static void
check_special_pow_si ()
{
mpfr_t a, b;
mp_exp_t emin;
mpfr_init (a);
mpfr_init (b);
mpfr_set_str (a, "2E100000000", 10, GMP_RNDN);
mpfr_set_si (b, -10, GMP_RNDN);
test_pow (b, a, b, GMP_RNDN);
if (!MPFR_IS_ZERO(b))
{
printf("Pow(2E10000000, -10) failed\n");
mpfr_dump (a);
mpfr_dump (b);
exit(1);
}
emin = mpfr_get_emin ();
mpfr_set_emin (-10);
mpfr_set_si (a, -2, GMP_RNDN);
mpfr_pow_si (b, a, -10000, GMP_RNDN);
if (!MPFR_IS_ZERO (b))
{
printf ("Pow_so (1, -10000) doesn't underflow if emin=-10.\n");
mpfr_dump (a);
mpfr_dump (b);
exit (1);
}
mpfr_set_emin (emin);
mpfr_clear (a);
mpfr_clear (b);
}
static void
pow_si_long_min (void)
{
mpfr_t x, y, z;
int inex;
mpfr_inits2 (sizeof(long) * CHAR_BIT + 32, x, y, z, (void *) 0);
mpfr_set_si_2exp (x, 3, -1, GMP_RNDN); /* 1.5 */
inex = mpfr_set_si (y, LONG_MIN, GMP_RNDN);
MPFR_ASSERTN (inex == 0);
mpfr_nextbelow (y);
mpfr_pow (y, x, y, GMP_RNDD);
inex = mpfr_set_si (z, LONG_MIN, GMP_RNDN);
MPFR_ASSERTN (inex == 0);
mpfr_nextabove (z);
mpfr_pow (z, x, z, GMP_RNDU);
mpfr_pow_si (x, x, LONG_MIN, GMP_RNDN); /* 1.5^LONG_MIN */
if (mpfr_cmp (x, y) < 0 || mpfr_cmp (x, z) > 0)
{
printf ("Error in pow_si_long_min\n");
exit (1);
}
mpfr_clears (x, y, z, (void *) 0);
}
static int
pm2 (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd_mode)
{
return mpfr_pow_si (y, x, -2, rnd_mode);
}
static void
special ()
{
mpfr_t x, y, z, t;
mpfr_init2 (x, 53);
mpfr_init2 (y, 53);
mpfr_init2 (z, 53);
mpfr_init2 (t, 2);
mpfr_set_ui (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, -2, GMP_RNDN);
if (mpfr_cmp_ui_2exp (x, 1, -2))
{
printf ("Error in pow_si(x,x,-2) for x=2\n");
exit (1);
}
mpfr_set_ui (x, 2, GMP_RNDN);
mpfr_set_si (y, -2, GMP_RNDN);
test_pow (x, x, y, GMP_RNDN);
if (mpfr_cmp_ui_2exp (x, 1, -2))
{
printf ("Error in pow(x,x,y) for x=2, y=-2\n");
exit (1);
}
mpfr_set_prec (x, 2);
mpfr_set_str_binary (x, "1.0e-1");
mpfr_set_prec (y, 53);
mpfr_set_str_binary (y, "0.11010110011100101010110011001010100111000001000101110E-1");
mpfr_set_prec (z, 2);
test_pow (z, x, y, GMP_RNDZ);
mpfr_set_str_binary (x, "1.0e-1");
if (mpfr_cmp (x, z))
{
printf ("Error in mpfr_pow (1)\n");
exit (1);
}
mpfr_set_prec (x, 64);
mpfr_set_prec (y, 64);
mpfr_set_prec (z, 64);
mpfr_set_prec (t, 64);
mpfr_set_str_binary (x, "0.111011000111100000111010000101010100110011010000011");
mpfr_set_str_binary (y, "0.111110010100110000011101100011010111000010000100101");
mpfr_set_str_binary (t, "0.1110110011110110001000110100100001001111010011111000010000011001");
test_pow (z, x, y, GMP_RNDN);
if (mpfr_cmp (z, t))
{
printf ("Error in mpfr_pow for prec=64, rnd=GMP_RNDN\n");
exit (1);
}
mpfr_set_prec (x, 53);
mpfr_set_prec (y, 53);
mpfr_set_prec (z, 53);
mpfr_set_str (x, "5.68824667828621954868e-01", 10, GMP_RNDN);
mpfr_set_str (y, "9.03327850535952658895e-01", 10, GMP_RNDN);
test_pow (z, x, y, GMP_RNDZ);
if (mpfr_cmp_str1 (z, "0.60071044650456473235"))
{
printf ("Error in mpfr_pow for prec=53, rnd=GMP_RNDZ\n");
exit (1);
}
mpfr_set_prec (t, 2);
