/* Binary segmentation, using simple shift+add method for processing p.
* Faster than twiddling bits, but not nearly as fast as import/export.
* mpz_import and mpz_export were added in GMP 4.1 released in 2002.
*/
void poly_mod_mul(mpz_t* px, mpz_t* py, UV r, mpz_t mod, mpz_t p, mpz_t p2, mpz_t t)
{
UV i, d, bits;
UV degree = r-1;
mpz_mul(t, mod, mod);
mpz_mul_ui(t, t, r);
bits = mpz_sizeinbase(t, 2);
mpz_set_ui(p, 0);
for (i = 0; i < r; i++) {
mpz_mul_2exp(p, p, bits);
mpz_add(p, p, px[r-i-1]);
}
if (px == py) {
mpz_mul(p, p, p);
} else {
mpz_set_ui(p2, 0);
for (i = 0; i < r; i++) {
mpz_mul_2exp(p2, p2, bits);
mpz_add(p2, p2, py[r-i-1]);
}
mpz_mul(p, p, p2);
}
for (d = 0; d <= 2*degree; d++) {
mpz_tdiv_r_2exp(t, p, bits);
mpz_tdiv_q_2exp(p, p, bits);
if (d < r)
mpz_set(px[d], t);
else
mpz_add(px[d-r], px[d-r], t);
}
for (i = 0; i < r; i++)
mpz_mod(px[i], px[i], mod);
}
void
hex_random_bit_op (enum hex_random_op op, unsigned long maxbits,
char **ap, unsigned long *b, char **rp)
{
mpz_t a, r;
unsigned long abits, bbits;
unsigned signs;
mpz_init (a);
mpz_init (r);
abits = gmp_urandomb_ui (state, 32) % maxbits;
bbits = gmp_urandomb_ui (state, 32) % (maxbits + 100);
mpz_rrandomb (a, state, abits);
signs = gmp_urandomb_ui (state, 1);
if (signs & 1)
mpz_neg (a, a);
switch (op)
{
default:
abort ();
case OP_SETBIT:
mpz_set (r, a);
mpz_setbit (r, bbits);
break;
case OP_CLRBIT:
mpz_set (r, a);
mpz_clrbit (r, bbits);
break;
case OP_COMBIT:
mpz_set (r, a);
mpz_combit (r, bbits);
break;
case OP_CDIV_Q_2:
mpz_cdiv_q_2exp (r, a, bbits);
break;
case OP_CDIV_R_2:
mpz_cdiv_r_2exp (r, a, bbits);
break;
case OP_FDIV_Q_2:
mpz_fdiv_q_2exp (r, a, bbits);
break;
case OP_FDIV_R_2:
mpz_fdiv_r_2exp (r, a, bbits);
break;
case OP_TDIV_Q_2:
mpz_tdiv_q_2exp (r, a, bbits);
break;
case OP_TDIV_R_2:
mpz_tdiv_r_2exp (r, a, bbits);
break;
}
gmp_asprintf (ap, "%Zx", a);
*b = bbits;
gmp_asprintf (rp, "%Zx", r);
mpz_clear (a);
mpz_clear (r);
}
void
print (int limb_bits, int nail_bits)
{
int i;
mpz_t mhi, mlo;
printf ("/* This file generated by gen-psqr.c - DO NOT EDIT. */\n");
printf ("\n");
printf ("#if GMP_LIMB_BITS != %d || GMP_NAIL_BITS != %d\n",
limb_bits, nail_bits);
printf ("Error, error, this data is for %d bit limb and %d bit nail\n",
limb_bits, nail_bits);
printf ("#endif\n");
printf ("\n");
printf ("/* Non-zero bit indicates a quadratic residue mod 0x100.\n");
printf (" This test identifies %.2f%% as non-squares (%d/256). */\n",
(1.0 - sq_res_0x100_fraction) * 100.0,
0x100 - sq_res_0x100_num);
printf ("static const mp_limb_t\n");
printf ("sq_res_0x100[%d] = {\n", nsq_res_0x100);
for (i = 0; i < nsq_res_0x100; i++)
{
printf (" CNST_LIMB(0x");
mpz_out_str (stdout, 16, sq_res_0x100[i]);
printf ("),\n");
}
printf ("};\n");
printf ("\n");
