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/* Math module -- standard C math library functions, pi and e */
/* Here are some comments from Tim Peters, extracted from the
discussion attached to http://bugs.python.org/issue1640. They
describe the general aims of the math module with respect to
special values, IEEE-754 floating-point exceptions, and Python
exceptions.
These are the "spirit of 754" rules:
1. If the mathematical result is a real number, but of magnitude too
large to approximate by a machine float, overflow is signaled and the
result is an infinity (with the appropriate sign).
2. If the mathematical result is a real number, but of magnitude too
small to approximate by a machine float, underflow is signaled and the
result is a zero (with the appropriate sign).
3. At a singularity (a value x such that the limit of f(y) as y
approaches x exists and is an infinity), "divide by zero" is signaled
and the result is an infinity (with the appropriate sign). This is
complicated a little by that the left-side and right-side limits may
not be the same; e.g., 1/x approaches +inf or -inf as x approaches 0
from the positive or negative directions. In that specific case, the
sign of the zero determines the result of 1/0.
4. At a point where a function has no defined result in the extended
reals (i.e., the reals plus an infinity or two), invalid operation is
signaled and a NaN is returned.
And these are what Python has historically /tried/ to do (but not
always successfully, as platform libm behavior varies a lot):
For #1, raise OverflowError.
For #2, return a zero (with the appropriate sign if that happens by
accident ;-)).
For #3 and #4, raise ValueError. It may have made sense to raise
Python's ZeroDivisionError in #3, but historically that's only been
raised for division by zero and mod by zero.
*/
/*
In general, on an IEEE-754 platform the aim is to follow the C99
standard, including Annex 'F', whenever possible. Where the
standard recommends raising the 'divide-by-zero' or 'invalid'
floating-point exceptions, Python should raise a ValueError. Where
the standard recommends raising 'overflow', Python should raise an
OverflowError. In all other circumstances a value should be
returned.
*/
#include "Python.h"
#include "longintrepr.h" /* just for SHIFT */
#ifdef _OSF_SOURCE
/* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
extern double copysign(double, double);
#endif
/* Call is_error when errno != 0, and where x is the result libm
* returned. is_error will usually set up an exception and return
* true (1), but may return false (0) without setting up an exception.
*/
static int
is_error(double x)
{
int result = 1; /* presumption of guilt */
assert(errno); /* non-zero errno is a precondition for calling */
if (errno == EDOM)
PyErr_SetString(PyExc_ValueError, "math domain error");
else if (errno == ERANGE) {
/* ANSI C generally requires libm functions to set ERANGE
* on overflow, but also generally *allows* them to set
* ERANGE on underflow too. There's no consistency about
* the latter across platforms.
* Alas, C99 never requires that errno be set.
* Here we suppress the underflow errors (libm functions
* should return a zero on underflow, and +- HUGE_VAL on
* overflow, so testing the result for zero suffices to
* distinguish the cases).
*/
if (x)
PyErr_SetString(PyExc_OverflowError,
"math range error");
else
result = 0;
}
else
/* Unexpected math error */
PyErr_SetFromErrno(PyExc_ValueError);
return result;
}
/*
wrapper for atan2 that deals directly with special cases before
delegating to the platform libm for the remaining cases. This
is necessary to get consistent behaviour across platforms.
Windows, FreeBSD and alpha Tru64 are amongst platforms that don't
always follow C99.
*/
static double
m_atan2(double y, double x)
{
if (Py_IS_NAN(x) || Py_IS_NAN(y))
return Py_NAN;
if (Py_IS_INFINITY(y)) {
if (Py_IS_INFINITY(x)) {
if (copysign(1., x) == 1.)
/* atan2(+-inf, +inf) == +-pi/4 */
return copysign(0.25*Py_MATH_PI, y);
else
/* atan2(+-inf, -inf) == +-pi*3/4 */
return copysign(0.75*Py_MATH_PI, y);
}
/* atan2(+-inf, x) == +-pi/2 for finite x */
return copysign(0.5*Py_MATH_PI, y);
}
if (Py_IS_INFINITY(x) || y == 0.) {
if (copysign(1., x) == 1.)
