cpython/Objects/complexobject.c

/* Complex object implementation */

/* Borrows heavily from floatobject.c */

/* Submitted by Jim Hugunin */

#include "Python.h"
#include "structmember.h"

#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif

#ifndef WITHOUT_COMPLEX

/* Precisions used by repr() and str(), respectively.

   The repr() precision (17 significant decimal digits) is the minimal number
   that is guaranteed to have enough precision so that if the number is read
   back in the exact same binary value is recreated.  This is true for IEEE
   floating point by design, and also happens to work for all other modern
   hardware.

   The str() precision is chosen so that in most cases, the rounding noise
   created by various operations is suppressed, while giving plenty of
   precision for practical use.
*/

#define PREC_REPR	17
#define PREC_STR	12

/* elementary operations on complex numbers */

static Py_complex c_1 = {1., 0.};

Py_complex
c_sum(Py_complex a, Py_complex b)
{
	Py_complex r;
	r.real = a.real + b.real;
	r.imag = a.imag + b.imag;
	return r;
}

Py_complex
c_diff(Py_complex a, Py_complex b)
{
	Py_complex r;
	r.real = a.real - b.real;
	r.imag = a.imag - b.imag;
	return r;
}

Py_complex
c_neg(Py_complex a)
{
	Py_complex r;
	r.real = -a.real;
	r.imag = -a.imag;
	return r;
}

Py_complex
c_prod(Py_complex a, Py_complex b)
{
	Py_complex r;
	r.real = a.real*b.real - a.imag*b.imag;
	r.imag = a.real*b.imag + a.imag*b.real;
	return r;
}

Py_complex
c_quot(Py_complex a, Py_complex b)
{
	/******************************************************************
	This was the original algorithm.  It's grossly prone to spurious
	overflow and underflow errors.  It also merrily divides by 0 despite
	checking for that(!).  The code still serves a doc purpose here, as
	the algorithm following is a simple by-cases transformation of this
	one:

	Py_complex r;
	double d = b.real*b.real + b.imag*b.imag;
	if (d == 0.)
		errno = EDOM;
	r.real = (a.real*b.real + a.imag*b.imag)/d;
	r.imag = (a.imag*b.real - a.real*b.imag)/d;
	return r;
	******************************************************************/

	/* This algorithm is better, and is pretty obvious:  first divide the
	 * numerators and denominator by whichever of {b.real, b.imag} has
	 * larger magnitude.  The earliest reference I found was to CACM
	 * Algorithm 116 (Complex Division, Robert L. Smith, Stanford
	 * University).  As usual, though, we're still ignoring all IEEE
	 * endcases.
	 */
	 Py_complex r;	/* the result */
 	 const double abs_breal = b.real < 0 ? -b.real : b.real;
	 const double abs_bimag = b.imag < 0 ? -b.imag : b.imag;

	 if (abs_breal >= abs_bimag) {
 		/* divide tops and bottom by b.real */
	 	if (abs_breal == 0.0) {
	 		errno = EDOM;
	 		r.real = r.imag = 0.0;
	 	}
	 	else {
	 		const double ratio = b.imag / b.real;
	 		const double denom = b.real + b.imag * ratio;
	 		r.real = (a.real + a.imag * ratio) / denom;
	 		r.imag = (a.imag - a.real * ratio) / denom;
	 	}
	}
	else {
		/* divide tops and bottom by b.imag */
		const double ratio = b.real / b.imag;
		const double denom = b.real * ratio + b.imag;
		assert(b.imag != 0.0);
		r.real = (a.real * ratio + a.imag) / denom;
		r.imag = (a.imag * ratio - a.real) / denom;
	}
	return r;
}

Py_complex
c_pow(Py_complex a, Py_complex b)
{
	Py_complex r;
	double vabs,len,at,phase;
	if (b.real == 0. && b.imag == 0.) {
		r.real = 1.;
		r.imag = 0.;
	}
	else if (a.real == 0. && a.imag == 0.) {
		if (b.imag != 0. || b.real < 0.)
			errno = EDOM;
		r.real = 0.;
		r.imag = 0.;
	}
	else {
		vabs = hypot(a.real,a.imag);
		len = pow(vabs,b.real);
		at = atan2(a.imag, a.real);
		phase = at*b.real;
		if (b.imag != 0.0) {
			len /= exp(at*b.imag);
			phase += b.imag*log(vabs);
		}
		r.real = len*cos(phase);
		r.imag = len*sin(phase);
	}
	return r;
}

static Py_complex
c_powu(Py_complex x, long n)
{
	Py_complex r, p;
	long mask = 1;
	r = c_1;
	p = x;
	while (mask > 0 && n >= mask) {
		if (n & mask)
			r = c_prod(r,p);
		mask <<= 1;
		p = c_prod(p,p);
	}
	return r;
}

static Py_complex
c_powi(Py_complex x, long n)
{
	Py_complex cn;

	if (n > 100 || n < -100) {
		cn.real = (double) n;
		cn.imag = 0.;
		return c_pow(x,cn);
	}
	else if (n > 0)
		return c_powu(x,n);
	else
		return c_quot(c_1,c_powu(x,-n));

