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mini-gmp.c

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/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
Contributed to the GNU project by Niels Möller
Copyright 1991-1997, 1999-2016 Free Software Foundation, Inc.
This file is part of the GNU MP Library.
The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of either:
* the GNU Lesser General Public License as published by the Free
Software Foundation; either version 3 of the License, or (at your
option) any later version.
or
* the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any
later version.
or both in parallel, as here.
The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library. If not,
see https://www.gnu.org/licenses/. */
/* NOTE: All functions in this file which are not declared in
mini-gmp.h are internal, and are not intended to be compatible
neither with GMP nor with future versions of mini-gmp. */
/* Much of the material copied from GMP files, including: gmp-impl.h,
longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c,
mpn/generic/lshift.c, mpn/generic/mul_1.c,
mpn/generic/mul_basecase.c, mpn/generic/rshift.c,
mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c,
mpn/generic/submul_1.c. */
#include <assert.h>
#include <ctype.h>
#include <limits.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "mini-gmp.h"
/* Macros */
#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
#define GMP_LIMB_MAX (~ (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_LLIMB_MASK (GMP_HLIMB_BIT - 1)
#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT)
#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1))
#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x))
#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1))
#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)))
#define gmp_assert_nocarry(x) do { \
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; \
for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \
__clz_x <<= 1; \
(count) = __clz_c; \
} while (0)
#define gmp_ctz(count, x) do { \
mp_limb_t __ctz_x = (x); \
unsigned __ctz_c = 0; \
gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \
(count) = GMP_LIMB_BITS - 1 - __ctz_c; \
} while (0)
#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \
do { \
mp_limb_t __x; \
__x = (al) + (bl); \
(sh) = (ah) + (bh) + (__x < (al)); \
(sl) = __x; \
} while (0)
#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \
do { \
mp_limb_t __x; \
__x = (al) - (bl); \
(sh) = (ah) - (bh) - ((al) < (bl)); \
(sl) = __x; \
} while (0)
#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); \
\
__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; \
\
__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); \
} while (0)
#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
do { \
mp_limb_t _qh, _ql, _r, _mask; \
gmp_umul_ppmm (_qh, _ql, (nh), (di)); \
gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \
_r = (nl) - _qh * (d); \
_mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \
_qh += _mask; \
_r += _mask & (d); \
if (_r >= (d)) \
{ \
_r -= (d); \
_qh++; \
} \
\
(r) = _r; \
(q) = _qh; \
} while (0)
#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \
do { \
mp_limb_t _q0, _t1, _t0, _mask; \
gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \
gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \
\
/* Compute the two most significant limbs of n - q'd */ \
(r1) = (n1) - (d1) * (q); \
gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \
