static PyObject *
math_fmod(PyObject *self, PyObject *args)
{
PyObject *ox, *oy;
double r, x, y;
if (! PyArg_UnpackTuple(args, "fmod", 2, 2, &ox, &oy))
return NULL;
x = PyFloat_AsDouble(ox);
y = PyFloat_AsDouble(oy);
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
return NULL;
/* fmod(x, +/-Inf) returns x for finite x. */
if (Py_IS_INFINITY(y) && Py_IS_FINITE(x))
return PyFloat_FromDouble(x);
errno = 0;
PyFPE_START_PROTECT("in math_fmod", return 0);
r = fmod(x, y);
PyFPE_END_PROTECT(r);
if (Py_IS_NAN(r)) {
if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
errno = EDOM;
else
errno = 0;
}
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(r);
}
static PyObject *
complex_pow(PyComplexObject *v, PyObject *w, PyComplexObject *z)
{
Py_complex p;
Py_complex exponent;
long int_exponent;
if ((PyObject *)z!=Py_None) {
PyErr_SetString(PyExc_ValueError, "complex modulo");
return NULL;
}
PyFPE_START_PROTECT("complex_pow", return 0)
errno = 0;
exponent = ((PyComplexObject*)w)->cval;
int_exponent = (long)exponent.real;
if (exponent.imag == 0. && exponent.real == int_exponent)
p = c_powi(v->cval,int_exponent);
else
p = c_pow(v->cval,exponent);
PyFPE_END_PROTECT(p)
Py_ADJUST_ERANGE2(p.real, p.imag);
if (errno == EDOM) {
PyErr_SetString(PyExc_ZeroDivisionError,
"0.0 to a negative or complex power");
return NULL;
}
else if (errno == ERANGE) {
PyErr_SetString(PyExc_OverflowError,
"complex exponentiation");
return NULL;
}
return PyComplex_FromCComplex(p);
}
static PyObject *
math_2(PyObject *args, double (*func) (double, double), char *funcname)
{
PyObject *ox, *oy;
double x, y, r;
if (! PyArg_UnpackTuple(args, funcname, 2, 2, &ox, &oy))
return NULL;
x = PyFloat_AsDouble(ox);
y = PyFloat_AsDouble(oy);
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
return NULL;
errno = 0;
PyFPE_START_PROTECT("in math_2", return 0);
r = (*func)(x, y);
PyFPE_END_PROTECT(r);
if (Py_IS_NAN(r)) {
if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
errno = EDOM;
else
errno = 0;
}
else if (Py_IS_INFINITY(r)) {
if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
errno = ERANGE;
else
errno = 0;
}
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(r);
}
static PyObject *
math_1_to_whatever(PyObject *arg, double (*func) (double),
PyObject *(*from_double_func) (double),
int can_overflow)
{
double x, r;
x = PyFloat_AsDouble(arg);
if (x == -1.0 && PyErr_Occurred())
return NULL;
errno = 0;
PyFPE_START_PROTECT("in math_1", return 0);
r = (*func)(x);
PyFPE_END_PROTECT(r);
if (Py_IS_NAN(r) && !Py_IS_NAN(x)) {
PyErr_SetString(PyExc_ValueError,
"math domain error"); /* invalid arg */
return NULL;
}
if (Py_IS_INFINITY(r) && Py_IS_FINITE(x)) {
if (can_overflow)
PyErr_SetString(PyExc_OverflowError,
"math range error"); /* overflow */
else
PyErr_SetString(PyExc_ValueError,
"math domain error"); /* singularity */
return NULL;
}
if (Py_IS_FINITE(r) && errno && is_error(r))
/* this branch unnecessary on most platforms */
return NULL;
return (*from_double_func)(r);
}
static bool FLOAT_ADD_INCREMENTAL(PyObject **operand1, PyObject *operand2) {
assert(PyFloat_CheckExact(*operand1));
assert(PyFloat_CheckExact(operand2));
PyFPE_START_PROTECT("add", return false);
PyFloat_AS_DOUBLE(*operand1) += PyFloat_AS_DOUBLE(operand2);
PyFPE_END_PROTECT(*operand1);
return true;
}
static PyObject *
math_1(PyObject *args, Py_complex (*func)(Py_complex))
{
Py_complex x;
if (!PyArg_ParseTuple(args, "D", &x))
return NULL;
errno = 0;
PyFPE_START_PROTECT("complex function", return 0)
x = (*func)(x);
PyFPE_END_PROTECT(x)
Py_ADJUST_ERANGE2(x.real, x.imag);
if (errno != 0)
return math_error();
else
return PyComplex_FromCComplex(x);
