /* Check Ds up to square root (in case, n is prime)
+ or avoid overflows */
+ maxD = (Qk->_mp_size == 1) ? Qk->_mp_d [0] - 1 : GMP_LIMB_MAX;
+
+ D = 3;
+ /* Search a D such that (D/n) = -1 in the sequence 5,-7,9,-11,.. */
+ /* For those Ds we have (D/n) = (n/|D|) */
+ do
+ {
+ if (D >= maxD)
+ return 1 + (D != GMP_LIMB_MAX); /* (1 + ! ~ D) */
+ D += 2;
+ tl = mpz_tdiv_ui (n, D);
+ if (tl == 0)
+ return 0;
+ }
+ while (gmp_jacobi_coprime (tl, D) == 1);
+
+ mpz_init (V);
+
+ /* n-(D/n) = n+1 = d*2^{b0}, with d = (n>>b0) | 1 */
+ b0 = mpz_scan0 (n, 0);
+
+ /* D= P^2 - 4Q; P = 1; Q = (1-D)/4 */
+ Q = (D & 2) ? (long) (D >> 2) + 1 : -(long) (D >> 2);
+
+ if (! gmp_lucas_mod (V, Qk, Q, b0, n)) /* If Ud != 0 */
+ while (V->_mp_size != 0 && --b0 != 0) /* while Vk != 0 */
+ /* V <- V ^ 2 - 2Q^k */
+ /* Q^{2k} = (Q^k)^2 */
+ gmp_lucas_step_k_2k (V, Qk, n);
+
+ mpz_clear (V);
+ return (b0 != 0);
+}
+
+static int
+gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y,
+ const mpz_t q, mp_bitcnt_t k)
+{
+ assert (k > 0);
+
+ /* Caller must initialize y to the base. */
+ mpz_powm (y, y, q, n);
+
+ if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
+ return 1;
+
+ while (--k > 0)
+ {
+ mpz_powm_ui (y, y, 2, n);
+ if (mpz_cmp (y, nm1) == 0)
+ return 1;
+ /* y == 1 means that the previous y was a non-trivial square root
+ of 1 (mod n). y == 0 means that n is a power of the base.
+ In either case, n is not prime. */
+ if (mpz_cmp_ui (y, 1) <= 0)
+ return 0;
+ }
+ return 0;
+}
+
+/* This product is 0xc0cfd797, and fits in 32 bits. */
+#define GMP_PRIME_PRODUCT \
+ (3UL*5UL*7UL*11UL*13UL*17UL*19UL*23UL*29UL)
+
+/* Bit (p+1)/2 is set, for each odd prime <= 61 */
+#define GMP_PRIME_MASK 0xc96996dcUL
+
+int
+mpz_probab_prime_p (const mpz_t n, int reps)
+{
+ mpz_t nm1;
+ mpz_t q;
+ mpz_t y;
+ mp_bitcnt_t k;
+ int is_prime;
+ int j;
+
+ /* Note that we use the absolute value of n only, for compatibility
+ with the real GMP. */
+ if (mpz_even_p (n))
+ return (mpz_cmpabs_ui (n, 2) == 0) ? 2 : 0;
+
+ /* Above test excludes n == 0 */
+ assert (n->_mp_size != 0);
+
+ if (mpz_cmpabs_ui (n, 64) < 0)
+ return (GMP_PRIME_MASK >> (n->_mp_d[0] >> 1)) & 2;
+
+ if (mpz_gcd_ui (NULL, n, GMP_PRIME_PRODUCT) != 1)
+ return 0;
+
+ /* All prime factors are >= 31. */
+ if (mpz_cmpabs_ui (n, 31*31) < 0)
+ return 2;
+
+ mpz_init (nm1);
+ mpz_init (q);
+
+ /* Find q and k, where q is odd and n = 1 + 2**k * q. */
+ mpz_abs (nm1, n);
+ nm1->_mp_d[0] -= 1;
+ k = mpz_scan1 (nm1, 0);
+ mpz_tdiv_q_2exp (q, nm1, k);
+
+ /* BPSW test */
+ mpz_init_set_ui (y, 2);
+ is_prime = gmp_millerrabin (n, nm1, y, q, k) && gmp_stronglucas (n, y);
+ reps -= 24; /* skip the first 24 repetitions */
+
+ /* Use Miller-Rabin, with a deterministic sequence of bases, a[j] =
+ j^2 + j + 41 using Euler's polynomial. We potentially stop early,
+ if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps >
+ 30 (a[30] == 971 > 31*31 == 961). */
+
+ for (j = 0; is_prime & (j < reps); j++)
+ {
+ mpz_set_ui (y, (unsigned long) j*j+j+41);
+ if (mpz_cmp (y, nm1) >= 0)
+ {
+ /* Don't try any further bases. This "early" break does not affect
+ the result for any reasonable reps value (<=5000 was tested) */
+ assert (j >= 30);
+ break;
+ }
+ is_prime = gmp_millerrabin (n, nm1, y, q, k);
+ }
+ mpz_clear (nm1);
+ mpz_clear (q);
+ mpz_clear (y);
+
+ return is_prime;
+}
+
\f
/* Logical operations and bit manipulation. */
/* Numbers are treated as if represented in two's complement (and
infinitely sign extended). For a negative values we get the two's
- complement from -x = ~x + 1, where ~ is bitwise complementt.