mpfr_set_prec (x, 30);
mpfr_set_prec (y, 30);
mpfr_set_prec (z, 30);
mpfr_set_str (x, "1.00000000001010111110001111011e1", 2, GMP_RNDN);
mpfr_set_str (t, "-0.5", 10, GMP_RNDN);
test_pow (z, x, t, GMP_RNDN);
mpfr_set_str (y, "1.01101001111010101110000101111e-1", 2, GMP_RNDN);
if (mpfr_cmp (z, y))
{
printf ("Error in mpfr_pow for prec=30, rnd=GMP_RNDN\n");
exit (1);
}
mpfr_set_prec (x, 21);
mpfr_set_prec (y, 21);
mpfr_set_prec (z, 21);
mpfr_set_str (x, "1.11111100100001100101", 2, GMP_RNDN);
test_pow (z, x, t, GMP_RNDZ);
mpfr_set_str (y, "1.01101011010001100000e-1", 2, GMP_RNDN);
if (mpfr_cmp (z, y))
{
printf ("Error in mpfr_pow for prec=21, rnd=GMP_RNDZ\n");
printf ("Expected ");
mpfr_out_str (stdout, 2, 0, y, GMP_RNDN);
printf ("\nGot ");
mpfr_out_str (stdout, 2, 0, z, GMP_RNDN);
printf ("\n");
exit (1);
}
/* From http://www.terra.es/personal9/ismaeljc/hall.htm */
mpfr_set_prec (x, 113);
mpfr_set_prec (y, 2);
mpfr_set_prec (z, 169);
mpfr_set_str1 (x, "6078673043126084065007902175846955");
mpfr_set_ui_2exp (y, 3, -1, GMP_RNDN);
test_pow (z, x, y, GMP_RNDZ);
if (mpfr_cmp_str1 (z, "473928882491000966028828671876527456070714790264144"))
{
printf ("Error in mpfr_pow for 6078673043126084065007902175846955");
printf ("^(3/2), GMP_RNDZ\nExpected ");
printf ("4.73928882491000966028828671876527456070714790264144e50");
printf ("\nGot ");
mpfr_out_str (stdout, 10, 0, z, GMP_RNDN);
printf ("\n");
exit (1);
}
test_pow (z, x, y, GMP_RNDU);
if (mpfr_cmp_str1 (z, "473928882491000966028828671876527456070714790264145"))
{
printf ("Error in mpfr_pow for 6078673043126084065007902175846955");
printf ("^(3/2), GMP_RNDU\nExpected ");
printf ("4.73928882491000966028828671876527456070714790264145e50");
printf ("\nGot ");
mpfr_out_str (stdout, 10, 0, z, GMP_RNDN);
printf ("\n");
exit (1);
}
mpfr_set_inf (x, 1);
mpfr_set_prec (y, 2);
mpfr_set_str_binary (y, "1E10");
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_set_inf (x, -1);
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_set_prec (y, 10);
mpfr_set_str_binary (y, "1.000000001E9");
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_NEG(z));
mpfr_set_str_binary (y, "1.000000001E8");
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_set_inf (x, -1);
mpfr_set_prec (y, 2 * mp_bits_per_limb);
mpfr_set_ui (y, 1, GMP_RNDN);
mpfr_mul_2exp (y, y, mp_bits_per_limb - 1, GMP_RNDN);
/* y = 2^(mp_bits_per_limb - 1) */
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_nextabove (y);
test_pow (z, x, y, GMP_RNDN);
/* y = 2^(mp_bits_per_limb - 1) + epsilon */
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_nextbelow (y);
mpfr_div_2exp (y, y, 1, GMP_RNDN);
mpfr_nextabove (y);
test_pow (z, x, y, GMP_RNDN);
/* y = 2^(mp_bits_per_limb - 2) + epsilon */
MPFR_ASSERTN(mpfr_inf_p (z) && MPFR_IS_POS(z));
mpfr_set_si (x, -1, GMP_RNDN);
mpfr_set_prec (y, 2);
mpfr_set_str_binary (y, "1E10");
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (z, 1) == 0);
/* Check (-0)^(17.0001) */
mpfr_set_prec (x, 6);
mpfr_set_prec (y, 640);