}
static PyObject *
math_1(PyObject *args, double (*func) (double), char *argsfmt)
{
double x;
if (! PyArg_ParseTuple(args, argsfmt, &x))
return NULL;
errno = 0;
PyFPE_START_PROTECT("in math_1", return 0)
x = (*func)(x);
PyFPE_END_PROTECT(x)
Py_SET_ERANGE_IF_OVERFLOW(x);
if (errno && is_error(x))
return NULL;
else
return PyFloat_FromDouble(x);
}
static PyObject *
math_2(PyObject *args, double (*func) (double, double), char *argsfmt)
{
double x, y;
if (! PyArg_ParseTuple(args, argsfmt, &x, &y))
return NULL;
errno = 0;
PyFPE_START_PROTECT("in math_2", return 0)
x = (*func)(x, y);
PyFPE_END_PROTECT(x)
Py_SET_ERRNO_ON_MATH_ERROR(x);
if (errno && is_error(x))
return NULL;
else
return PyFloat_FromDouble(x);
}
static PyObject *
math_ldexp(PyObject *self, PyObject *args)
{
double x;
int exp;
if (! PyArg_ParseTuple(args, "di:ldexp", &x, &exp))
return NULL;
errno = 0;
PyFPE_START_PROTECT("ldexp", return 0)
x = ldexp(x, exp);
PyFPE_END_PROTECT(x)
Py_SET_ERANGE_IF_OVERFLOW(x);
if (errno && is_error(x))
return NULL;
else
return PyFloat_FromDouble(x);
}
static PyObject *
math_frexp(PyObject *self, PyObject *arg)
{
int i;
double x = PyFloat_AsDouble(arg);
if (x == -1.0 && PyErr_Occurred())
return NULL;
/* deal with special cases directly, to sidestep platform
differences */
if (Py_IS_NAN(x) || Py_IS_INFINITY(x) || !x) {
i = 0;
}
else {
PyFPE_START_PROTECT("in math_frexp", return 0);
x = frexp(x, &i);
PyFPE_END_PROTECT(x);
}
return Py_BuildValue("(di)", x, i);
}
static PyObject *
math_modf(PyObject *self, PyObject *arg)
{
double y, x = PyFloat_AsDouble(arg);
if (x == -1.0 && PyErr_Occurred())
return NULL;
/* some platforms don't do the right thing for NaNs and
infinities, so we take care of special cases directly. */
if (!Py_IS_FINITE(x)) {
if (Py_IS_INFINITY(x))
return Py_BuildValue("(dd)", copysign(0., x), x);
else if (Py_IS_NAN(x))
return Py_BuildValue("(dd)", x, x);
}
errno = 0;
PyFPE_START_PROTECT("in math_modf", return 0);
x = modf(x, &y);
PyFPE_END_PROTECT(x);
return Py_BuildValue("(dd)", x, y);
}
static PyObject *
math_hypot(PyObject *self, PyObject *args)
{
PyObject *ox, *oy;
double r, x, y;
if (! PyArg_UnpackTuple(args, "hypot", 2, 2, &ox, &oy))
return NULL;
x = PyFloat_AsDouble(ox);
y = PyFloat_AsDouble(oy);
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
return NULL;
/* hypot(x, +/-Inf) returns Inf, even if x is a NaN. */
if (Py_IS_INFINITY(x))
return PyFloat_FromDouble(fabs(x));
if (Py_IS_INFINITY(y))
return PyFloat_FromDouble(fabs(y));
errno = 0;
PyFPE_START_PROTECT("in math_hypot", return 0);
r = hypot(x, y);
PyFPE_END_PROTECT(r);
if (Py_IS_NAN(r)) {
if (!Py_IS_NAN(x) && !Py_IS_NAN(y))
errno = EDOM;
else
errno = 0;
}
else if (Py_IS_INFINITY(r)) {
if (Py_IS_FINITE(x) && Py_IS_FINITE(y))
errno = ERANGE;
else
errno = 0;
}
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(r);
}
static PyObject *bip_sum(term_t t) {
PyObject *seq;
PyObject *result = NULL;
PyObject *temp, *item, *iter;
if (!PL_get_arg(1, t, t))
return NULL;
seq = term_to_python(t, true);
iter = PyObject_GetIter(seq);
if (iter == NULL)
return NULL;
if (result == NULL) {
#if PY_MAJOR_VERSION < 3
result = PyInt_FromLong(0);
#else
result = PyLong_FromLong(0);
#endif
if (result == NULL) {
Py_DECREF(iter);
return NULL;
}
} else {
#if PY_MAJOR_VERSION < 3
/* reject string values for 'start' parameter */
if (PyObject_TypeCheck(result, &PyBaseString_Type)) {
PyErr_SetString(PyExc_TypeError,
"sum() can't sum strings [use ''.join(seq) instead]");
Py_DECREF(iter);
return NULL;
}
Py_INCREF(result);
#endif
}
#ifndef SLOW_SUM
/* Fast addition by keeping temporary sums in C instead of new Python objects.