if (mpz_sgn (pp) != 0)
{
printf ("/* mpn_mod_34lsub1 not used due to %s */\n", mod34_excuse);
printf ("/* PERFSQR_PP = ");
}
else
printf ("/* 2^%d-1 = ", mod34_bits);
for (i = 0; i < nrawfactor; i++)
{
if (i != 0)
printf (" * ");
printf ("%d", rawfactor[i].divisor);
if (rawfactor[i].multiplicity != 1)
printf ("^%d", rawfactor[i].multiplicity);
}
printf (" %s*/\n", mpz_sgn (pp) == 0 ? "... " : "");
printf ("#define PERFSQR_MOD_BITS %d\n", mod_bits);
if (mpz_sgn (pp) != 0)
{
printf ("#define PERFSQR_PP CNST_LIMB(0x");
mpz_out_str (stdout, 16, pp);
printf (")\n");
printf ("#define PERFSQR_PP_NORM CNST_LIMB(0x");
mpz_out_str (stdout, 16, pp_norm);
printf (")\n");
printf ("#define PERFSQR_PP_INVERTED CNST_LIMB(0x");
mpz_out_str (stdout, 16, pp_inverted);
printf (")\n");
}
printf ("\n");
mpz_init (mhi);
mpz_init (mlo);
printf ("/* This test identifies %.2f%% as non-squares. */\n",
(1.0 - total_fraction) * 100.0);
printf ("#define PERFSQR_MOD_TEST(up, usize) \\\n");
printf (" do { \\\n");
printf (" mp_limb_t r; \\\n");
if (mpz_sgn (pp) != 0)
printf (" PERFSQR_MOD_PP (r, up, usize); \\\n");
else
printf (" PERFSQR_MOD_34 (r, up, usize); \\\n");
for (i = 0; i < nfactor; i++)
{
printf (" \\\n");
printf (" /* %5.2f%% */ \\\n",
(1.0 - factor[i].fraction) * 100.0);
printf (" PERFSQR_MOD_%d (r, CNST_LIMB(%2d), CNST_LIMB(0x",
factor[i].divisor <= limb_bits ? 1 : 2,
factor[i].divisor);
mpz_out_str (stdout, 16, factor[i].inverse);
printf ("), \\\n");
printf (" CNST_LIMB(0x");
if ( factor[i].divisor <= limb_bits)
{
mpz_out_str (stdout, 16, factor[i].mask);
}
else
{
mpz_tdiv_r_2exp (mlo, factor[i].mask, (unsigned long) limb_bits);
mpz_tdiv_q_2exp (mhi, factor[i].mask, (unsigned long) limb_bits);
mpz_out_str (stdout, 16, mhi);
printf ("), CNST_LIMB(0x");
mpz_out_str (stdout, 16, mlo);
}
printf (")); \\\n");
}
printf (" } while (0)\n");
printf ("\n");
printf ("/* Grand total sq_res_0x100 and PERFSQR_MOD_TEST, %.2f%% non-squares. */\n",
(1.0 - (total_fraction * 44.0/256.0)) * 100.0);
printf ("\n");
printf ("/* helper for tests/mpz/t-perfsqr.c */\n");
printf ("#define PERFSQR_DIVISORS { 256,");
for (i = 0; i < nfactor; i++)
printf (" %d,", factor[i].divisor);
printf (" }\n");
mpz_clear (mhi);
mpz_clear (mlo);
}
static PyObject *
GMPy_MPZ_unpack(PyObject *self, PyObject *args)
{
mp_bitcnt_t nbits, total_bits, guard_bit, extra_bits, temp_bits;
Py_ssize_t index = 0, lst_count, i, lst_ptr = 0;
PyObject *result;
mpz_t temp;
mp_limb_t extra = 0;
MPZ_Object *item, *tempx = NULL;
CTXT_Object *context = NULL;
if (PyTuple_GET_SIZE(args) != 2) {
TYPE_ERROR("unpack() requires 'int','int' arguments");
return NULL;
}
nbits = mp_bitcnt_t_From_Integer(PyTuple_GET_ITEM(args, 1));
if (nbits == (mp_bitcnt_t)(-1) && PyErr_Occurred()) {
return NULL;