MPFR_SET_ZERO (x);
MPFR_SET_NEG (x);
mpfr_set_ui (y, 17, GMP_RNDN);
mpfr_nextabove (y);
test_pow (z, x, y, GMP_RNDN);
MPFR_ASSERTN (MPFR_IS_ZERO (z) && MPFR_IS_POS (z));
mpfr_clear (x);
mpfr_clear (y);
mpfr_clear (z);
mpfr_clear (t);
}
MpfrFloat MpfrFloat::pow(const MpfrFloat& value, long exponent)
{
MpfrFloat retval(MpfrFloat::kNoInitialization);
mpfr_pow_si(retval.mData->mFloat, value.mData->mFloat, exponent, GMP_RNDN);
return retval;
}
static void
check_pow_si (void)
{
mpfr_t x;
mpfr_init (x);
mpfr_set_nan (x);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_nan_p (x));
mpfr_set_inf (x, 1);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS(x));
mpfr_set_inf (x, -1);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_NEG(x));
mpfr_set_inf (x, -1);
mpfr_pow_si (x, x, -2, GMP_RNDN);
MPFR_ASSERTN(mpfr_cmp_ui (x, 0) == 0 && MPFR_IS_POS(x));
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
mpfr_pow_si (x, x, -1, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) < 0);
mpfr_set_ui (x, 0, GMP_RNDN);
mpfr_neg (x, x, GMP_RNDN);
mpfr_pow_si (x, x, -2, GMP_RNDN);
MPFR_ASSERTN(mpfr_inf_p (x) && mpfr_sgn (x) > 0);
mpfr_set_si (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, LONG_MAX, GMP_RNDN); /* 2^LONG_MAX */
if (LONG_MAX > mpfr_get_emax () - 1) /* LONG_MAX + 1 > emax */
{
MPFR_ASSERTN (mpfr_inf_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 1, LONG_MAX));
}
mpfr_set_si (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, LONG_MIN, GMP_RNDN); /* 2^LONG_MIN */
if (LONG_MIN + 1 < mpfr_get_emin ())
{
MPFR_ASSERTN (mpfr_zero_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 1, LONG_MIN));
}
mpfr_set_si (x, 2, GMP_RNDN);
mpfr_pow_si (x, x, LONG_MIN + 1, GMP_RNDN); /* 2^(LONG_MIN+1) */
if (mpfr_nan_p (x))
{
printf ("Error in pow_si(2, LONG_MIN+1): got NaN\n");
exit (1);
}
if (LONG_MIN + 2 < mpfr_get_emin ())
{
MPFR_ASSERTN (mpfr_zero_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 1, LONG_MIN + 1));
}
mpfr_set_si_2exp (x, 1, -1, GMP_RNDN); /* 0.5 */
mpfr_pow_si (x, x, LONG_MIN, GMP_RNDN); /* 2^(-LONG_MIN) */
if (LONG_MIN < 1 - mpfr_get_emax ()) /* 1 - LONG_MIN > emax */
{
MPFR_ASSERTN (mpfr_inf_p (x));
}
else
{
MPFR_ASSERTN (mpfr_cmp_si_2exp (x, 2, - (LONG_MIN + 1)));
}
mpfr_clear (x);
}
static PyObject *
GMPy_Real_Pow(PyObject *base, PyObject *exp, PyObject *mod, CTXT_Object *context)
{
MPFR_Object *tempb = NULL, *tempe = NULL, *result = NULL;
MPZ_Object *tempz = NULL;
MPC_Object *mpc_result = NULL;
if (mod != Py_None) {
TYPE_ERROR("pow() 3rd argument not allowed unless all arguments are integers");
return NULL;
}
CHECK_CONTEXT(context);
result = GMPy_MPFR_New(0, context);
tempb = GMPy_MPFR_From_Real(base, 1, context);
if (!result || !tempb) {
goto err;
}
mpfr_clear_flags();
if (PyIntOrLong_Check(exp)) {
int error;
long temp_exp = GMPy_Integer_AsLongAndError(exp, &error);
if (!error) {
result->rc = mpfr_pow_si(result->f, tempb->f, temp_exp, GET_MPFR_ROUND(context));
}
else {
mpz_t tempzz;
mpz_inoc(tempzz);