+ complement from -x = ~x + 1, where ~ is bitwise complement.
Negation transforms
xxxx10...0
{
/* d < 0. Check if any of the bits below is set: If so, our bit
must be complemented. */
- if (shift > 0 && (w << (GMP_LIMB_BITS - shift)) > 0)
+ if (shift > 0 && (mp_limb_t) (w << (GMP_LIMB_BITS - shift)) > 0)
return bit ^ 1;
- while (limb_index-- > 0)
+ while (--limb_index >= 0)
if (d->_mp_d[limb_index] > 0)
return bit ^ 1;
}
gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
dn - limb_index, bit));
- dn -= (dp[dn-1] == 0);
+ dn = mpn_normalized_size (dp, dn);
d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
}
void
mpz_com (mpz_t r, const mpz_t u)
{
- mpz_neg (r, u);
- mpz_sub_ui (r, r, 1);
+ mpz_add_ui (r, u, 1);
+ mpz_neg (r, r);
}
void
/* If the smaller input is positive, higher limbs don't matter. */
rn = vx ? un : vn;
- rp = MPZ_REALLOC (r, rn + rc);
+ rp = MPZ_REALLOC (r, rn + (mp_size_t) rc);
up = u->_mp_d;
vp = v->_mp_d;
- for (i = 0; i < vn; i++)
+ i = 0;
+ do
{
ul = (up[i] ^ ux) + uc;
uc = ul < uc;
rc = rl < rc;
rp[i] = rl;
}
+ while (++i < vn);
assert (vc == 0);
for (; i < rn; i++)
don't matter. */
rn = vx ? vn : un;
- rp = MPZ_REALLOC (r, rn + rc);
+ rp = MPZ_REALLOC (r, rn + (mp_size_t) rc);
up = u->_mp_d;
vp = v->_mp_d;
- for (i = 0; i < vn; i++)
+ i = 0;
+ do
{
ul = (up[i] ^ ux) + uc;
uc = ul < uc;
rc = rl < rc;
rp[i] = rl;
}
+ while (++i < vn);
assert (vc == 0);
for (; i < rn; i++)
vx = -vc;
rx = -rc;
- rp = MPZ_REALLOC (r, un + rc);
+ rp = MPZ_REALLOC (r, un + (mp_size_t) rc);
up = u->_mp_d;
vp = v->_mp_d;
- for (i = 0; i < vn; i++)
+ i = 0;
+ do
{
ul = (up[i] ^ ux) + uc;
uc = ul < uc;
rc = rl < rc;
rp[i] = rl;
}
+ while (++i < vn);
assert (vc == 0);
for (; i < un; i++)
unsigned c;
/* Do 16 bits at a time, to avoid limb-sized constants. */
- for (c = 0; x > 0; x >>= 16)
+ int LOCAL_SHIFT_BITS = 16;
+ for (c = 0; x > 0;)
{
- unsigned w = ((x >> 1) & 0x5555) + (x & 0x5555);
+ unsigned w = x - ((x >> 1) & 0x5555);
w = ((w >> 2) & 0x3333) + (w & 0x3333);
- w = ((w >> 4) & 0x0f0f) + (w & 0x0f0f);
- w = (w >> 8) + (w & 0x00ff);
+ w = (w >> 4) + w;
+ w = ((w >> 8) & 0x000f) + (w & 0x000f);
c += w;
+ if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS)
+ x >>= LOCAL_SHIFT_BITS;
+ else
+ x = 0;
}
return c;
}
mp_bitcnt_t
-mpz_popcount (const mpz_t u)
+mpn_popcount (mp_srcptr p, mp_size_t n)
{
- mp_size_t un, i;
+ mp_size_t i;
mp_bitcnt_t c;
+ for (c = 0, i = 0; i < n; i++)
+ c += gmp_popcount_limb (p[i]);
+
+ return c;
+}
+
+mp_bitcnt_t
+mpz_popcount (const mpz_t u)
+{
+ mp_size_t un;
+
un = u->_mp_size;
if (un < 0)
return ~(mp_bitcnt_t) 0;
- for (c = 0, i = 0; i < un; i++)
- c += gmp_popcount_limb (u->_mp_d[i]);
-
- return c;
+ return mpn_popcount (u->_mp_d, un);
}
mp_bitcnt_t
if ( (un ^ vn) < 0)
return ~(mp_bitcnt_t) 0;
- if (un < 0)
+ comp = - (uc = vc = (un < 0));
+ if (uc)
{
assert (vn < 0);
un = -un;
vn = -vn;
- uc = vc = 1;
- comp = - (mp_limb_t) 1;
}
- else
- uc = vc = comp = 0;
up = u->_mp_d;
vp = v->_mp_d;
{
mp_ptr up;
mp_size_t us, un, i;
- mp_limb_t limb, ux, uc;
- unsigned cnt;
+ mp_limb_t limb, ux;
- up = u->_mp_d;