/* atan2(+-y, +inf) = atan2(+-0, +x) = +-0. */
return copysign(0., y);
else
/* atan2(+-y, -inf) = atan2(+-0., -x) = +-pi. */
return copysign(Py_MATH_PI, y);
}
return atan2(y, x);
}
/*
math_1 is used to wrap a libm function f that takes a double
arguments and returns a double.
The error reporting follows these rules, which are designed to do
the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
platforms.
- a NaN result from non-NaN inputs causes ValueError to be raised
- an infinite result from finite inputs causes OverflowError to be
raised if can_overflow is 1, or raises ValueError if can_overflow
is 0.
- if the result is finite and errno == EDOM then ValueError is
raised
- if the result is finite and nonzero and errno == ERANGE then
OverflowError is raised
The last rule is used to catch overflow on platforms which follow
C89 but for which HUGE_VAL is not an infinity.
For the majority of one-argument functions these rules are enough
to ensure that Python's functions behave as specified in 'Annex F'
of the C99 standard, with the 'invalid' and 'divide-by-zero'
floating-point exceptions mapping to Python's ValueError and the
'overflow' floating-point exception mapping to OverflowError.
math_1 only works for functions that don't have singularities *and*
the possibility of overflow; fortunately, that covers everything we
care about right now.
*/
static PyObject *
math_1(PyObject *arg, 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)) {
if (!Py_IS_NAN(x))
errno = EDOM;
else
errno = 0;
}
else if (Py_IS_INFINITY(r)) {
if (Py_IS_FINITE(x))
errno = can_overflow ? ERANGE : EDOM;
else
errno = 0;
}
if (errno && is_error(r))
return NULL;
else
return PyFloat_FromDouble(r);
}
/*
math_2 is used to wrap a libm function f that takes two double
arguments and returns a double.
The error reporting follows these rules, which are designed to do
the right thing on C89/C99 platforms and IEEE 754/non IEEE 754
platforms.
- a NaN result from non-NaN inputs causes ValueError to be raised
- an infinite result from finite inputs causes OverflowError to be
raised.
- if the result is finite and errno == EDOM then ValueError is
raised
- if the result is finite and nonzero and errno == ERANGE then
OverflowError is raised
The last rule is used to catch overflow on platforms which follow
C89 but for which HUGE_VAL is not an infinity.
For most two-argument functions (copysign, fmod, hypot, atan2)
these rules are enough to ensure that Python's functions behave as
specified in 'Annex F' of the C99 standard, with the 'invalid' and
'divide-by-zero' floating-point exceptions mapping to Python's
ValueError and the 'overflow' floating-point exception mapping to
OverflowError.
*/
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);
}
#define FUNC1(funcname, func, can_overflow, docstring) \
static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
return math_1(args, func, can_overflow); \
}\
PyDoc_STRVAR(math_##funcname##_doc, docstring);
#define FUNC2(funcname, func, docstring) \
static PyObject * math_##funcname(PyObject *self, PyObject *args) { \
return math_2(args, func, #funcname); \
}\
PyDoc_STRVAR(math_##funcname##_doc, docstring);
FUNC1(acos, acos, 0,
"acos(x)\n\nReturn the arc cosine (measured in radians) of x.")
FUNC1(acosh, acosh, 0,
"acosh(x)\n\nReturn the hyperbolic arc cosine (measured in radians) of x.")
FUNC1(asin, asin, 0,
"asin(x)\n\nReturn the arc sine (measured in radians) of x.")
FUNC1(asinh, asinh, 0,
"asinh(x)\n\nReturn the hyperbolic arc sine (measured in radians) of x.")
FUNC1(atan, atan, 0,
"atan(x)\n\nReturn the arc tangent (measured in radians) of x.")
FUNC2(atan2, m_atan2,
"atan2(y, x)\n\nReturn the arc tangent (measured in radians) of y/x.\n"
"Unlike atan(y/x), the signs of both x and y are considered.")
FUNC1(atanh, atanh, 0,
"atanh(x)\n\nReturn the hyperbolic arc tangent (measured in radians) of x.")