gmp_umul_ppmm (_t1, _t0, (d0), (q)); \
gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \
(q)++; \
\
/* Conditionally adjust q and the remainders */ \
_mask = - (mp_limb_t) ((r1) >= _q0); \
(q) += _mask; \
gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \
if ((r1) >= (d1)) \
{ \
if ((r1) > (d1) || (r0) >= (d0)) \
{ \
(q)++; \
gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \
} \
} \
} while (0)
/* Swap macros. */
#define MP_LIMB_T_SWAP(x, y) \
do { \
mp_limb_t __mp_limb_t_swap__tmp = (x); \
(x) = (y); \
(y) = __mp_limb_t_swap__tmp; \
} while (0)
#define MP_SIZE_T_SWAP(x, y) \
do { \
mp_size_t __mp_size_t_swap__tmp = (x); \
(x) = (y); \
(y) = __mp_size_t_swap__tmp; \
} while (0)
#define MP_BITCNT_T_SWAP(x,y) \
do { \
mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \
(x) = (y); \
(y) = __mp_bitcnt_t_swap__tmp; \
} while (0)
#define MP_PTR_SWAP(x, y) \
do { \
mp_ptr __mp_ptr_swap__tmp = (x); \
(x) = (y); \
(y) = __mp_ptr_swap__tmp; \
} while (0)
#define MP_SRCPTR_SWAP(x, y) \
do { \
mp_srcptr __mp_srcptr_swap__tmp = (x); \
(x) = (y); \
(y) = __mp_srcptr_swap__tmp; \
} while (0)
#define MPN_PTR_SWAP(xp,xs, yp,ys) \
do { \
MP_PTR_SWAP (xp, yp); \
MP_SIZE_T_SWAP (xs, ys); \
} while(0)
#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
do { \
MP_SRCPTR_SWAP (xp, yp); \
MP_SIZE_T_SWAP (xs, ys); \
} while(0)
#define MPZ_PTR_SWAP(x, y) \
do { \
mpz_ptr __mpz_ptr_swap__tmp = (x); \
(x) = (y); \
(y) = __mpz_ptr_swap__tmp; \
} while (0)
#define MPZ_SRCPTR_SWAP(x, y) \
do { \
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;
/* Memory allocation and other helper functions. */
static void
gmp_die (const char *msg)
{
fprintf (stderr, "%s\n", msg);
abort();
}
static void *
gmp_default_alloc (size_t size)
{
void *p;
assert (size > 0);
p = malloc (size);
if (!p)
gmp_die("gmp_default_alloc: Virtual memory exhausted.");
return p;
}
static void *
gmp_default_realloc (void *old, size_t old_size, size_t new_size)
{
void * p;
p = realloc (old, new_size);
if (!p)
gmp_die("gmp_default_realloc: Virtual memory exhausted.");
return p;
}
static void
gmp_default_free (void *p, size_t size)
{
free (p);
}
static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc;
static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc;
static void (*gmp_free_func) (void *, size_t) = gmp_default_free;
void
mp_get_memory_functions (void *(**alloc_func) (size_t),
void *(**realloc_func) (void *, size_t, size_t),
void (**free_func) (void *, size_t))
{
if (alloc_func)
*alloc_func = gmp_allocate_func;
if (realloc_func)
*realloc_func = gmp_reallocate_func;
if (free_func)
*free_func = gmp_free_func;
}
void
mp_set_memory_functions (void *(*alloc_func) (size_t),
void *(*realloc_func) (void *, size_t, size_t),
void (*free_func) (void *, size_t))
{
if (!alloc_func)
alloc_func = gmp_default_alloc;
if (!realloc_func)
realloc_func = gmp_default_realloc;
if (!free_func)
free_func = gmp_default_free;
gmp_allocate_func = alloc_func;
gmp_reallocate_func = realloc_func;
gmp_free_func = free_func;
}
#define gmp_xalloc(size) ((*gmp_allocate_func)((size)))
#define gmp_free(p) ((*gmp_free_func) ((p), 0))
static mp_ptr
gmp_xalloc_limbs (mp_size_t size)
{
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 (mp_ptr) (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
}
/* MPN interface */
void
mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
{
mp_size_t i;
for (i = 0; i < n; i++)
d[i] = s[i];
}
void
mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
{