}

double
c_abs(Py_complex z)
{
	/* sets errno = ERANGE on overflow;  otherwise errno = 0 */
	double result;

	if (!Py_IS_FINITE(z.real) || !Py_IS_FINITE(z.imag)) {
		/* C99 rules: if either the real or the imaginary part is an
		   infinity, return infinity, even if the other part is a
		   NaN. */
		if (Py_IS_INFINITY(z.real)) {
			result = fabs(z.real);
			errno = 0;
			return result;
		}
		if (Py_IS_INFINITY(z.imag)) {
			result = fabs(z.imag);
			errno = 0;
			return result;
		}
		/* either the real or imaginary part is a NaN,
		   and neither is infinite. Result should be NaN. */
		return Py_NAN;
	}
	result = hypot(z.real, z.imag);
	if (!Py_IS_FINITE(result))
		errno = ERANGE;
	else
		errno = 0;
	return result;
}

static PyObject *
complex_subtype_from_c_complex(PyTypeObject *type, Py_complex cval)
{
	PyObject *op;

	op = type->tp_alloc(type, 0);
	if (op != NULL)
		((PyComplexObject *)op)->cval = cval;
	return op;
}

PyObject *
PyComplex_FromCComplex(Py_complex cval)
{
	register PyComplexObject *op;

	/* Inline PyObject_New */
	op = (PyComplexObject *) PyObject_MALLOC(sizeof(PyComplexObject));
	if (op == NULL)
		return PyErr_NoMemory();
	PyObject_INIT(op, &PyComplex_Type);
	op->cval = cval;
	return (PyObject *) op;
}

static PyObject *
complex_subtype_from_doubles(PyTypeObject *type, double real, double imag)
{
	Py_complex c;
	c.real = real;
	c.imag = imag;
	return complex_subtype_from_c_complex(type, c);
}

PyObject *
PyComplex_FromDoubles(double real, double imag)
{
	Py_complex c;
	c.real = real;
	c.imag = imag;
	return PyComplex_FromCComplex(c);
}

double
PyComplex_RealAsDouble(PyObject *op)
{
	if (PyComplex_Check(op)) {
		return ((PyComplexObject *)op)->cval.real;
	}
	else {
		return PyFloat_AsDouble(op);
	}
}

double
PyComplex_ImagAsDouble(PyObject *op)
{
	if (PyComplex_Check(op)) {
		return ((PyComplexObject *)op)->cval.imag;
	}
	else {
		return 0.0;
	}
}

Py_complex
PyComplex_AsCComplex(PyObject *op)
{
	Py_complex cv;
	PyObject *newop = NULL;
	static PyObject *complex_str = NULL;

	assert(op);
	/* If op is already of type PyComplex_Type, return its value */
	if (PyComplex_Check(op)) {
		return ((PyComplexObject *)op)->cval;
	}
	/* If not, use op's __complex__  method, if it exists */

	/* return -1 on failure */
	cv.real = -1.;
	cv.imag = 0.;

	if (complex_str == NULL) {
		if (!(complex_str = PyString_InternFromString("__complex__")))
			return cv;
	}
	
	if (PyInstance_Check(op)) {
		/* this can go away in python 3000 */
		if (PyObject_HasAttr(op, complex_str)) {
			newop = PyObject_CallMethod(op, "__complex__", NULL);
			if (!newop)
				return cv;
		}
		/* else try __float__ */
	} else {
		PyObject *complexfunc;
		complexfunc = _PyType_Lookup(op->ob_type, complex_str);
		/* complexfunc is a borrowed reference */
		if (complexfunc) {
			newop = PyObject_CallFunctionObjArgs(complexfunc, op, NULL);
			if (!newop)
				return cv;
		}
	}

	if (newop) {
		if (!PyComplex_Check(newop)) {
			PyErr_SetString(PyExc_TypeError,
				"__complex__ should return a complex object");
			Py_DECREF(newop);
			return cv;
		}
		cv = ((PyComplexObject *)newop)->cval;
		Py_DECREF(newop);
		return cv;
	}
	/* If neither of the above works, interpret op as a float giving the
	   real part of the result, and fill in the imaginary part as 0. */
	else {
		/* PyFloat_AsDouble will return -1 on failure */
		cv.real = PyFloat_AsDouble(op);
		return cv;
	}
}

static void
complex_dealloc(PyObject *op)
{
	op->ob_type->tp_free(op);
}


static PyObject *
complex_format(PyComplexObject *v, char format_code)
{
	PyObject *result = NULL;
	Py_ssize_t len;