mpz_set_PyIntOrLong(tempzz, exp);
result->rc = mpfr_pow_z(result->f, tempb->f, tempzz, GET_MPFR_ROUND(context));
mpz_cloc(tempzz);
}
}
else if (IS_INTEGER(exp)) {
if (!(tempz = GMPy_MPZ_From_Integer(exp, context))) {
goto err;
}
result->rc = mpfr_pow_z(result->f, tempb->f, tempz->z, GET_MPFR_ROUND(context));
}
else {
if (!(tempe = GMPy_MPFR_From_Real(exp, 1, context))) {
goto err;
}
result->rc = mpfr_pow(result->f, tempb->f, tempe->f, GET_MPFR_ROUND(context));
}
/* If the result is NaN, check if a complex result works. */
if (result && mpfr_nanflag_p() && context->ctx.allow_complex) {
mpc_result = (MPC_Object*)GMPy_Complex_Pow(base, exp, Py_None, context);
if (!mpc_result || MPC_IS_NAN_P(mpc_result)) {
Py_XDECREF((PyObject*)mpc_result);
context->ctx.invalid = 1;
GMPY_INVALID("pow() invalid operation");
goto err;
}
/* return a valid complex result */
Py_XDECREF((PyObject*)tempe);
Py_XDECREF((PyObject*)tempz);
Py_XDECREF((PyObject*)tempb);
Py_XDECREF((PyObject*)result);
return (PyObject*)mpc_result;
}
GMPY_MPFR_CLEANUP(result, context, "pow()");
Py_XDECREF((PyObject*)tempz);
Py_XDECREF((PyObject*)tempe);
Py_XDECREF((PyObject*)tempb);
return (PyObject*)result;
err:
Py_XDECREF((PyObject*)result);
Py_XDECREF((PyObject*)tempz);
Py_XDECREF((PyObject*)tempe);
Py_XDECREF((PyObject*)tempb);
return NULL;
}
void power(ElementType &result, const ElementType& a, int n) const
{
mpfr_pow_si(&result, &a, n, GMP_RNDN);
}
/* Compare the result (z1,inex1) of mpfr_pow with all flags cleared
with those of mpfr_pow with all flags set and of the other power
functions. Arguments x and y are the input values; sx and sy are
their string representations (sx may be null); rnd contains the
rounding mode; s is a string containing the function that called
test_others. */
static void
test_others (const void *sx, const char *sy, mpfr_rnd_t rnd,
mpfr_srcptr x, mpfr_srcptr y, mpfr_srcptr z1,
int inex1, unsigned int flags, const char *s)
{
mpfr_t z2;
int inex2;
int spx = sx != NULL;
if (!spx)
sx = x;
mpfr_init2 (z2, mpfr_get_prec (z1));
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_pow (z2, x, y, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_pow, flags set");
/* If y is an integer that fits in an unsigned long and is not -0,
we can test mpfr_pow_ui. */
if (MPFR_IS_POS (y) && mpfr_integer_p (y) &&
mpfr_fits_ulong_p (y, MPFR_RNDN))
{
unsigned long yy = mpfr_get_ui (y, MPFR_RNDN);
mpfr_clear_flags ();
inex2 = mpfr_pow_ui (z2, x, yy, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_pow_ui, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_pow_ui (z2, x, yy, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_pow_ui, flags set");
/* If x is an integer that fits in an unsigned long and is not -0,
we can also test mpfr_ui_pow_ui. */
if (MPFR_IS_POS (x) && mpfr_integer_p (x) &&
mpfr_fits_ulong_p (x, MPFR_RNDN))
{
unsigned long xx = mpfr_get_ui (x, MPFR_RNDN);
mpfr_clear_flags ();