while (--n >= 0)
d[n] = s[n];
}
int
mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
{
while (--n >= 0)
{
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 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)
{
while (n > 0 && xp[n-1] == 0)
--n;
return n;
}
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);
i = 0;
do
{
mp_limb_t r = ap[i] + b;
/* Carry out */
b = (r < b);
rp[i] = r;
}
while (++i < n);
return b;
}
mp_limb_t
mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
{
mp_size_t i;
mp_limb_t cy;
for (i = 0, cy = 0; i < n; i++)
{
mp_limb_t a, b, r;
a = ap[i]; b = bp[i];
r = a + cy;
cy = (r < cy);
r += b;
cy += (r < b);
rp[i] = r;
}
return cy;
}
mp_limb_t
mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
{
mp_limb_t cy;
assert (an >= bn);
cy = mpn_add_n (rp, ap, bp, bn);
if (an > bn)
cy = mpn_add_1 (rp + bn, ap + bn, an - bn, cy);
return cy;
}
mp_limb_t
mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
{
mp_size_t i;
assert (n > 0);
i = 0;
do
{
mp_limb_t a = ap[i];
/* Carry out */
mp_limb_t cy = a < b;
rp[i] = a - b;
b = cy;
}
while (++i < n);
return b;
}
mp_limb_t
mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
{
mp_size_t i;
mp_limb_t cy;
for (i = 0, cy = 0; i < n; i++)
{
mp_limb_t a, b;
a = ap[i]; b = bp[i];
b += cy;
cy = (b < cy);
cy += (a < b);
rp[i] = a - b;
}
return cy;
}
mp_limb_t
mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
{
mp_limb_t cy;
assert (an >= bn);
cy = mpn_sub_n (rp, ap, bp, bn);
if (an > bn)
cy = mpn_sub_1 (rp + bn, ap + bn, an - bn, cy);
return cy;
}
mp_limb_t
mpn_mul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
{
mp_limb_t ul, cl, hpl, lpl;
assert (n >= 1);
cl = 0;
do
{
ul = *up++;
gmp_umul_ppmm (hpl, lpl, ul, vl);
lpl += cl;
cl = (lpl < cl) + hpl;
*rp++ = lpl;
}
while (--n != 0);
return cl;
}
mp_limb_t
mpn_addmul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
{
mp_limb_t ul, cl, hpl, lpl, rl;
assert (n >= 1);
cl = 0;
do
{
ul = *up++;
gmp_umul_ppmm (hpl, lpl, ul, vl);
lpl += cl;
cl = (lpl < cl) + hpl;
rl = *rp;
lpl = rl + lpl;
cl += lpl < rl;
*rp++ = lpl;
}
while (--n != 0);
return cl;
}
mp_limb_t
mpn_submul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
{
mp_limb_t ul, cl, hpl, lpl, rl;
assert (n >= 1);
cl = 0;
do
{
ul = *up++;
gmp_umul_ppmm (hpl, lpl, ul, vl);
lpl += cl;
cl = (lpl < cl) + hpl;
rl = *rp;
lpl = rl - lpl;
cl += lpl > rl;
*rp++ = lpl;
}
while (--n != 0);
return cl;
}
mp_limb_t
mpn_mul (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn)
{
assert (un >= vn);
assert (vn >= 1);
/* 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]);
/* Now accumulate the product of up[] and the next higher limb from
vp[]. */
while (--vn >= 1)
{
rp += 1, vp += 1;
rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
}
return rp[un];
}
void
mpn_mul_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
{
mpn_mul (rp, ap, n, bp, n);
}
void
mpn_sqr (mp_ptr rp, mp_srcptr ap, mp_size_t n)
{
mpn_mul (rp, ap, n, ap, n);
}
mp_limb_t
mpn_lshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
{
mp_limb_t high_limb, low_limb;
unsigned int tnc;
mp_limb_t retval;
assert (n >= 1);
assert (cnt >= 1);
assert (cnt < GMP_LIMB_BITS);
up += n;
rp += n;
tnc = GMP_LIMB_BITS - cnt;
low_limb = *--up;
retval = low_limb >> tnc;
high_limb = (low_limb << cnt);
while (--n != 0)
{
low_limb = *--up;
*--rp = high_limb | (low_limb >> tnc);
high_limb = (low_limb << cnt);
}
*--rp = high_limb;
return retval;
}
mp_limb_t
mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
{