	/* If these are non-NULL, they'll need to be freed. */
	char *pre = NULL;
	char *im = NULL;
	char *buf = NULL;

	/* These do not need to be freed. re is either an alias
	   for pre or a pointer to a constant.  lead and tail
	   are pointers to constants. */
	char *re = NULL;
	char *lead = "";
	char *tail = "";

	if (v->cval.real == 0. && copysign(1.0, v->cval.real)==1.0) {
		re = "";
		im = PyOS_double_to_string(v->cval.imag, format_code,
					   0, 0, NULL);
		if (!im) {
			PyErr_NoMemory();
			goto done;
		}
	} else {
		/* Format imaginary part with sign, real part without */
		pre = PyOS_double_to_string(v->cval.real, format_code,
					    0, 0, NULL);
		if (!pre) {
			PyErr_NoMemory();
			goto done;
		}
		re = pre;

		im = PyOS_double_to_string(v->cval.imag, format_code,
					   0, Py_DTSF_SIGN, NULL);
		if (!im) {
			PyErr_NoMemory();
			goto done;
		}
		lead = "(";
		tail = ")";
	}
	/* Alloc the final buffer. Add one for the "j" in the format string,
	   and one for the trailing zero. */
	len = strlen(lead) + strlen(re) + strlen(im) + strlen(tail) + 2;
	buf = PyMem_Malloc(len);
	if (!buf) {
		PyErr_NoMemory();
		goto done;
	}
	PyOS_snprintf(buf, len, "%s%s%sj%s", lead, re, im, tail);
	result = PyString_FromString(buf);
  done:
	PyMem_Free(im);
	PyMem_Free(pre);
	PyMem_Free(buf);

	return result;
}

static int
complex_print(PyComplexObject *v, FILE *fp, int flags)
{
	PyObject *formatv;
	char *buf;
	formatv = complex_format(v, (flags & Py_PRINT_RAW) ? 's' : 'r');
	if (formatv == NULL)
		return -1;
	buf = PyString_AS_STRING(formatv);
	Py_BEGIN_ALLOW_THREADS
	fputs(buf, fp);
	Py_END_ALLOW_THREADS
	Py_DECREF(formatv);
	return 0;
}

static PyObject *
complex_repr(PyComplexObject *v)
{
	return complex_format(v, 'r');
}

static PyObject *
complex_str(PyComplexObject *v)
{
	return complex_format(v, 's');
}

static long
complex_hash(PyComplexObject *v)
{
	long hashreal, hashimag, combined;
	hashreal = _Py_HashDouble(v->cval.real);
	if (hashreal == -1)
		return -1;
	hashimag = _Py_HashDouble(v->cval.imag);
	if (hashimag == -1)
		return -1;
	/* Note:  if the imaginary part is 0, hashimag is 0 now,
	 * so the following returns hashreal unchanged.  This is
	 * important because numbers of different types that
	 * compare equal must have the same hash value, so that
	 * hash(x + 0*j) must equal hash(x).
	 */
	combined = hashreal + 1000003 * hashimag;
	if (combined == -1)
		combined = -2;
	return combined;
}

/* This macro may return! */
#define TO_COMPLEX(obj, c) \
	if (PyComplex_Check(obj)) \
		c = ((PyComplexObject *)(obj))->cval; \
	else if (to_complex(&(obj), &(c)) < 0) \
		return (obj)

static int
to_complex(PyObject **pobj, Py_complex *pc)
{
    PyObject *obj = *pobj;

    pc->real = pc->imag = 0.0;
    if (PyInt_Check(obj)) {
        pc->real = PyInt_AS_LONG(obj);
        return 0;
    }
    if (PyLong_Check(obj)) {
        pc->real = PyLong_AsDouble(obj);
        if (pc->real == -1.0 && PyErr_Occurred()) {
            *pobj = NULL;
            return -1;
        }
        return 0;
    }
    if (PyFloat_Check(obj)) {
        pc->real = PyFloat_AsDouble(obj);
        return 0;
    }
    Py_INCREF(Py_NotImplemented);
    *pobj = Py_NotImplemented;
    return -1;
}
		