inex2 = mpfr_ui_pow_ui (z2, xx, yy, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_ui_pow_ui, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_ui_pow_ui (z2, xx, yy, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_ui_pow_ui, flags set");
}
}
/* If y is an integer but not -0 and not huge, we can test mpfr_pow_z,
and possibly mpfr_pow_si (and possibly mpfr_ui_div). */
if (MPFR_IS_ZERO (y) ? MPFR_IS_POS (y) :
(mpfr_integer_p (y) && MPFR_GET_EXP (y) < 256))
{
mpz_t yyy;
/* If y fits in a long, we can test mpfr_pow_si. */
if (mpfr_fits_slong_p (y, MPFR_RNDN))
{
long yy = mpfr_get_si (y, MPFR_RNDN);
mpfr_clear_flags ();
inex2 = mpfr_pow_si (z2, x, yy, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_pow_si, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_pow_si (z2, x, yy, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_pow_si, flags set");
/* If y = -1, we can test mpfr_ui_div. */
if (yy == -1)
{
mpfr_clear_flags ();
inex2 = mpfr_ui_div (z2, 1, x, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_ui_div, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_ui_div (z2, 1, x, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_ui_div, flags set");
}
/* If y = 2, we can test mpfr_sqr. */
if (yy == 2)
{
mpfr_clear_flags ();
inex2 = mpfr_sqr (z2, x, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_sqr, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_sqr (z2, x, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_sqr, flags set");
}
}
/* Test mpfr_pow_z. */
mpz_init (yyy);
mpfr_get_z (yyy, y, MPFR_RNDN);
mpfr_clear_flags ();
inex2 = mpfr_pow_z (z2, x, yyy, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_pow_z, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_pow_z (z2, x, yyy, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_pow_z, flags set");
mpz_clear (yyy);
}
/* If y = 0.5, we can test mpfr_sqrt, except if x is -0 or -Inf (because
the rule for mpfr_pow on these special values is different). */
if (MPFR_IS_PURE_FP (y) && mpfr_cmp_str1 (y, "0.5") == 0 &&
! ((MPFR_IS_ZERO (x) || MPFR_IS_INF (x)) && MPFR_IS_NEG (x)))
{
mpfr_clear_flags ();
inex2 = mpfr_sqrt (z2, x, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_sqrt, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_sqrt (z2, x, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_sqrt, flags set");
}
#if MPFR_VERSION >= MPFR_VERSION_NUM(2,4,0)
/* If y = -0.5, we can test mpfr_rec_sqrt, except if x = -Inf
(because the rule for mpfr_pow on -Inf is different). */
if (MPFR_IS_PURE_FP (y) && mpfr_cmp_str1 (y, "-0.5") == 0 &&
! (MPFR_IS_INF (x) && MPFR_IS_NEG (x)))
{
mpfr_clear_flags ();
inex2 = mpfr_rec_sqrt (z2, x, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_rec_sqrt, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_rec_sqrt (z2, x, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_rec_sqrt, flags set");
}
#endif
/* If x is an integer that fits in an unsigned long and is not -0,
we can test mpfr_ui_pow. */
if (MPFR_IS_POS (x) && mpfr_integer_p (x) &&
mpfr_fits_ulong_p (x, MPFR_RNDN))
{
unsigned long xx = mpfr_get_ui (x, MPFR_RNDN);
mpfr_clear_flags ();