us = u->_mp_size;
un = GMP_ABS (us);
i = starting_bit / GMP_LIMB_BITS;
if (i >= un)
return (us >= 0 ? ~(mp_bitcnt_t) 0 : starting_bit);
- if (us < 0)
- {
- ux = GMP_LIMB_MAX;
- uc = mpn_zero_p (up, i);
- }
- else
- ux = uc = 0;
-
- limb = (ux ^ up[i]) + uc;
- uc = limb < uc;
-
- /* Mask to 0 all bits before starting_bit, thus ignoring them. */
- limb &= (GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS));
+ up = u->_mp_d;
+ ux = 0;
+ limb = up[i];
- while (limb == 0)
+ if (starting_bit != 0)
{
- i++;
- if (i == un)
+ if (us < 0)
{
- assert (uc == 0);
- /* For the u > 0 case, this can happen only for the first
- masked limb. For the u < 0 case, it happens when the
- highest limbs of the absolute value are all ones. */
- return (us >= 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
+ ux = mpn_zero_p (up, i);
+ limb = ~ limb + ux;
+ ux = - (mp_limb_t) (limb >= ux);
}
- limb = (ux ^ up[i]) + uc;
- uc = limb < uc;
+
+ /* Mask to 0 all bits before starting_bit, thus ignoring them. */
+ limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
}
- gmp_ctz (cnt, limb);
- return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
+
+ return mpn_common_scan (limb, i, up, un, ux);
}
mp_bitcnt_t
{
mp_ptr up;
mp_size_t us, un, i;
- mp_limb_t limb, ux, uc;
- unsigned cnt;
+ mp_limb_t limb, ux;
- up = u->_mp_d;
us = u->_mp_size;
+ ux = - (mp_limb_t) (us >= 0);
un = GMP_ABS (us);
i = starting_bit / GMP_LIMB_BITS;
/* When past end, there's an immediate 0 bit for u>=0, or no 0 bits for
u<0. Notice this test picks up all cases of u==0 too. */
if (i >= un)
- return (us >= 0 ? starting_bit : ~(mp_bitcnt_t) 0);
+ return (ux ? starting_bit : ~(mp_bitcnt_t) 0);
- if (us < 0)
- {
- ux = GMP_LIMB_MAX;
- uc = mpn_zero_p (up, i);
- }
- else
- ux = uc = 0;
+ up = u->_mp_d;
+ limb = up[i] ^ ux;
- limb = (ux ^ up[i]) + uc;
- uc = limb < uc;
+ if (ux == 0)
+ limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */
- /* Mask to 1 all bits before starting_bit, thus ignoring them. */
- limb |= ((mp_limb_t) 1 << (starting_bit % GMP_LIMB_BITS)) - 1;
+ /* Mask all bits before starting_bit, thus ignoring them. */
+ limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
- while (limb == GMP_LIMB_MAX)
- {
- i++;
- if (i == un)
- {
- assert (uc == 0);
- return (us >= 0 ? un * GMP_LIMB_BITS : ~(mp_bitcnt_t) 0);
- }
- limb = (ux ^ up[i]) + uc;
- uc = limb < uc;
- }
- gmp_ctz (cnt, ~limb);
- return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
+ return mpn_common_scan (limb, i, up, un, ux);
}
\f
size_t ndigits;
assert (base >= 2);
- assert (base <= 36);
+ assert (base <= 62);
un = GMP_ABS (u->_mp_size);
if (un == 0)
mpn_copyi (tp, up, un);
mpn_div_qr_1_invert (&bi, base);
- for (ndigits = 0; un > 0; ndigits++)
+ ndigits = 0;
+ do
{
+ ndigits++;
mpn_div_qr_1_preinv (tp, tp, un, &bi);
un -= (tp[un-1] == 0);
}
+ while (un > 0);
+
gmp_free (tp);
return ndigits;
}
mp_size_t un;
size_t i, sn;
- if (base >= 0)
+ digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
+ if (base > 1)
{
- digits = "0123456789abcdefghijklmnopqrstuvwxyz";
+ if (base <= 36)