static PyObject *
complex_add(PyComplexObject *v, PyComplexObject *w)
{
	Py_complex result;
	PyFPE_START_PROTECT("complex_add", return 0)
	result = c_sum(v->cval,w->cval);
	PyFPE_END_PROTECT(result)
	return PyComplex_FromCComplex(result);
}

static PyObject *
complex_sub(PyComplexObject *v, PyComplexObject *w)
{
	Py_complex result;
	PyFPE_START_PROTECT("complex_sub", return 0)
	result = c_diff(v->cval,w->cval);
	PyFPE_END_PROTECT(result)
	return PyComplex_FromCComplex(result);
}

static PyObject *
complex_mul(PyComplexObject *v, PyComplexObject *w)
{
	Py_complex result;
	PyFPE_START_PROTECT("complex_mul", return 0)
	result = c_prod(v->cval,w->cval);
	PyFPE_END_PROTECT(result)
	return PyComplex_FromCComplex(result);
}

static PyObject *
complex_div(PyComplexObject *v, PyComplexObject *w)
{
	Py_complex quot;

	PyFPE_START_PROTECT("complex_div", return 0)
	errno = 0;
	quot = c_quot(v->cval,w->cval);
	PyFPE_END_PROTECT(quot)
	if (errno == EDOM) {
		PyErr_SetString(PyExc_ZeroDivisionError, "complex division");
		return NULL;
	}
	return PyComplex_FromCComplex(quot);
}

static PyObject *
complex_classic_div(PyComplexObject *v, PyComplexObject *w)
{
	Py_complex quot;

	if (Py_DivisionWarningFlag >= 2 &&
	    PyErr_Warn(PyExc_DeprecationWarning,
		       "classic complex division") < 0)
		return NULL;

	PyFPE_START_PROTECT("complex_classic_div", return 0)
	errno = 0;
	quot = c_quot(v->cval,w->cval);
	PyFPE_END_PROTECT(quot)
	if (errno == EDOM) {
		PyErr_SetString(PyExc_ZeroDivisionError, "complex division");
		return NULL;
	}
	return PyComplex_FromCComplex(quot);
}

static PyObject *
complex_remainder(PyComplexObject *v, PyComplexObject *w)
{
	Py_complex div, mod;

	if (PyErr_Warn(PyExc_DeprecationWarning,
		       "complex divmod(), // and % are deprecated") < 0)
		return NULL;

	errno = 0;
	div = c_quot(v->cval,w->cval); /* The raw divisor value. */
	if (errno == EDOM) {
		PyErr_SetString(PyExc_ZeroDivisionError, "complex remainder");
		return NULL;
	}
	div.real = floor(div.real); /* Use the floor of the real part. */
	div.imag = 0.0;
	mod = c_diff(v->cval, c_prod(w->cval, div));

	return PyComplex_FromCComplex(mod);
}


static PyObject *
complex_divmod(PyComplexObject *v, PyComplexObject *w)
{
	Py_complex div, mod;
	PyObject *d, *m, *z;

	if (PyErr_Warn(PyExc_DeprecationWarning,
		       "complex divmod(), // and % are deprecated") < 0)
		return NULL;

	errno = 0;
	div = c_quot(v->cval,w->cval); /* The raw divisor value. */
	if (errno == EDOM) {
		PyErr_SetString(PyExc_ZeroDivisionError, "complex divmod()");
		return NULL;
	}
	div.real = floor(div.real); /* Use the floor of the real part. */
	div.imag = 0.0;
	mod = c_diff(v->cval, c_prod(w->cval, div));
	d = PyComplex_FromCComplex(div);
	m = PyComplex_FromCComplex(mod);
	z = PyTuple_Pack(2, d, m);
	Py_XDECREF(d);
	Py_XDECREF(m);
	return z;
}

static PyObject *
complex_pow(PyObject *v, PyObject *w, PyObject *z)
{
	Py_complex p;
	Py_complex exponent;
	long int_exponent;
	Py_complex a, b;
	TO_COMPLEX(v, a);
	TO_COMPLEX(w, b);

 	if (z!=Py_None) {
		PyErr_SetString(PyExc_ValueError, "complex modulo");
		return NULL;
	}
	PyFPE_START_PROTECT("complex_pow", return 0)
	errno = 0;
	exponent = b;
	int_exponent = (long)exponent.real;
	if (exponent.imag == 0. && exponent.real == int_exponent)
		p = c_powi(a,int_exponent);
	else
		p = c_pow(a,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 *
complex_int_div(PyComplexObject *v, PyComplexObject *w)
{
	PyObject *t, *r;
	