inex2 = mpfr_ui_pow (z2, xx, y, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_ui_pow, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_ui_pow (z2, xx, y, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_ui_pow, flags set");
/* If x = 2, we can test mpfr_exp2. */
if (xx == 2)
{
mpfr_clear_flags ();
inex2 = mpfr_exp2 (z2, y, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_exp2, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_exp2 (z2, y, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_exp2, flags set");
}
/* If x = 10, we can test mpfr_exp10. */
if (xx == 10)
{
mpfr_clear_flags ();
inex2 = mpfr_exp10 (z2, y, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, flags,
s, "mpfr_exp10, flags cleared");
__gmpfr_flags = MPFR_FLAGS_ALL;
inex2 = mpfr_exp10 (z2, y, rnd);
cmpres (spx, sx, sy, rnd, z1, inex1, z2, inex2, MPFR_FLAGS_ALL,
s, "mpfr_exp10, flags set");
}
}
mpfr_clear (z2);
}
/* The computation of z = pow(x,y) is done by
z = exp(y * log(x)) = x^y */
int
mpfr_pow (mpfr_ptr z, mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd_mode)
{
int inexact = 0;
if (MPFR_IS_NAN(x) || MPFR_IS_NAN(y))
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
if (MPFR_IS_INF(y))
{
mpfr_t one;
int cmp;
if (MPFR_SIGN(y) > 0)
{
if (MPFR_IS_INF(x))
{
MPFR_CLEAR_FLAGS(z);
if (MPFR_SIGN(x) > 0)
MPFR_SET_INF(z);
else
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
MPFR_CLEAR_FLAGS(z);
if (MPFR_IS_ZERO(x))
{
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
mpfr_init2(one, BITS_PER_MP_LIMB);
mpfr_set_ui(one, 1, GMP_RNDN);
cmp = mpfr_cmp_abs(x, one);
mpfr_clear(one);
if (cmp > 0)
{
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else if (cmp < 0)
{
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
}
else
{
if (MPFR_IS_INF(x))
{
MPFR_CLEAR_FLAGS(z);
if (MPFR_SIGN(x) > 0)
MPFR_SET_ZERO(z);
else
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
if (MPFR_IS_ZERO(x))
{
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
mpfr_init2(one, BITS_PER_MP_LIMB);
mpfr_set_ui(one, 1, GMP_RNDN);
cmp = mpfr_cmp_abs(x, one);
mpfr_clear(one);
MPFR_CLEAR_FLAGS(z);
if (cmp > 0)
{
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else if (cmp < 0)
{
MPFR_SET_INF(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
}
}
if (MPFR_IS_ZERO(y))
{
return mpfr_set_ui (z, 1, GMP_RNDN);
}
if (mpfr_isinteger (y))
{
mpz_t zi;
long int zii;
int exptol;
mpz_init(zi);
exptol = mpfr_get_z_exp (zi, y);
if (exptol>0)
mpz_mul_2exp(zi, zi, exptol);
else
mpz_tdiv_q_2exp(zi, zi, (unsigned long int) (-exptol));
zii=mpz_get_ui(zi);
mpz_clear(zi);
return mpfr_pow_si (z, x, zii, rnd_mode);
}
if (MPFR_IS_INF(x))
{
if (MPFR_SIGN(x) > 0)
{
MPFR_CLEAR_FLAGS(z);
if (MPFR_SIGN(y) > 0)
MPFR_SET_INF(z);
else
MPFR_SET_ZERO(z);
MPFR_SET_POS(z);
MPFR_RET(0);
}
else
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
}
if (MPFR_IS_ZERO(x))
{
MPFR_CLEAR_FLAGS(z);
MPFR_SET_ZERO(z);
MPFR_SET_SAME_SIGN(z, x);
MPFR_RET(0);
}
if (MPFR_SIGN(x) < 0)
{
MPFR_SET_NAN(z);