FUNC1(ceil, ceil, 0,
"ceil(x)\n\nReturn the ceiling of x as a float.\n"
"This is the smallest integral value >= x.")
FUNC2(copysign, copysign,
"copysign(x,y)\n\nReturn x with the sign of y.")
FUNC1(cos, cos, 0,
"cos(x)\n\nReturn the cosine of x (measured in radians).")
FUNC1(cosh, cosh, 1,
"cosh(x)\n\nReturn the hyperbolic cosine of x.")
FUNC1(exp, exp, 1,
"exp(x)\n\nReturn e raised to the power of x.")
FUNC1(fabs, fabs, 0,
"fabs(x)\n\nReturn the absolute value of the float x.")
FUNC1(floor, floor, 0,
"floor(x)\n\nReturn the floor of x as a float.\n"
"This is the largest integral value <= x.")
FUNC1(log1p, log1p, 1,
"log1p(x)\n\nReturn the natural logarithm of 1+x (base e).\n\
The result is computed in a way which is accurate for x near zero.")
FUNC1(sin, sin, 0,
"sin(x)\n\nReturn the sine of x (measured in radians).")
FUNC1(sinh, sinh, 1,
"sinh(x)\n\nReturn the hyperbolic sine of x.")
FUNC1(sqrt, sqrt, 0,
"sqrt(x)\n\nReturn the square root of x.")
FUNC1(tan, tan, 0,
"tan(x)\n\nReturn the tangent of x (measured in radians).")
FUNC1(tanh, tanh, 0,
"tanh(x)\n\nReturn the hyperbolic tangent of x.")
/* Precision summation function as msum() by Raymond Hettinger in
<http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/393090>,
enhanced with the exact partials sum and roundoff from Mark
Dickinson's post at <http://bugs.python.org/file10357/msum4.py>.
See both of those for more details, proofs and other references.
Note 1: IEEE 754 floating point format and semantics are assumed, but not
explicitly maintained. The following rules may not apply:
1. if the summands include a NaN, return a NaN,
2. if the summands include infinities of both signs, raise ValueError,
3. if the summands include infinities of only one sign, return infinity
with that sign,
4. otherwise (all summands are finite) if the result is infinite, raise
OverflowError. The result can never be a NaN if all summands are
finite.
Note 2: the implementation below not include the intermediate overflow
handling from Mark Dickinson's msum(). Therefore, sum([1e+308, 1e-308,
1e+308]) returns result 1e+308, however sum([1e+308, 1e+308, 1e-308])
raises an OverflowError due to intermediate overflow of the first
partial sum.
Note 3: aggressively optimizing compilers may eliminate the roundoff
expressions critical for accurate summation. For example, the compiler
may optimize the following expressions
hi = x + y;
lo = y - (hi - x);
to
hi = x + y;
lo = 0.0;
defeating the whole purpose. Using volatile variables and/or explicit
assignment of critical subexpressions to a volatile variable should
remedy the problem
volatile double v; // Deter compiler from algebraically optimizing
// this critical, intermediate value away
hi = x + y;
v = hi - x;
lo = y - v;
by forcing the compiler to compute the value for v. This may also help
when subexpression are not computed with the full double precision.
Note 4. the same summation functions may be in ./cmathmodule.c. Make
sure to update both when making changes.
*/
#define NUM_PARTIALS 32 /* initial partials array size, on stack */
/* Extend the partials array p[] by doubling its size.
*/
static int /* non-zero on error */
_sum_realloc(double **p_ptr, Py_ssize_t n,
double *ps, Py_ssize_t *m_ptr)
{
void *v = NULL;
Py_ssize_t m = *m_ptr;
m += m; /* double */
if (n < m && m < (PY_SSIZE_T_MAX / sizeof(double))) {
double *p = *p_ptr;
if (p == ps) {
v = PyMem_Malloc(sizeof(double) * m);
if (v != NULL)
memcpy(v, ps, sizeof(double) * n);
}
else
v = PyMem_Realloc(p, sizeof(double) * m);
}
if (v == NULL) { /* size overflow or no memory */
PyErr_SetString(PyExc_MemoryError, "math sum partials");
return 1;
}
*p_ptr = (double*) v;
*m_ptr = m;
return 0;
}
/* Full precision summation of a sequence of floats.