	if (PyErr_Warn(PyExc_DeprecationWarning,
		       "complex divmod(), // and % are deprecated") < 0)
		return NULL;

	t = complex_divmod(v, w);
	if (t != NULL) {
		r = PyTuple_GET_ITEM(t, 0);
		Py_INCREF(r);
		Py_DECREF(t);
		return r;
	}
	return NULL;
}

static PyObject *
complex_neg(PyComplexObject *v)
{
	Py_complex neg;
	neg.real = -v->cval.real;
	neg.imag = -v->cval.imag;
	return PyComplex_FromCComplex(neg);
}

static PyObject *
complex_pos(PyComplexObject *v)
{
	if (PyComplex_CheckExact(v)) {
		Py_INCREF(v);
		return (PyObject *)v;
	}
	else
		return PyComplex_FromCComplex(v->cval);
}

static PyObject *
complex_abs(PyComplexObject *v)
{
	double result;

	PyFPE_START_PROTECT("complex_abs", return 0)
	result = c_abs(v->cval);
	PyFPE_END_PROTECT(result)

	if (errno == ERANGE) {
		PyErr_SetString(PyExc_OverflowError,
				"absolute value too large");
		return NULL;
	}
	return PyFloat_FromDouble(result);
}

static int
complex_nonzero(PyComplexObject *v)
{
	return v->cval.real != 0.0 || v->cval.imag != 0.0;
}

static int
complex_coerce(PyObject **pv, PyObject **pw)
{
	Py_complex cval;
	cval.imag = 0.;
	if (PyInt_Check(*pw)) {
		cval.real = (double)PyInt_AsLong(*pw);
		*pw = PyComplex_FromCComplex(cval);
		Py_INCREF(*pv);
		return 0;
	}
	else if (PyLong_Check(*pw)) {
		cval.real = PyLong_AsDouble(*pw);
		if (cval.real == -1.0 && PyErr_Occurred())
			return -1;
		*pw = PyComplex_FromCComplex(cval);
		Py_INCREF(*pv);
		return 0;
	}
	else if (PyFloat_Check(*pw)) {
		cval.real = PyFloat_AsDouble(*pw);
		*pw = PyComplex_FromCComplex(cval);
		Py_INCREF(*pv);
		return 0;
	}
	else if (PyComplex_Check(*pw)) {
		Py_INCREF(*pv);
		Py_INCREF(*pw);
		return 0;
	}
	return 1; /* Can't do it */
}

static PyObject *
complex_richcompare(PyObject *v, PyObject *w, int op)
{
	int c;
	Py_complex i, j;
	PyObject *res;

	c = PyNumber_CoerceEx(&v, &w);
	if (c < 0)
		return NULL;
	if (c > 0) {
		Py_INCREF(Py_NotImplemented);
		return Py_NotImplemented;
	}
	/* Make sure both arguments are complex. */
	if (!(PyComplex_Check(v) && PyComplex_Check(w))) {
		Py_DECREF(v);
		Py_DECREF(w);
		Py_INCREF(Py_NotImplemented);
		return Py_NotImplemented;
	}

	i = ((PyComplexObject *)v)->cval;
	j = ((PyComplexObject *)w)->cval;
	Py_DECREF(v);
	Py_DECREF(w);

	if (op != Py_EQ && op != Py_NE) {
		PyErr_SetString(PyExc_TypeError,
			"no ordering relation is defined for complex numbers");
		return NULL;
	}

	if ((i.real == j.real && i.imag == j.imag) == (op == Py_EQ))
		res = Py_True;
	else
		res = Py_False;

	Py_INCREF(res);
	return res;
}

static PyObject *
complex_int(PyObject *v)
{
	PyErr_SetString(PyExc_TypeError,
		   "can't convert complex to int; use int(abs(z))");
	return NULL;
}

static PyObject *
complex_long(PyObject *v)
{
	PyErr_SetString(PyExc_TypeError,
		   "can't convert complex to long; use long(abs(z))");
	return NULL;
}

static PyObject *
complex_float(PyObject *v)
{
	PyErr_SetString(PyExc_TypeError,
		   "can't convert complex to float; use abs(z)");
	return NULL;
}

static PyObject *
complex_conjugate(PyObject *self)
{
	Py_complex c;
	c = ((PyComplexObject *)self)->cval;
	c.imag = -c.imag;
	return PyComplex_FromCComplex(c);
}