}
if (!(tempx = GMPy_MPZ_From_Integer(PyTuple_GET_ITEM(args, 0), context))) {
TYPE_ERROR("unpack() requires 'int','int' arguments");
return NULL;
}
if (mpz_sgn(tempx->z) < 0) {
VALUE_ERROR("unpack() requires x >= 0");
return NULL;
}
if (mpz_sgn(tempx->z) == 0) {
total_bits = 0;
}
else {
total_bits = mpz_sizeinbase(tempx->z, 2);
}
lst_count = total_bits / nbits;
if ((total_bits % nbits) || !lst_count) {
lst_count += 1;
}
if (!(result = PyList_New(lst_count))) {
Py_DECREF((PyObject*)tempx);
return NULL;
}
if (mpz_sgn(tempx->z) == 0) {
if (!(item = GMPy_MPZ_New(context))) {
Py_DECREF((PyObject*)tempx);
Py_DECREF(result);
return NULL;
}
mpz_set_ui(item->z, 0);
PyList_SET_ITEM(result, 0, (PyObject*)item);
Py_DECREF((PyObject*)tempx);
return result;
}
mpz_init(temp);
guard_bit = nbits + (2 * mp_bits_per_limb);
extra_bits = 0;
index = 0;
while (lst_ptr < lst_count) {
i = 0;
temp_bits = 0;
mpz_set_ui(temp, 0);
mpz_setbit(temp, guard_bit);
while (temp_bits + extra_bits < nbits) {
temp->_mp_d[i++] = mpz_getlimbn(tempx->z, index++);
temp_bits += mp_bits_per_limb;
}
mpz_clrbit(temp, guard_bit);
mpz_mul_2exp(temp, temp, extra_bits);
if (mpz_sgn(temp) == 0 && extra != 0) {
mpz_set_ui(temp, 1);
temp->_mp_d[0] = extra;
}
else {
mpn_add_1(temp->_mp_d, temp->_mp_d, mpz_size(temp), extra);
}
temp_bits += extra_bits;
while ((lst_ptr < lst_count) && (temp_bits >= nbits)) {
if(!(item = GMPy_MPZ_New(context))) {
mpz_clear(temp);
Py_DECREF((PyObject*)tempx);
Py_DECREF(result);
return NULL;
}
mpz_tdiv_r_2exp(item->z, temp, nbits);
PyList_SET_ITEM(result, lst_ptr++, (PyObject*)item);
mpz_tdiv_q_2exp(temp, temp, nbits);
temp_bits -= nbits;
}
extra = mpz_getlimbn(temp, 0);
extra_bits = temp_bits;
}
Py_DECREF((PyObject*)tempx);
mpz_clear(temp);
return result;
}
static PyObject *
Pympz_mpmath_normalize(PyObject *self, PyObject *args)
{
long sign = 0;
mpir_si bc = 0, prec = 0, shift, zbits, carry = 0;
PyObject *exp = 0, *newexp = 0, *newexp2 = 0, *tmp = 0, *rndstr = 0;
PympzObject *man = 0, *upper = 0, *lower = 0;
char rnd = 0;
if (PyTuple_GET_SIZE(args) == 6) {
/* Need better error-checking here. Under Python 3.0, overflow into
C-long is possible. */
sign = clong_From_Integer(PyTuple_GET_ITEM(args, 0));
man = (PympzObject *)PyTuple_GET_ITEM(args, 1);
exp = PyTuple_GET_ITEM(args, 2);
bc = SI_From_Integer(PyTuple_GET_ITEM(args, 3));
prec = SI_From_Integer(PyTuple_GET_ITEM(args, 4));
rndstr = PyTuple_GET_ITEM(args, 5);
if (PyErr_Occurred()) {
TYPE_ERROR("arguments long, PympzObject*, PyObject*, long, long, char needed");
return NULL;
}
}
else {
TYPE_ERROR("6 arguments required");
return NULL;
}
if (!Pympz_Check(man)) {
TYPE_ERROR("argument is not an mpz");
return NULL;
}
/* If rndstr really is a string, extract the first character. */
