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 *
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 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);
}
static void
complex_to_buf(char *buf, int bufsz, PyComplexObject *v, int precision)
{
char format[32];
if (v->cval.real == 0.) {
if (!Py_IS_FINITE(v->cval.imag)) {
if (Py_IS_NAN(v->cval.imag))
strncpy(buf, "nan*j", 6);
else if (copysign(1, v->cval.imag) == 1)
strncpy(buf, "inf*j", 6);
else
strncpy(buf, "-inf*j", 7);
}
else {
PyOS_snprintf(format, sizeof(format), "%%.%ig", precision);
PyOS_ascii_formatd(buf, bufsz - 1, format, v->cval.imag);
strncat(buf, "j", 1);
}
} else {
char re[64], im[64];
/* Format imaginary part with sign, real part without */
if (!Py_IS_FINITE(v->cval.real)) {
if (Py_IS_NAN(v->cval.real))
strncpy(re, "nan", 4);
/* else if (copysign(1, v->cval.real) == 1) */
else if (v->cval.real > 0)
strncpy(re, "inf", 4);
else
strncpy(re, "-inf", 5);
}
else {
PyOS_snprintf(format, sizeof(format), "%%.%ig", precision);
PyOS_ascii_formatd(re, sizeof(re), format, v->cval.real);
}
if (!Py_IS_FINITE(v->cval.imag)) {
if (Py_IS_NAN(v->cval.imag))
strncpy(im, "+nan*", 6);
/* else if (copysign(1, v->cval.imag) == 1) */
else if (v->cval.imag > 0)
strncpy(im, "+inf*", 6);
else
strncpy(im, "-inf*", 6);
}
else {
PyOS_snprintf(format, sizeof(format), "%%+.%ig", precision);
PyOS_ascii_formatd(im, sizeof(im), format, v->cval.imag);
}
PyOS_snprintf(buf, bufsz, "(%s%sj)", re, im);
}
}
double
_Py_asinh(double x)
{
double w;
double absx = fabs(x);
if (Py_IS_NAN(x) || Py_IS_INFINITY(x)) {
return x+x;
}
if (absx < two_pow_m28) { /* |x| < 2**-28 */
return x; /* return x inexact except 0 */
}
if (absx > two_pow_p28) { /* |x| > 2**28 */
w = log(absx)+ln2;
}
else if (absx > 2.0) { /* 2 < |x| < 2**28 */
w = log(2.0*absx + 1.0 / (sqrt(x*x + 1.0) + absx));
}
else { /* 2**-28 <= |x| < 2= */
double t = x*x;
w = m_log1p(absx + t / (1.0 + sqrt(1.0 + t)));
}
return copysign(w, x);
}
double
_Py_acosh(double x)
{
if (Py_IS_NAN(x)) {
return x+x;
}
if (x < 1.) { /* x < 1; return a signaling NaN */
errno = EDOM;
#ifdef Py_NAN
return Py_NAN;
#else
return (x-x)/(x-x);
#endif
}
else if (x >= two_pow_p28) { /* x > 2**28 */
if (Py_IS_INFINITY(x)) {
return x+x;
}
else {
return log(x)+ln2; /* acosh(huge)=log(2x) */
}
}
else if (x == 1.) {
return 0.0; /* acosh(1) = 0 */
}
else if (x > 2.) { /* 2 < x < 2**28 */
double t = x*x;
return log(2.0*x - 1.0 / (x + sqrt(t - 1.0)));
}
else { /* 1 < x <= 2 */
double t = x - 1.0;
return m_log1p(t + sqrt(2.0*t + t*t));
}
}
double
_Py_atanh(double x)
{
double absx;
double t;
if (Py_IS_NAN(x)) {
return x+x;
}
absx = fabs(x);
if (absx >= 1.) { /* |x| >= 1 */
errno = EDOM;
#ifdef Py_NAN
return Py_NAN;
#else
return x/zero;
#endif
}
if (absx < two_pow_m28) { /* |x| < 2**-28 */
return x;
}
if (absx < 0.5) { /* |x| < 0.5 */
t = absx+absx;
t = 0.5 * m_log1p(t + t*absx / (1.0 - absx));
}
else { /* 0.5 <= |x| <= 1.0 */
t = 0.5 * m_log1p((absx + absx) / (1.0 - absx));
}
return copysign(t, x);
}
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));
}
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 *
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_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_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;
}