def msum(iterable):
partials = [] # sorted, non-overlapping partial sums
for x in iterable:
i = 0
for y in partials:
if abs(x) < abs(y):
x, y = y, x
hi = x + y
lo = y - (hi - x)
if lo:
partials[i] = lo
i += 1
x = hi
partials[i:] = [x]
return sum_exact(partials)
Rounded x+y stored in hi with the roundoff stored in lo. Together hi+lo
are exactly equal to x+y. The inner loop applies hi/lo summation to each
partial so that the list of partial sums remains exact.
Sum_exact() adds the partial sums exactly and correctly rounds the final
result (using the round-half-to-even rule). The items in partials remain
non-zero, non-special, non-overlapping and strictly increasing in
magnitude, but possibly not all having the same sign.
Depends on IEEE 754 arithmetic guarantees.
*/
static PyObject*
math_sum(PyObject *self, PyObject *seq)
{
PyObject *item, *iter, *sum = NULL;
Py_ssize_t i, j, n = 0, m = NUM_PARTIALS;
double x, y, hi, lo=0.0, ps[NUM_PARTIALS], *p = ps;
iter = PyObject_GetIter(seq);
if (iter == NULL)
return NULL;
PyFPE_START_PROTECT("sum", Py_DECREF(iter); return NULL)
for(;;) { /* for x in iterable */
/* some invariants */
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 _sum_error;
else
break;
}
x = PyFloat_AsDouble(item);
Py_DECREF(item);
if (PyErr_Occurred())
goto _sum_error;
for (i = j = 0; j < n; j++) { /* for y in partials */
y = p[j];
hi = x + y;
lo = fabs(x) < fabs(y)
? x - (hi - y) /* volatile */
: y - (hi - x); /* volatile */
if (lo != 0.0)
p[i++] = lo;
x = hi;
}
/* ps[i:] = [x] */
n = i;
if (x != 0.0) {
/* if non-finite, reset partials, effectively
adding subsequent items without roundoff
and yielding correct non-finite results,
provided IEEE 754 rules are observed */
if (! Py_IS_FINITE(x))
n = 0;
else if (n >= m && _sum_realloc(&p, n, ps, &m))
goto _sum_error;
p[n++] = x;
}
}
assert(n <= m);
if (n > 0) {
hi = p[--n];
if (Py_IS_FINITE(hi)) {
/* sum_exact(ps, hi) from the top, stop
as soon as the sum becomes inexact */
while (n > 0) {
x = p[--n];
y = hi;
hi = x + y;
assert(fabs(x) < fabs(y));
lo = x - (hi - y); /* volatile */
if (lo != 0.0)
break;
}
/* round correctly if necessary */
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; /* volatile */
if (y == (x - hi))
hi = x;
}
}
else { /* raise corresponding error */
errno = Py_IS_NAN(hi) ? EDOM : ERANGE;
if (is_error(hi))
goto _sum_error;
}
}
else /* default */
hi = 0.0;
sum = PyFloat_FromDouble(hi);
_sum_error:
PyFPE_END_PROTECT(hi)
Py_DECREF(iter);
if (p != ps)
PyMem_Free(p);
return sum;
}
#undef NUM_PARTIALS
PyDoc_STRVAR(math_sum_doc,
"sum(sequence)\n\n\
Return the full precision sum of a sequence of numbers.\n\
When the sequence is empty, return zero.\n\n\
For accurate results, IEEE 754 floating point format\n\
and semantics and floating point radix 2 are required.");
static PyObject *
math_trunc(PyObject *self, PyObject *number)
{
return PyObject_CallMethod(number, "__trunc__", NULL);
}
PyDoc_STRVAR(math_trunc_doc,
"trunc(x:Real) -> Integral\n"
"\n"
"Truncates x to the nearest Integral toward 0. Uses the __trunc__ magic method.");
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);
}
PyDoc_STRVAR(math_frexp_doc,
"frexp(x)\n"
"\n"
"Return the mantissa and exponent of x, as pair (m, e).\n"
"m is a float and e is an int, such that x = m * 2.**e.\n"
"If x is 0, m and e are both 0. Else 0.5 <= abs(m) < 1.0.");
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 if (PyInt_Check(oexp)) {
exp = PyInt_AS_LONG(oexp);
}
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);
}
PyDoc_STRVAR(math_ldexp_doc,
"ldexp(x, i) -> x * (2**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);
}
PyDoc_STRVAR(math_modf_doc,
"modf(x)\n"
"\n"
"Return the fractional and integer parts of x. Both results carry the sign\n"
"of x. The integer part is returned as a real.");
/* A decent logarithm is easy to compute even for huge longs, but libm can't
do that by itself -- loghelper can. func is log or log10, and name is
"log" or "log10". Note that overflow isn't possible: a long can contain
no more than INT_MAX * SHIFT bits, so has value certainly less than
2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is
small enough to fit in an IEEE single. log and log10 are even smaller.