if (Py2or3String_Check(rndstr)) {
rnd = Py2or3String_AsString(rndstr)[0];
}
else {
VALUE_ERROR("invalid rounding mode specified");
return NULL;
}
/* If the mantissa is 0, return the normalized representation. */
if (!mpz_sgn(man->z)) {
Py_INCREF((PyObject*)man);
return mpmath_build_mpf(0, man, 0, 0);
}
/* if bc <= prec and the number is odd return it */
if ((bc <= prec) && mpz_odd_p(man->z)) {
Py_INCREF((PyObject*)man);
Py_INCREF((PyObject*)exp);
return mpmath_build_mpf(sign, man, exp, bc);
}
if (!(upper = (PympzObject*)Pympz_new()) ||
!(lower = (PympzObject*)Pympz_new())) {
Py_XDECREF((PyObject*)upper);
Py_XDECREF((PyObject*)lower);
}
shift = bc - prec;
if (shift>0) {
switch (rnd) {
case 'f':
if(sign) {
mpz_cdiv_q_2exp(upper->z, man->z, shift);
}
else {
mpz_fdiv_q_2exp(upper->z, man->z, shift);
}
break;
case 'c':
if(sign) {
mpz_fdiv_q_2exp(upper->z, man->z, shift);
}
else {
mpz_cdiv_q_2exp(upper->z, man->z, shift);
}
break;
case 'd':
mpz_fdiv_q_2exp(upper->z, man->z, shift);
break;
case 'u':
mpz_cdiv_q_2exp(upper->z, man->z, shift);
break;
case 'n':
default:
mpz_tdiv_r_2exp(lower->z, man->z, shift);
mpz_tdiv_q_2exp(upper->z, man->z, shift);
if (mpz_sgn(lower->z)) {
/* lower is not 0 so it must have at least 1 bit set */
if (mpz_sizeinbase(lower->z, 2) == shift) {
/* lower is >= 1/2 */
if (mpz_scan1(lower->z, 0) == shift-1) {
/* lower is exactly 1/2 */
if (mpz_odd_p(upper->z))
carry = 1;
}
else {
carry = 1;
}
}
}
if (carry)
mpz_add_ui(upper->z, upper->z, 1);
}
if (!(tmp = PyIntOrLong_FromSI(shift))) {
Py_DECREF((PyObject*)upper);
Py_DECREF((PyObject*)lower);
return NULL;
}
if (!(newexp = PyNumber_Add(exp, tmp))) {
Py_DECREF((PyObject*)upper);
Py_DECREF((PyObject*)lower);
Py_DECREF(tmp);
return NULL;
}
Py_DECREF(tmp);
bc = prec;
}
else {
mpz_set(upper->z, man->z);
newexp = exp;
Py_INCREF(newexp);
}
/* Strip trailing 0 bits. */
if ((zbits = mpz_scan1(upper->z, 0)))
mpz_tdiv_q_2exp(upper->z, upper->z, zbits);
if (!(tmp = PyIntOrLong_FromSI(zbits))) {
Py_DECREF((PyObject*)upper);
Py_DECREF((PyObject*)lower);
Py_DECREF(newexp);
return NULL;
}
if (!(newexp2 = PyNumber_Add(newexp, tmp))) {
Py_DECREF((PyObject*)upper);
Py_DECREF((PyObject*)lower);
Py_DECREF(tmp);
Py_DECREF(newexp);
return NULL;
}
Py_DECREF(newexp);
Py_DECREF(tmp);
bc -= zbits;
/* Check if one less than a power of 2 was rounded up. */
if (!mpz_cmp_ui(upper->z, 1))
bc = 1;
Py_DECREF((PyObject*)lower);
return mpmath_build_mpf(sign, upper, newexp2, bc);
}
static PyObject *
Pympz_mpmath_create(PyObject *self, PyObject *args)
{
long sign;
mpir_si bc, shift, zbits, carry = 0, prec = 0;
PyObject *exp = 0, *newexp = 0, *newexp2 = 0, *tmp = 0;
PympzObject *man = 0, *upper = 0, *lower = 0;
const char *rnd = "f";
if (PyTuple_GET_SIZE(args) < 2) {