Assumes all inputs are the same type. If the assumption fails, default
to the more general routine.
*/
#if PY_MAJOR_VERSION < 3
if (PyInt_CheckExact(result)) {
long i_result = PyInt_AS_LONG(result);
#else
if (PyLong_CheckExact(result)) {
long i_result = PyLong_AS_LONG(result);
#endif
Py_DECREF(result);
result = NULL;
while (result == NULL) {
item = PyIter_Next(iter);
if (item == NULL) {
Py_DECREF(iter);
if (PyErr_Occurred())
return NULL;
#if PY_MAJOR_VERSION < 3
return PyInt_FromLong(i_result);
#else
return PyLong_FromLong(i_result);
#endif
}
#if PY_MAJOR_VERSION < 3
if (PyInt_CheckExact(item)) {
long b = PyInt_AS_LONG(item);
#else
if (PyLong_CheckExact(item)) {
long b = PyLong_AS_LONG(item);
#endif
long x = i_result + b;
if ((x ^ i_result) >= 0 || (x ^ b) >= 0) {
i_result = x;
Py_DECREF(item);
continue;
}
}
/* Either overflowed or is not an int. Restore real objects and process normally
*/
#if PY_MAJOR_VERSION < 3
result = PyInt_FromLong(i_result);
#else
result = PyLong_FromLong(i_result);
#endif
temp = PyNumber_Add(result, item);
Py_DECREF(result);
Py_DECREF(item);
result = temp;
if (result == NULL) {
Py_DECREF(iter);
return NULL;
}
}
}
if (PyFloat_CheckExact(result)) {
double f_result = PyFloat_AS_DOUBLE(result);
Py_DECREF(result);
result = NULL;
while (result == NULL) {
item = PyIter_Next(iter);
if (item == NULL) {
Py_DECREF(iter);
if (PyErr_Occurred())
return NULL;
return PyFloat_FromDouble(f_result);
}
if (PyFloat_CheckExact(item)) {
PyFPE_START_PROTECT("add", Py_DECREF(item); Py_DECREF(iter); return 0)
f_result += PyFloat_AS_DOUBLE(item);
PyFPE_END_PROTECT(f_result) Py_DECREF(item);
continue;
}
#if PY_MAJOR_VERSION < 3
if (PyInt_CheckExact(item)) {
PyFPE_START_PROTECT("add", Py_DECREF(item); Py_DECREF(iter); return 0)
f_result += (double)PyInt_AS_LONG(item);
PyFPE_END_PROTECT(f_result) Py_DECREF(item);
continue;
}
#else
if (PyLong_CheckExact(item)) {
PyFPE_START_PROTECT("add", Py_DECREF(item); Py_DECREF(iter); return 0)
f_result += PyLong_AsDouble(item);
PyFPE_END_PROTECT(f_result) Py_DECREF(item);
continue;
}
#endif
result = PyFloat_FromDouble(f_result);
temp = PyNumber_Add(result, item);
Py_DECREF(result);
Py_DECREF(item);
result = temp;
if (result == NULL) {
Py_DECREF(iter);
return NULL;
}
}
#endif
}
for (;;) {
item = PyIter_Next(iter);
if (item == NULL) {
/* error, or end-of-sequence */
if (PyErr_Occurred()) {
Py_DECREF(result);
result = NULL;
}
break;
}
/* It's tempting to use PyNumber_InPlaceAdd instead of
PyNumber_Add here, to avoid quadratic running time
when doing 'sum(list_of_lists, [])'. However, this
would produce a change in behaviour: a snippet like
empty = []
sum([[x] for x in range(10)], empty)
would change the value of empty. */
temp = PyNumber_Add(result, item);
Py_DECREF(result);
Py_DECREF(item);
result = temp;
if (result == NULL)
break;
}
Py_DECREF(iter);
return result;
}
//@}
static long get_int(term_t arg, bool eval) {
long low;
if (!PL_get_long(arg, &low)) {
PyObject *low = term_to_python(arg, eval);
if (PyLong_Check(low)) {
return PyLong_AsLong(low);
#if PY_MAJOR_VERSION < 3
} else if (PyInt_Check(low)) {
return PyInt_AsLong(low);
#endif
} else {
return 0;
}
}
return low;
}
/* Return number of items in range/xrange (lo, hi, step). step > 0
* required. Return a value < 0 if & only if the true value is too
* large to fit in a signed long.