*/
static PyObject*
loghelper(PyObject* arg, double (*func)(double), char *funcname)
{
/* If it is long, do it ourselves. */
if (PyLong_Check(arg)) {
double x;
int e;
x = _PyLong_AsScaledDouble(arg, &e);
if (x <= 0.0) {
PyErr_SetString(PyExc_ValueError,
"math domain error");
return NULL;
}
/* Value is ~= x * 2**(e*PyLong_SHIFT), so the log ~=
log(x) + log(2) * e * PyLong_SHIFT.
CAUTION: e*PyLong_SHIFT may overflow using int arithmetic,
so force use of double. */
x = func(x) + (e * (double)PyLong_SHIFT) * func(2.0);
return PyFloat_FromDouble(x);
}
/* Else let libm handle it by itself. */
return math_1(arg, func, 0);
}
static PyObject *
math_log(PyObject *self, PyObject *args)
{
PyObject *arg;
PyObject *base = NULL;
PyObject *num, *den;
PyObject *ans;
if (!PyArg_UnpackTuple(args, "log", 1, 2, &arg, &base))
return NULL;
num = loghelper(arg, log, "log");
if (num == NULL || base == NULL)
return num;
den = loghelper(base, log, "log");
if (den == NULL) {
Py_DECREF(num);
return NULL;
}
ans = PyNumber_Divide(num, den);
Py_DECREF(num);
Py_DECREF(den);
return ans;
}
PyDoc_STRVAR(math_log_doc,
"log(x[, base]) -> the logarithm of x to the given base.\n\
If the base not specified, returns the natural logarithm (base e) of x.");
static PyObject *
math_log10(PyObject *self, PyObject *arg)
{
return loghelper(arg, log10, "log10");
}
PyDoc_STRVAR(math_log10_doc,
"log10(x) -> the base 10 logarithm of x.");
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);
}
PyDoc_STRVAR(math_fmod_doc,
"fmod(x,y)\n\nReturn fmod(x, y), according to platform C."
" x % y may differ.");
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);
}
PyDoc_STRVAR(math_hypot_doc,
"hypot(x,y)\n\nReturn the Euclidean distance, sqrt(x*x + y*y).");
/* pow can't use math_2, but needs its own wrapper: the problem is
that an infinite result can arise either as a result of overflow
(in which case OverflowError should be raised) or as a result of
e.g. 0.**-5. (for which ValueError needs to be raised.)