TYPE_ERROR("mpmath_create() expects 'mpz','int'[,'int','str'] arguments");
return NULL;
}
switch (PyTuple_GET_SIZE(args)) {
case 4:
rnd = Py2or3String_AsString(PyTuple_GET_ITEM(args, 3));
case 3:
prec = SI_From_Integer(PyTuple_GET_ITEM(args, 2));
if (prec == -1 && PyErr_Occurred())
return NULL;
prec = ABS(prec);
case 2:
exp = PyTuple_GET_ITEM(args, 1);
case 1:
man = Pympz_From_Integer(PyTuple_GET_ITEM(args, 0));
if (!man) {
TYPE_ERROR("mpmath_create() expects 'mpz','int'[,'int','str'] arguments");
return NULL;
}
}
/* If the mantissa is 0, return the normalized representation. */
if (!mpz_sgn(man->z)) {
return mpmath_build_mpf(0, man, 0, 0);
}
upper = (PympzObject*)Pympz_new();
lower = (PympzObject*)Pympz_new();
if (!upper || !lower) {
Py_DECREF((PyObject*)man);
Py_XDECREF((PyObject*)upper);
Py_XDECREF((PyObject*)lower);
return NULL;
}
/* Extract sign, make man positive, and set bit count */
sign = (mpz_sgn(man->z) == -1);
mpz_abs(upper->z, man->z);
bc = mpz_sizeinbase(upper->z, 2);
if (!prec) prec = bc;
shift = bc - prec;
if (shift > 0) {
switch (rnd[0]) {
case 'f':
if(sign) {
mpz_cdiv_q_2exp(upper->z, upper->z, shift);
}
else {
mpz_fdiv_q_2exp(upper->z, upper->z, shift);
}
break;
case 'c':
if(sign) {
mpz_fdiv_q_2exp(upper->z, upper->z, shift);
}
else {
mpz_cdiv_q_2exp(upper->z, upper->z, shift);
}
break;
case 'd':
mpz_fdiv_q_2exp(upper->z, upper->z, shift);
break;
case 'u':
mpz_cdiv_q_2exp(upper->z, upper->z, shift);
break;
case 'n':
default:
mpz_tdiv_r_2exp(lower->z, upper->z, shift);
mpz_tdiv_q_2exp(upper->z, upper->z, shift);
if (mpz_sgn(lower->z)) {
/* lower is not 0 so it must have at least 1 bit set */
if (mpz_sizeinbase(lower->z, 2)==shift) {
/* lower is >= 1/2 */
if (mpz_scan1(lower->z, 0)==shift-1) {
/* lower is exactly 1/2 */
if (mpz_odd_p(upper->z))
carry = 1;
}
else {
carry = 1;
}
}
}
if (carry)
mpz_add_ui(upper->z, upper->z, 1);
}
if (!(tmp = PyIntOrLong_FromSI(shift))) {
Py_DECREF((PyObject*)upper);
Py_DECREF((PyObject*)lower);
return NULL;
}
if (!(newexp = PyNumber_Add(exp, tmp))) {
Py_DECREF((PyObject*)man);
Py_DECREF((PyObject*)upper);
Py_DECREF((PyObject*)lower);
Py_DECREF(tmp);
return NULL;
}
Py_DECREF(tmp);
bc = prec;
}
else {
newexp = exp;
Py_INCREF(newexp);
}
/* Strip trailing 0 bits. */
if ((zbits = mpz_scan1(upper->z, 0)))
mpz_tdiv_q_2exp(upper->z, upper->z, zbits);
if (!(tmp = PyIntOrLong_FromSI(zbits))) {
Py_DECREF((PyObject*)man);
Py_DECREF((PyObject*)upper);
Py_DECREF((PyObject*)lower);
Py_DECREF(newexp);
return NULL;
}
if (!(newexp2 = PyNumber_Add(newexp, tmp))) {
Py_DECREF((PyObject*)man);
Py_DECREF((PyObject*)upper);
Py_DECREF((PyObject*)lower);
Py_DECREF(tmp);
Py_DECREF(newexp);
return NULL;
}
Py_DECREF(newexp);
Py_DECREF(tmp);
bc -= zbits;
/* Check if one less than a power of 2 was rounded up. */