*/
static long get_len_of_range(long lo, long hi, long step) {
/* -------------------------------------------------------------
If lo >= hi, the range is empty.
Else if n values are in the range, the last one is
lo + (n-1)*step, which must be <= hi-1. Rearranging,
n <= (hi - lo - 1)/step + 1, so taking the floor of the RHS gives
the proper value. Since lo < hi in this case, hi-lo-1 >= 0, so
the RHS is non-negative and so truncation is the same as the
floor. Letting M be the largest positive long, the worst case
for the RHS numerator is hi=M, lo=-M-1, and then
hi-lo-1 = M-(-M-1)-1 = 2*M. Therefore unsigned long has enough
precision to compute the RHS exactly.
---------------------------------------------------------------*/
long n = 0;
if (lo < hi) {
unsigned long uhi = (unsigned long)hi;
unsigned long ulo = (unsigned long)lo;
unsigned long diff = uhi - ulo - 1;
n = (long)(diff / (unsigned long)step + 1);
}
return n;
}
static PyObject *
math_pow(PyObject *self, PyObject *args)
{
PyObject *ox, *oy;
double r, x, y;
int odd_y;
if (! PyArg_UnpackTuple(args, "pow", 2, 2, &ox, &oy))
return NULL;
x = PyFloat_AsDouble(ox);
y = PyFloat_AsDouble(oy);
if ((x == -1.0 || y == -1.0) && PyErr_Occurred())
return NULL;
/* deal directly with IEEE specials, to cope with problems on various
platforms whose semantics don't exactly match C99 */
r = 0.; /* silence compiler warning */
if (!Py_IS_FINITE(x) || !Py_IS_FINITE(y)) {
errno = 0;
if (Py_IS_NAN(x))
r = y == 0. ? 1. : x; /* NaN**0 = 1 */
else if (Py_IS_NAN(y))
r = x == 1. ? 1. : y; /* 1**NaN = 1 */
else if (Py_IS_INFINITY(x)) {
odd_y = Py_IS_FINITE(y) && fmod(fabs(y), 2.0) == 1.0;
if (y > 0.)
r = odd_y ? x : fabs(x);
else if (y == 0.)
r = 1.;
else /* y < 0. */
r = odd_y ? copysign(0., x) : 0.;
}
else if (Py_IS_INFINITY(y)) {
if (fabs(x) == 1.0)
r = 1.;
else if (y > 0. && fabs(x) > 1.0)
r = y;
else if (y < 0. && fabs(x) < 1.0) {
r = -y; /* result is +inf */
if (x == 0.) /* 0**-inf: divide-by-zero */
errno = EDOM;
}
else
r = 0.;
}
}
else {
/* let libm handle finite**finite */
errno = 0;
PyFPE_START_PROTECT("in math_pow", return 0);
r = pow(x, y);
PyFPE_END_PROTECT(r);
/* a NaN result should arise only from (-ve)**(finite
non-integer); in this case we want to raise ValueError. */
if (!Py_IS_FINITE(r)) {
if (Py_IS_NAN(r)) {
errno = EDOM;
}
/*
an infinite result here arises either from:
(A) (+/-0.)**negative (-> divide-by-zero)
(B) overflow of x**y with x and y finite
*/
else if (Py_IS_INFINITY(r)) {
if (x == 0.)