+ digits = "0123456789abcdefghijklmnopqrstuvwxyz";
+ else if (base > 62)
+ return NULL;
}
+ else if (base >= -1)
+ base = 10;
else
{
base = -base;
- digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
+ if (base > 36)
+ return NULL;
}
- if (base <= 1)
- base = 10;
- if (base > 36)
- return NULL;
sn = 1 + mpz_sizeinbase (u, base);
if (!sp)
- sp = gmp_xalloc (1 + sn);
+ sp = (char *) gmp_xalloc (1 + sn);
un = GMP_ABS (u->_mp_size);
int
mpz_set_str (mpz_t r, const char *sp, int base)
{
- unsigned bits;
+ unsigned bits, value_of_a;
mp_size_t rn, alloc;
mp_ptr rp;
- size_t sn;
size_t dn;
int sign;
unsigned char *dp;
- assert (base == 0 || (base >= 2 && base <= 36));
+ assert (base == 0 || (base >= 2 && base <= 62));
while (isspace( (unsigned char) *sp))
sp++;
- if (*sp == '-')
- {
- sign = 1;
- sp++;
- }
- else
- sign = 0;
+ sign = (*sp == '-');
+ sp += sign;
if (base == 0)
{
- if (*sp == '0')
+ if (sp[0] == '0')
{
- sp++;
- if (*sp == 'x' || *sp == 'X')
+ if (sp[1] == 'x' || sp[1] == 'X')
{
base = 16;
- sp++;
+ sp += 2;
}
- else if (*sp == 'b' || *sp == 'B')
+ else if (sp[1] == 'b' || sp[1] == 'B')
{
base = 2;
- sp++;
+ sp += 2;
}
else
base = 8;
base = 10;
}
- sn = strlen (sp);
- dp = gmp_xalloc (sn + (sn == 0));
+ if (!*sp)
+ {
+ r->_mp_size = 0;
+ return -1;
+ }
+ dp = (unsigned char *) gmp_xalloc (strlen (sp));
+ value_of_a = (base > 36) ? 36 : 10;
for (dn = 0; *sp; sp++)
{
unsigned digit;
if (isspace ((unsigned char) *sp))
continue;
- if (*sp >= '0' && *sp <= '9')
+ else if (*sp >= '0' && *sp <= '9')
digit = *sp - '0';
else if (*sp >= 'a' && *sp <= 'z')
- digit = *sp - 'a' + 10;
+ digit = *sp - 'a' + value_of_a;
else if (*sp >= 'A' && *sp <= 'Z')
digit = *sp - 'A' + 10;
else
digit = base; /* fail */
- if (digit >= base)
+ if (digit >= (unsigned) base)
{
gmp_free (dp);
r->_mp_size = 0;
dp[dn++] = digit;
}
+ if (!dn)
+ {
+ gmp_free (dp);
+ r->_mp_size = 0;
+ return -1;
+ }
bits = mpn_base_power_of_two_p (base);
if (bits > 0)
{
- alloc = (sn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
+ alloc = (dn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
rp = MPZ_REALLOC (r, alloc);
rn = mpn_set_str_bits (rp, dp, dn, bits);
}
{
struct mpn_base_info info;
mpn_get_base_info (&info, base);
- alloc = (sn + info.exp - 1) / info.exp;
+ alloc = (dn + info.exp - 1) / info.exp;
rp = MPZ_REALLOC (r, alloc);
rn = mpn_set_str_other (rp, dp, dn, base, &info);
+ /* Normalization, needed for all-zero input. */
+ assert (rn > 0);
+ rn -= rp[rn-1] == 0;
}
assert (rn <= alloc);
gmp_free (dp);
static int
gmp_detect_endian (void)
{
- static const int i = 1;
+ static const int i = 2;
const unsigned char *p = (const unsigned char *) &i;
- if (*p == 1)
- /* Little endian */
- return -1;
- else
- /* Big endian */
- return 1;
+ return 1 - *p;
}
/* Import and export. Does not support nails. */
}
}
}
- if (bytes > 0)
+ assert (i + (bytes > 0) == rn);
+ if (limb != 0)
rp[i++] = limb;
- assert (i == rn);
+ else
+ i = mpn_normalized_size (rp, i);
- r->_mp_size = mpn_normalized_size (rp, i);
+ r->_mp_size = i;
}
void *
mpz_export (void *r, size_t *countp, int order, size_t size, int endian,