PyDoc_STRVAR(complex_conjugate_doc,
"complex.conjugate() -> complex\n"
"\n"
"Returns the complex conjugate of its argument. (3-4j).conjugate() == 3+4j.");

static PyObject *
complex_getnewargs(PyComplexObject *v)
{
	Py_complex c = v->cval;
	return Py_BuildValue("(dd)", c.real, c.imag);
}

PyDoc_STRVAR(complex__format__doc,
"complex.__format__() -> str\n"
"\n"
"Converts to a string according to format_spec.");

static PyObject *
complex__format__(PyObject* self, PyObject* args)
{
    PyObject *format_spec;

    if (!PyArg_ParseTuple(args, "O:__format__", &format_spec))
        return NULL;
    if (PyBytes_Check(format_spec))
        return _PyComplex_FormatAdvanced(self,
                                         PyBytes_AS_STRING(format_spec),
                                         PyBytes_GET_SIZE(format_spec));
    if (PyUnicode_Check(format_spec)) {
        /* Convert format_spec to a str */
        PyObject *result;
        PyObject *str_spec = PyObject_Str(format_spec);

        if (str_spec == NULL)
            return NULL;

        result = _PyComplex_FormatAdvanced(self,
                                           PyBytes_AS_STRING(str_spec),
                                           PyBytes_GET_SIZE(str_spec));

        Py_DECREF(str_spec);
        return result;
    }
    PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode");
    return NULL;
}

#if 0
static PyObject *
complex_is_finite(PyObject *self)
{
	Py_complex c;
	c = ((PyComplexObject *)self)->cval;
	return PyBool_FromLong((long)(Py_IS_FINITE(c.real) &&
				      Py_IS_FINITE(c.imag)));
}

PyDoc_STRVAR(complex_is_finite_doc,
"complex.is_finite() -> bool\n"
"\n"
"Returns True if the real and the imaginary part is finite.");
#endif

static PyMethodDef complex_methods[] = {
	{"conjugate",	(PyCFunction)complex_conjugate,	METH_NOARGS,
	 complex_conjugate_doc},
#if 0
	{"is_finite",	(PyCFunction)complex_is_finite,	METH_NOARGS,
	 complex_is_finite_doc},
#endif
	{"__getnewargs__",	(PyCFunction)complex_getnewargs,	METH_NOARGS},
	{"__format__",          (PyCFunction)complex__format__,
                                           METH_VARARGS, complex__format__doc},
	{NULL,		NULL}		/* sentinel */
};

static PyMemberDef complex_members[] = {
	{"real", T_DOUBLE, offsetof(PyComplexObject, cval.real), READONLY,
	 "the real part of a complex number"},
	{"imag", T_DOUBLE, offsetof(PyComplexObject, cval.imag), READONLY,
	 "the imaginary part of a complex number"},
	{0},
};

static PyObject *
complex_subtype_from_string(PyTypeObject *type, PyObject *v)
{
	const char *s, *start;
	char *end;
	double x=0.0, y=0.0, z;
	int got_bracket=0;
#ifdef Py_USING_UNICODE
	char s_buffer[256];
#endif
	Py_ssize_t len;

	if (PyString_Check(v)) {
		s = PyString_AS_STRING(v);
		len = PyString_GET_SIZE(v);
	}
#ifdef Py_USING_UNICODE
	else if (PyUnicode_Check(v)) {
		if (PyUnicode_GET_SIZE(v) >= (Py_ssize_t)sizeof(s_buffer)) {
			PyErr_SetString(PyExc_ValueError,
				 "complex() literal too large to convert");
			return NULL;
		}
		if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v),
					    PyUnicode_GET_SIZE(v),
					    s_buffer,
					    NULL))
			return NULL;
		s = s_buffer;
		len = strlen(s);
	}
#endif
	else if (PyObject_AsCharBuffer(v, &s, &len)) {
		PyErr_SetString(PyExc_TypeError,
				"complex() arg is not a string");
		return NULL;
	}

	/* position on first nonblank */
	start = s;
	while (Py_ISSPACE(*s))
		s++;
	if (*s == '(') {
		/* Skip over possible bracket from repr(). */
		got_bracket = 1;
		s++;
		while (Py_ISSPACE(*s))
			s++;
	}

	/* a valid complex string usually takes one of the three forms:

	     <float>                  - real part only
	     <float>j                 - imaginary part only
	     <float><signed-float>j   - real and imaginary parts

	   where <float> represents any numeric string that's accepted by the
	   float constructor (including 'nan', 'inf', 'infinity', etc.), and
	   <signed-float> is any string of the form <float> whose first
	   character is '+' or '-'.