MPFR_RET_NAN;
}
MPFR_CLEAR_FLAGS(z);
/* General case */
{
/* Declaration of the intermediary variable */
mpfr_t t, te, ti;
int loop = 0, ok;
/* Declaration of the size variable */
mp_prec_t Nx = MPFR_PREC(x); /* Precision of input variable */
mp_prec_t Ny = MPFR_PREC(y); /* Precision of input variable */
mp_prec_t Nt; /* Precision of the intermediary variable */
long int err; /* Precision of error */
/* compute the precision of intermediary variable */
Nt=MAX(Nx,Ny);
/* the optimal number of bits : see algorithms.ps */
Nt=Nt+5+_mpfr_ceil_log2(Nt);
/* initialise of intermediary variable */
mpfr_init(t);
mpfr_init(ti);
mpfr_init(te);
do
{
loop ++;
/* reactualisation of the precision */
mpfr_set_prec (t, Nt);
mpfr_set_prec (ti, Nt);
mpfr_set_prec (te, Nt);
/* compute exp(y*ln(x)) */
mpfr_log (ti, x, GMP_RNDU); /* ln(n) */
mpfr_mul (te, y, ti, GMP_RNDU); /* y*ln(n) */
mpfr_exp (t, te, GMP_RNDN); /* exp(x*ln(n))*/
/* estimation of the error -- see pow function in algorithms.ps*/
err = Nt - (MPFR_EXP(te) + 3);
/* actualisation of the precision */
Nt += 10;
ok = mpfr_can_round (t, err, GMP_RNDN, rnd_mode, Ny);
/* check exact power */
if (ok == 0 && loop == 1)
ok = mpfr_pow_is_exact (x, y);
}
while (err < 0 || ok == 0);
inexact = mpfr_set (z, t, rnd_mode);
mpfr_clear (t);
mpfr_clear (ti);
mpfr_clear (te);
}
return inexact;
}
SeedValue seed_mpfr_pow (SeedContext ctx,
SeedObject function,
SeedObject this_object,
gsize argument_count,
const SeedValue args[],
SeedException * exception)
{
mpfr_rnd_t rnd;
mpfr_ptr rop, op1, op2;
gint ret;
glong iop;
gulong uiop1, uiop2;
seed_mpfr_t argt1, argt2;
/* only want 1 double argument. alternatively, could accept 2,
add those, and set from the result*/
CHECK_ARG_COUNT("mpfr.pow", 3);
rop = seed_object_get_private(this_object);
rnd = seed_value_to_mpfr_rnd_t(ctx, args[2], exception);
argt1 = seed_mpfr_arg_type(ctx, args[0], exception);
argt2 = seed_mpfr_arg_type(ctx, args[1], exception);
if ( (argt1 & argt2) == SEED_MPFR_MPFR )
{
/* both mpfr_t */
op1 = seed_object_get_private(args[0]);
op2 = seed_object_get_private(args[1]);
ret = mpfr_pow(rop, op1, op2, rnd);
}
else if ( (argt1 | argt2) == (SEED_MPFR_MPFR | SEED_MPFR_DOUBLE) )
{
/* a double and an mpfr_t. Figure out the order */
/* FIXME: is this switching ui and si bad? si_pow doesn't exist,
and it's all from double anyway */
if ( argt1 == SEED_MPFR_MPFR )
{
op1 = seed_object_get_private(args[0]);
iop = seed_value_to_long(ctx, args[1], exception);
ret = mpfr_pow_si(rop, op1, iop, rnd);
}
else
{
uiop1 = seed_value_to_ulong(ctx, args[0], exception);
op2 = seed_object_get_private(args[1]);
ret = mpfr_ui_pow(rop, uiop1, op2, rnd);
}
}
else if ( (argt1 & argt2) == SEED_MPFR_DOUBLE )
{
/* pretend both ui */
uiop1 = seed_value_to_ulong(ctx, args[0], exception);
uiop2 = seed_value_to_ulong(ctx, args[1], exception);
ret = mpfr_ui_pow_ui(rop, uiop1, uiop2, rnd);
}
else
{
TYPE_EXCEPTION("mpfr.pow", "int or unsigned int and mpfr_t");
}
return seed_value_from_int(ctx, ret, exception);
}