if (!mpz_cmp_ui(upper->z, 1))
bc = 1;
Py_DECREF((PyObject*)lower);
Py_DECREF((PyObject*)man);
return mpmath_build_mpf(sign, upper, newexp2, bc);
}
static int
mpfr_rem1 (mpfr_ptr rem, long *quo, mpfr_rnd_t rnd_q,
mpfr_srcptr x, mpfr_srcptr y, mpfr_rnd_t rnd)
{
mpfr_exp_t ex, ey;
int compare, inex, q_is_odd, sign, signx = MPFR_SIGN (x);
mpz_t mx, my, r;
int tiny = 0;
MPFR_ASSERTD (rnd_q == MPFR_RNDN || rnd_q == MPFR_RNDZ);
if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x) || MPFR_IS_SINGULAR (y)))
{
if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y) || MPFR_IS_INF (x)
|| MPFR_IS_ZERO (y))
{
/* for remquo, quo is undefined */
MPFR_SET_NAN (rem);
MPFR_RET_NAN;
}
else /* either y is Inf and x is 0 or non-special,
or x is 0 and y is non-special,
in both cases the quotient is zero. */
{
if (quo)
*quo = 0;
return mpfr_set (rem, x, rnd);
}
}
/* now neither x nor y is NaN, Inf or zero */
mpz_init (mx);
mpz_init (my);
mpz_init (r);
ex = mpfr_get_z_2exp (mx, x); /* x = mx*2^ex */
ey = mpfr_get_z_2exp (my, y); /* y = my*2^ey */
/* to get rid of sign problems, we compute it separately:
quo(-x,-y) = quo(x,y), rem(-x,-y) = -rem(x,y)
quo(-x,y) = -quo(x,y), rem(-x,y) = -rem(x,y)
thus quo = sign(x/y)*quo(|x|,|y|), rem = sign(x)*rem(|x|,|y|) */
sign = (signx == MPFR_SIGN (y)) ? 1 : -1;
mpz_abs (mx, mx);
mpz_abs (my, my);
q_is_odd = 0;
/* divide my by 2^k if possible to make operations mod my easier */
{
unsigned long k = mpz_scan1 (my, 0);
ey += k;
mpz_fdiv_q_2exp (my, my, k);
}
if (ex <= ey)
{
/* q = x/y = mx/(my*2^(ey-ex)) */
/* First detect cases where q=0, to avoid creating a huge number
my*2^(ey-ex): if sx = mpz_sizeinbase (mx, 2) and sy =
mpz_sizeinbase (my, 2), we have x < 2^(ex + sx) and
y >= 2^(ey + sy - 1), thus if ex + sx <= ey + sy - 1
the quotient is 0 */
if (ex + (mpfr_exp_t) mpz_sizeinbase (mx, 2) <
ey + (mpfr_exp_t) mpz_sizeinbase (my, 2))
{
tiny = 1;
mpz_set (r, mx);
mpz_set_ui (mx, 0);
}
else
{
mpz_mul_2exp (my, my, ey - ex); /* divide mx by my*2^(ey-ex) */
/* since mx > 0 and my > 0, we can use mpz_tdiv_qr in all cases */
mpz_tdiv_qr (mx, r, mx, my);
/* 0 <= |r| <= |my|, r has the same sign as mx */
}
if (rnd_q == MPFR_RNDN)
q_is_odd = mpz_tstbit (mx, 0);
if (quo) /* mx is the quotient */
{
mpz_tdiv_r_2exp (mx, mx, WANTED_BITS);
*quo = mpz_get_si (mx);
}
}
else /* ex > ey */
{
if (quo) /* remquo case */
/* for remquo, to get the low WANTED_BITS more bits of the quotient,
we first compute R = X mod Y*2^WANTED_BITS, where X and Y are
defined below. Then the low WANTED_BITS of the quotient are
floor(R/Y). */
mpz_mul_2exp (my, my, WANTED_BITS); /* 2^WANTED_BITS*Y */
else if (rnd_q == MPFR_RNDN) /* remainder case */
/* Let X = mx*2^(ex-ey) and Y = my. Then both X and Y are integers.