	   For backwards compatibility, the extra forms

	     <float><sign>j
	     <sign>j
	     j

	   are also accepted, though support for these forms may be removed from
	   a future version of Python.
	*/

	/* first look for forms starting with <float> */
	errno = 0;
	z = PyOS_ascii_strtod(s, &end);
	if (end == s && errno == ENOMEM)
		return PyErr_NoMemory();
	if (errno == ERANGE && fabs(z) >= 1.0)
		goto overflow;

	if (end != s) {
		/* all 4 forms starting with <float> land here */
		s = end;
		if (*s == '+' || *s == '-') {
			/* <float><signed-float>j | <float><sign>j */
			x = z;
			errno = 0;
			y = PyOS_ascii_strtod(s, &end);
			if (end == s && errno == ENOMEM)
				return PyErr_NoMemory();
			if (errno == ERANGE && fabs(y) >= 1.0)
				goto overflow;
			if (end != s)
				/* <float><signed-float>j */
				s = end;
			else {
				/* <float><sign>j */
				y = *s == '+' ? 1.0 : -1.0;
				s++;
			}
			if (!(*s == 'j' || *s == 'J'))
				goto parse_error;
			s++;
		}
		else if (*s == 'j' || *s == 'J') {
			/* <float>j */
			s++;
			y = z;
		}
		else
			/* <float> */
			x = z;
	}
	else {
		/* not starting with <float>; must be <sign>j or j */
		if (*s == '+' || *s == '-') {
			/* <sign>j */
			y = *s == '+' ? 1.0 : -1.0;
			s++;
		}
		else
			/* j */
			y = 1.0;
		if (!(*s == 'j' || *s == 'J'))
			goto parse_error;
		s++;
	}

	/* trailing whitespace and closing bracket */
	while (Py_ISSPACE(*s))
		s++;
	if (got_bracket) {
		/* if there was an opening parenthesis, then the corresponding
		   closing parenthesis should be right here */
		if (*s != ')')
			goto parse_error;
		s++;
		while (Py_ISSPACE(*s))
			s++;
	}

	/* we should now be at the end of the string */
	if (s-start != len)
		goto parse_error;

	return complex_subtype_from_doubles(type, x, y);

  parse_error:
	PyErr_SetString(PyExc_ValueError,
			"complex() arg is a malformed string");
	return NULL;

  overflow:
	PyErr_SetString(PyExc_OverflowError,
			"complex() arg overflow");
	return NULL;
}

static PyObject *
complex_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
	PyObject *r, *i, *tmp, *f;
	PyNumberMethods *nbr, *nbi = NULL;
	Py_complex cr, ci;
	int own_r = 0;
	int cr_is_complex = 0;
	int ci_is_complex = 0;
	static PyObject *complexstr;
	static char *kwlist[] = {"real", "imag", 0};

	r = Py_False;
	i = NULL;
	if (!PyArg_ParseTupleAndKeywords(args, kwds, "|OO:complex", kwlist,
					 &r, &i))
		return NULL;

	/* Special-case for a single argument when type(arg) is complex. */
	if (PyComplex_CheckExact(r) && i == NULL &&
	    type == &PyComplex_Type) {
		/* Note that we can't know whether it's safe to return
		   a complex *subclass* instance as-is, hence the restriction
		   to exact complexes here.  If either the input or the
		   output is a complex subclass, it will be handled below 
		   as a non-orthogonal vector.  */
		Py_INCREF(r);
		return r;
	}
	if (PyString_Check(r) || PyUnicode_Check(r)) {
		if (i != NULL) {
			PyErr_SetString(PyExc_TypeError,
					"complex() can't take second arg"
					" if first is a string");
			return NULL;
		}
		return complex_subtype_from_string(type, r);
	}
	if (i != NULL && (PyString_Check(i) || PyUnicode_Check(i))) {
		PyErr_SetString(PyExc_TypeError,
				"complex() second arg can't be a string");
		return NULL;
	}

	/* XXX Hack to support classes with __complex__ method */
	if (complexstr == NULL) {
		complexstr = PyString_InternFromString("__complex__");
		if (complexstr == NULL)
			return NULL;
	}
	f = PyObject_GetAttr(r, complexstr);
	if (f == NULL)
		PyErr_Clear();
	else {
		PyObject *args = PyTuple_New(0);
		if (args == NULL)
			return NULL;
		r = PyEval_CallObject(f, args);
		Py_DECREF(args);
		Py_DECREF(f);
		if (r == NULL)
			return NULL;
		own_r = 1;
	}
	nbr = r->ob_type->tp_as_number;
	if (i != NULL)
		nbi = i->ob_type->tp_as_number;
	if (nbr == NULL || nbr->nb_float == NULL ||
	    ((i != NULL) && (nbi == NULL || nbi->nb_float == NULL))) {
		PyErr_SetString(PyExc_TypeError,
			   "complex() argument must be a string or a number");
		if (own_r) {
			Py_DECREF(r);
		}
		return NULL;
	}

	/* If we get this far, then the "real" and "imag" parts should
	   both be treated as numbers, and the constructor should return a
	   complex number equal to (real + imag*1j).