size_t nails, const mpz_t u)
{
- unsigned char *p;
- ptrdiff_t word_step;
- size_t count, k;
+ size_t count;
mp_size_t un;
- /* The current (partial) limb. */
- mp_limb_t limb;
- /* The number of bytes left to to in this limb. */
- size_t bytes;
- /* The index where the limb was read. */
- mp_size_t i;
-
if (nails != 0)
gmp_die ("mpz_import: Nails not supported.");
assert (endian >= -1 && endian <= 1);
assert (size > 0 || u->_mp_size == 0);
- un = GMP_ABS (u->_mp_size);
- if (un == 0)
- {
- if (countp)
- *countp = 0;
- return r;
- }
+ un = u->_mp_size;
+ count = 0;
+ if (un != 0)
+ {
+ size_t k;
+ unsigned char *p;
+ ptrdiff_t word_step;
+ /* The current (partial) limb. */
+ mp_limb_t limb;
+ /* The number of bytes left to to in this limb. */
+ size_t bytes;
+ /* The index where the limb was read. */
+ mp_size_t i;
- /* Count bytes in top limb. */
- for (limb = u->_mp_d[un-1], k = 0; limb > 0; k++, limb >>= CHAR_BIT)
- ;
+ un = GMP_ABS (un);
- assert (k > 0);
+ /* Count bytes in top limb. */
+ limb = u->_mp_d[un-1];
+ assert (limb != 0);
- count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
+ k = (GMP_LIMB_BITS <= CHAR_BIT);
+ if (!k)
+ {
+ do {
+ int LOCAL_CHAR_BIT = CHAR_BIT;
+ k++; limb >>= LOCAL_CHAR_BIT;
+ } while (limb != 0);
+ }
+ /* else limb = 0; */
- if (!r)
- r = gmp_xalloc (count * size);
+ count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
- if (endian == 0)
- endian = gmp_detect_endian ();
+ if (!r)
+ r = gmp_xalloc (count * size);
- p = (unsigned char *) r;
+ if (endian == 0)
+ endian = gmp_detect_endian ();
- word_step = (order != endian) ? 2 * size : 0;
+ p = (unsigned char *) r;
- /* Process bytes from the least significant end, so point p at the
- least significant word. */
- if (order == 1)
- {
- p += size * (count - 1);
- word_step = - word_step;
- }
+ word_step = (order != endian) ? 2 * size : 0;
- /* And at least significant byte of that word. */
- if (endian == 1)
- p += (size - 1);
+ /* Process bytes from the least significant end, so point p at the
+ least significant word. */
+ if (order == 1)
+ {
+ p += size * (count - 1);
+ word_step = - word_step;
+ }
- for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step)
- {
- size_t j;
- for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
- {
- if (bytes == 0)
- {
- if (i < un)
- limb = u->_mp_d[i++];
- bytes = sizeof (mp_limb_t);
- }
- *p = limb;
- limb >>= CHAR_BIT;
- bytes--;
- }
- }
- assert (i == un);
- assert (k == count);
+ /* And at least significant byte of that word. */
+ if (endian == 1)
+ p += (size - 1);
+
+ for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step)
+ {
+ size_t j;
+ for (j = 0; j < size; ++j, p -= (ptrdiff_t) endian)
+ {
+ if (sizeof (mp_limb_t) == 1)
+ {
+ if (i < un)
+ *p = u->_mp_d[i++];
+ else
+ *p = 0;
+ }
+ else
+ {
+ int LOCAL_CHAR_BIT = CHAR_BIT;
+ if (bytes == 0)
+ {
+ if (i < un)
+ limb = u->_mp_d[i++];
+ bytes = sizeof (mp_limb_t);
+ }
+ *p = limb;
+ limb >>= LOCAL_CHAR_BIT;
+ bytes--;
+ }
+ }
+ }
+ assert (i == un);
+ assert (k == count);
+ }
if (countp)
*countp = count;
projects / oweals / minetest.git / commitdiff