mp_limb_t high_limb, low_limb;
unsigned int tnc;
mp_limb_t retval;
assert (n >= 1);
assert (cnt >= 1);
assert (cnt < GMP_LIMB_BITS);
tnc = GMP_LIMB_BITS - cnt;
high_limb = *up++;
retval = (high_limb << tnc);
low_limb = high_limb >> cnt;
while (--n != 0)
{
high_limb = *up++;
*rp++ = low_limb | (high_limb << tnc);
low_limb = high_limb >> cnt;
}
*rp = low_limb;
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;
}
/* 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, ql;
unsigned ul, uh, qh;
assert (u1 >= GMP_LIMB_HIGHBIT);
/* 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);
/* 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 / uh;
/* Adjust to get a half-limb 3/2 inverse, i.e., we want
qh' = floor( (b^3 - 1) / u) - b = floor ((b^3 - b u - 1) / u
= floor( (b (~u) + b-1) / u),
and the remainder
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 >= (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 invers of u1. If u0 > 0, adjust it to become a
3/2 inverse. */
if (u0 > 0)
{
mp_limb_t th, tl;
r = ~r;
r += u0;
if (r < u0)
{
m--;
if (r >= u1)
{
m--;
r -= u1;
}
r -= u1;
}
gmp_umul_ppmm (th, tl, u0, m);
r += th;
if (r < th)
{
m--;
m -= ((r > u1) | ((r == u1) & (tl > u0)));
}
}
return m;
}
struct gmp_div_inverse
{
/* Normalization shift count. */
unsigned shift;
/* Normalized divisor (d0 unused for mpn_div_qr_1) */
mp_limb_t d1, d0;
/* Inverse, for 2/1 or 3/2. */
mp_limb_t di;
};
static void
mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d)
{
unsigned shift;
assert (d > 0);
gmp_clz (shift, d);
inv->shift = shift;
inv->d1 = d << shift;
inv->di = mpn_invert_limb (inv->d1);
}
static void
mpn_div_qr_2_invert (struct gmp_div_inverse *inv,
mp_limb_t d1, mp_limb_t d0)
{
unsigned shift;
assert (d1 > 0);
gmp_clz (shift, d1);
inv->shift = shift;
if (shift > 0)
{
d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
d0 <<= shift;
}
inv->d1 = d1;
inv->d0 = d0;
inv->di = mpn_invert_3by2 (d1, d0);
}
static void
mpn_div_qr_invert (struct gmp_div_inverse *inv,
mp_srcptr dp, mp_size_t dn)
{
assert (dn > 0);
if (dn == 1)
mpn_div_qr_1_invert (inv, dp[0]);
else if (dn == 2)
mpn_div_qr_2_invert (inv, dp[1], dp[0]);
else
{
unsigned shift;
mp_limb_t d1, d0;
d1 = dp[dn-1];
d0 = dp[dn-2];
assert (d1 > 0);
gmp_clz (shift, d1);
inv->shift = shift;
if (shift > 0)
{
d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
d0 = (d0 << shift) | (dp[dn-3] >> (GMP_LIMB_BITS - shift));
}
inv->d1 = d1;
inv->d0 = d0;
inv->di = mpn_invert_3by2 (d1, d0);
}
}
/* Not matching current public gmp interface, rather corresponding to
the sbpi1_div_* functions. */
static mp_limb_t
mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
const struct gmp_div_inverse *inv)
{
mp_limb_t d, di;
mp_limb_t r;
mp_ptr tp = NULL;
if (inv->shift > 0)
{
tp = gmp_xalloc_limbs (nn);
r = mpn_lshift (tp, np, nn, inv->shift);
np = tp;
}
else
r = 0;
d = inv->d1;
di = inv->di;
while (--nn >= 0)
{
mp_limb_t q;
gmp_udiv_qrnnd_preinv (q, r, r, np[nn], d, di);
if (qp)
qp[nn] = q;
}
if (inv->shift > 0)
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 & (d-1)) == 0)
{
mp_limb_t r = np[0] & (d-1);
if (qp)
{
if (d <= 1)
mpn_copyi (qp, np, nn);
else
{
unsigned shift;
gmp_ctz (shift, d);
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,
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;
d1 = inv->d1;
d0 = inv->d0;
di = inv->di;
if (shift > 0)
{
tp = gmp_xalloc_limbs (nn);
r1 = mpn_lshift (tp, np, nn, shift);
np = tp;
}
else
r1 = 0;
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