errno = EDOM;
else
errno = ERANGE;
}
}
}
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(r);
}
static PyObject *
math_ldexp(PyObject *self, PyObject *args)
{
double x, r;
PyObject *oexp;
long exp;
if (! PyArg_ParseTuple(args, "dO:ldexp", &x, &oexp))
return NULL;
if (PyLong_Check(oexp)) {
/* on overflow, replace exponent with either LONG_MAX
or LONG_MIN, depending on the sign. */
exp = PyLong_AsLong(oexp);
if (exp == -1 && PyErr_Occurred()) {
if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
if (Py_SIZE(oexp) < 0) {
exp = LONG_MIN;
}
else {
exp = LONG_MAX;
}
PyErr_Clear();
}
else {
/* propagate any unexpected exception */
return NULL;
}
}
}
else {
PyErr_SetString(PyExc_TypeError,
"Expected an int or long as second argument "
"to ldexp.");
return NULL;
}
if (x == 0. || !Py_IS_FINITE(x)) {
/* NaNs, zeros and infinities are returned unchanged */
r = x;
errno = 0;
} else if (exp > INT_MAX) {
/* overflow */
r = copysign(Py_HUGE_VAL, x);
errno = ERANGE;
} else if (exp < INT_MIN) {
/* underflow to +-0 */
r = copysign(0., x);
errno = 0;
} else {
errno = 0;
PyFPE_START_PROTECT("in math_ldexp", return 0);
r = ldexp(x, (int)exp);
PyFPE_END_PROTECT(r);
if (Py_IS_INFINITY(r))
errno = ERANGE;
}
if (errno && is_error(r))
return NULL;
return PyFloat_FromDouble(r);
}
static PyObject*
math_fsum(PyObject *self, PyObject *seq)
{
PyObject *item, *iter, *sum = NULL;
Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
double x, y, t, ps[NUM_PARTIALS], *p = ps;
double xsave, special_sum = 0.0, inf_sum = 0.0;
volatile double hi, yr, lo;
iter = PyObject_GetIter(seq);
if (iter == NULL)
return NULL;
PyFPE_START_PROTECT("fsum", Py_DECREF(iter); return NULL)
for(;;) { /* for x in iterable */
assert(0 <= n && n <= m);
assert((m == NUM_PARTIALS && p == ps) ||
(m > NUM_PARTIALS && p != NULL));
item = PyIter_Next(iter);
if (item == NULL) {
if (PyErr_Occurred())
goto _fsum_error;
break;
}
x = PyFloat_AsDouble(item);
Py_DECREF(item);
if (PyErr_Occurred())
goto _fsum_error;
xsave = x;
for (i = j = 0; j < n; j++) { /* for y in partials */
y = p[j];
if (fabs(x) < fabs(y)) {
t = x; x = y; y = t;
}
hi = x + y;
yr = hi - x;
lo = y - yr;
if (lo != 0.0)
p[i++] = lo;
x = hi;
}
n = i; /* ps[i:] = [x] */
if (x != 0.0) {
if (! Py_IS_FINITE(x)) {
/* a nonfinite x could arise either as
a result of intermediate overflow, or
as a result of a nan or inf in the
summands */
if (Py_IS_FINITE(xsave)) {
PyErr_SetString(PyExc_OverflowError,
"intermediate overflow in fsum");
goto _fsum_error;
}
if (Py_IS_INFINITY(xsave))
inf_sum += xsave;
special_sum += xsave;
/* reset partials */
n = 0;
}
else if (n >= m && _fsum_realloc(&p, n, ps, &m))
goto _fsum_error;
else
p[n++] = x;
}
}
if (special_sum != 0.0) {
if (Py_IS_NAN(inf_sum))
PyErr_SetString(PyExc_ValueError,
"-inf + inf in fsum");
else
sum = PyFloat_FromDouble(special_sum);
goto _fsum_error;
}
hi = 0.0;
if (n > 0) {
hi = p[--n];
/* sum_exact(ps, hi) from the top, stop when the sum becomes
inexact. */
while (n > 0) {
x = hi;
y = p[--n];
assert(fabs(y) < fabs(x));
hi = x + y;
yr = hi - x;
lo = y - yr;
if (lo != 0.0)
break;
}
/* Make half-even rounding work across multiple partials.
Needed so that sum([1e-16, 1, 1e16]) will round-up the last
digit to two instead of down to zero (the 1e-16 makes the 1
slightly closer to two). With a potential 1 ULP rounding
error fixed-up, math.fsum() can guarantee commutativity. */
if (n > 0 && ((lo < 0.0 && p[n-1] < 0.0) ||
(lo > 0.0 && p[n-1] > 0.0))) {
y = lo * 2.0;
x = hi + y;
yr = x - hi;
if (y == yr)
hi = x;
}
}
sum = PyFloat_FromDouble(hi);
_fsum_error:
PyFPE_END_PROTECT(hi)
Py_DECREF(iter);
if (p != ps)
PyMem_Free(p);
return sum;
}