Assume X = R mod Y, then x = X*2^ey = R*2^ey mod (Y*2^ey=y).
To be able to perform the rounding, we need the least significant
bit of the quotient, i.e., one more bit in the remainder,
which is obtained by dividing by 2Y. */
mpz_mul_2exp (my, my, 1); /* 2Y */
mpz_set_ui (r, 2);
mpz_powm_ui (r, r, ex - ey, my); /* 2^(ex-ey) mod my */
mpz_mul (r, r, mx);
mpz_mod (r, r, my);
if (quo) /* now 0 <= r < 2^WANTED_BITS*Y */
{
mpz_fdiv_q_2exp (my, my, WANTED_BITS); /* back to Y */
mpz_tdiv_qr (mx, r, r, my);
/* oldr = mx*my + newr */
*quo = mpz_get_si (mx);
q_is_odd = *quo & 1;
}
else if (rnd_q == MPFR_RNDN) /* now 0 <= r < 2Y in the remainder case */
{
mpz_fdiv_q_2exp (my, my, 1); /* back to Y */
/* least significant bit of q */
q_is_odd = mpz_cmpabs (r, my) >= 0;
if (q_is_odd)
mpz_sub (r, r, my);
}
/* now 0 <= |r| < |my|, and if needed,
q_is_odd is the least significant bit of q */
}
if (mpz_cmp_ui (r, 0) == 0)
{
inex = mpfr_set_ui (rem, 0, MPFR_RNDN);
/* take into account sign of x */
if (signx < 0)
mpfr_neg (rem, rem, MPFR_RNDN);
}
else
{
if (rnd_q == MPFR_RNDN)
{
/* FIXME: the comparison 2*r < my could be done more efficiently
at the mpn level */
mpz_mul_2exp (r, r, 1);
/* if tiny=1, we should compare r with my*2^(ey-ex) */
if (tiny)
{
if (ex + (mpfr_exp_t) mpz_sizeinbase (r, 2) <
ey + (mpfr_exp_t) mpz_sizeinbase (my, 2))
compare = 0; /* r*2^ex < my*2^ey */
else
{
mpz_mul_2exp (my, my, ey - ex);
compare = mpz_cmpabs (r, my);
}
}
else
compare = mpz_cmpabs (r, my);
mpz_fdiv_q_2exp (r, r, 1);
compare = ((compare > 0) ||
((rnd_q == MPFR_RNDN) && (compare == 0) && q_is_odd));
/* if compare != 0, we need to subtract my to r, and add 1 to quo */
if (compare)
{
mpz_sub (r, r, my);
if (quo && (rnd_q == MPFR_RNDN))
*quo += 1;
}
}
/* take into account sign of x */
if (signx < 0)
mpz_neg (r, r);
inex = mpfr_set_z_2exp (rem, r, ex > ey ? ey : ex, rnd);
}
if (quo)
*quo *= sign;
mpz_clear (mx);
mpz_clear (my);
mpz_clear (r);
return inex;
}