*/
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);
}
PyDoc_STRVAR(math_pow_doc,
"pow(x,y)\n\nReturn x**y (x to the power of y).");
static const double degToRad = Py_MATH_PI / 180.0;
static const double radToDeg = 180.0 / Py_MATH_PI;
static PyObject *
math_degrees(PyObject *self, PyObject *arg)
{
double x = PyFloat_AsDouble(arg);
if (x == -1.0 && PyErr_Occurred())
return NULL;
return PyFloat_FromDouble(x * radToDeg);
}
PyDoc_STRVAR(math_degrees_doc,
"degrees(x) -> converts angle x from radians to degrees");
static PyObject *
math_radians(PyObject *self, PyObject *arg)
{
double x = PyFloat_AsDouble(arg);
if (x == -1.0 && PyErr_Occurred())
return NULL;
return PyFloat_FromDouble(x * degToRad);
}
PyDoc_STRVAR(math_radians_doc,
"radians(x) -> converts angle x from degrees to radians");
static PyObject *
math_isnan(PyObject *self, PyObject *arg)
{
double x = PyFloat_AsDouble(arg);
if (x == -1.0 && PyErr_Occurred())
return NULL;
return PyBool_FromLong((long)Py_IS_NAN(x));
}
PyDoc_STRVAR(math_isnan_doc,
"isnan(x) -> bool\n\
Checks if float x is not a number (NaN)");
static PyObject *
math_isinf(PyObject *self, PyObject *arg)
{
double x = PyFloat_AsDouble(arg);
if (x == -1.0 && PyErr_Occurred())
return NULL;
return PyBool_FromLong((long)Py_IS_INFINITY(x));
}
PyDoc_STRVAR(math_isinf_doc,
"isinf(x) -> bool\n\
Checks if float x is infinite (positive or negative)");
static PyMethodDef math_methods[] = {
{"acos", math_acos, METH_O, math_acos_doc},
{"acosh", math_acosh, METH_O, math_acosh_doc},
{"asin", math_asin, METH_O, math_asin_doc},
{"asinh", math_asinh, METH_O, math_asinh_doc},
{"atan", math_atan, METH_O, math_atan_doc},
{"atan2", math_atan2, METH_VARARGS, math_atan2_doc},
{"atanh", math_atanh, METH_O, math_atanh_doc},
{"ceil", math_ceil, METH_O, math_ceil_doc},
{"copysign", math_copysign, METH_VARARGS, math_copysign_doc},
{"cos", math_cos, METH_O, math_cos_doc},
{"cosh", math_cosh, METH_O, math_cosh_doc},
{"degrees", math_degrees, METH_O, math_degrees_doc},
{"exp", math_exp, METH_O, math_exp_doc},
{"fabs", math_fabs, METH_O, math_fabs_doc},
{"floor", math_floor, METH_O, math_floor_doc},
{"fmod", math_fmod, METH_VARARGS, math_fmod_doc},
{"frexp", math_frexp, METH_O, math_frexp_doc},
{"hypot", math_hypot, METH_VARARGS, math_hypot_doc},
{"isinf", math_isinf, METH_O, math_isinf_doc},
{"isnan", math_isnan, METH_O, math_isnan_doc},
{"ldexp", math_ldexp, METH_VARARGS, math_ldexp_doc},
{"log", math_log, METH_VARARGS, math_log_doc},
{"log1p", math_log1p, METH_O, math_log1p_doc},
{"log10", math_log10, METH_O, math_log10_doc},
{"modf", math_modf, METH_O, math_modf_doc},
{"pow", math_pow, METH_VARARGS, math_pow_doc},
{"radians", math_radians, METH_O, math_radians_doc},
{"sin", math_sin, METH_O, math_sin_doc},
{"sinh", math_sinh, METH_O, math_sinh_doc},
{"sqrt", math_sqrt, METH_O, math_sqrt_doc},
{"sum", math_sum, METH_O, math_sum_doc},
{"tan", math_tan, METH_O, math_tan_doc},
{"tanh", math_tanh, METH_O, math_tanh_doc},
{"trunc", math_trunc, METH_O, math_trunc_doc},
{NULL, NULL} /* sentinel */
};
PyDoc_STRVAR(module_doc,
"This module is always available. It provides access to the\n"
"mathematical functions defined by the C standard.");
PyMODINIT_FUNC
initmath(void)
{
PyObject *m;
m = Py_InitModule3("math", math_methods, module_doc);
if (m == NULL)
goto finally;
PyModule_AddObject(m, "pi", PyFloat_FromDouble(Py_MATH_PI));
PyModule_AddObject(m, "e", PyFloat_FromDouble(Py_MATH_E));
finally:
return;
}
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