 	   Note that we do NOT assume the input to already be in canonical
	   form; the "real" and "imag" parts might themselves be complex
	   numbers, which slightly complicates the code below. */
	if (PyComplex_Check(r)) {
		/* Note that if r is of a complex subtype, we're only
		   retaining its real & imag parts here, and the return
		   value is (properly) of the builtin complex type. */
		cr = ((PyComplexObject*)r)->cval;
		cr_is_complex = 1;
		if (own_r) {
			Py_DECREF(r);
		}
	}
	else {
		/* The "real" part really is entirely real, and contributes
		   nothing in the imaginary direction.  
		   Just treat it as a double. */
		tmp = PyNumber_Float(r);
		if (own_r) {
			/* r was a newly created complex number, rather
			   than the original "real" argument. */
			Py_DECREF(r);
		}
		if (tmp == NULL)
			return NULL;
		if (!PyFloat_Check(tmp)) {
			PyErr_SetString(PyExc_TypeError,
					"float(r) didn't return a float");
			Py_DECREF(tmp);
			return NULL;
		}
		cr.real = PyFloat_AsDouble(tmp);
		cr.imag = 0.0; /* Shut up compiler warning */
		Py_DECREF(tmp);
	}
	if (i == NULL) {
		ci.real = 0.0;
	}
	else if (PyComplex_Check(i)) {
		ci = ((PyComplexObject*)i)->cval;
		ci_is_complex = 1;
	} else {
		/* The "imag" part really is entirely imaginary, and
		   contributes nothing in the real direction.
		   Just treat it as a double. */
		tmp = (*nbi->nb_float)(i);
		if (tmp == NULL)
			return NULL;
		ci.real = PyFloat_AsDouble(tmp);
		Py_DECREF(tmp);
	}
	/*  If the input was in canonical form, then the "real" and "imag"
	    parts are real numbers, so that ci.imag and cr.imag are zero.
	    We need this correction in case they were not real numbers. */

	if (ci_is_complex) {
		cr.real -= ci.imag;
	}
	if (cr_is_complex) {
		ci.real += cr.imag;
	}
	return complex_subtype_from_doubles(type, cr.real, ci.real);
}

PyDoc_STRVAR(complex_doc,
"complex(real[, imag]) -> complex number\n"
"\n"
"Create a complex number from a real part and an optional imaginary part.\n"
"This is equivalent to (real + imag*1j) where imag defaults to 0.");

static PyNumberMethods complex_as_number = {
	(binaryfunc)complex_add, 		/* nb_add */
	(binaryfunc)complex_sub, 		/* nb_subtract */
	(binaryfunc)complex_mul, 		/* nb_multiply */
	(binaryfunc)complex_classic_div,	/* nb_divide */
	(binaryfunc)complex_remainder,		/* nb_remainder */
	(binaryfunc)complex_divmod,		/* nb_divmod */
	(ternaryfunc)complex_pow,		/* nb_power */
	(unaryfunc)complex_neg,			/* nb_negative */
	(unaryfunc)complex_pos,			/* nb_positive */
	(unaryfunc)complex_abs,			/* nb_absolute */
	(inquiry)complex_nonzero,		/* nb_nonzero */
	0,					/* nb_invert */
	0,					/* nb_lshift */
	0,					/* nb_rshift */
	0,					/* nb_and */
	0,					/* nb_xor */
	0,					/* nb_or */
	complex_coerce,				/* nb_coerce */
	complex_int,				/* nb_int */
	complex_long,				/* nb_long */
	complex_float,				/* nb_float */
	0,					/* nb_oct */
	0,					/* nb_hex */
	0,					/* nb_inplace_add */
	0,					/* nb_inplace_subtract */
	0,					/* nb_inplace_multiply*/
	0,					/* nb_inplace_divide */
	0,					/* nb_inplace_remainder */
	0, 					/* nb_inplace_power */
	0,					/* nb_inplace_lshift */
	0,					/* nb_inplace_rshift */
	0,					/* nb_inplace_and */
	0,					/* nb_inplace_xor */
	0,					/* nb_inplace_or */
	(binaryfunc)complex_int_div,		/* nb_floor_divide */
	(binaryfunc)complex_div,		/* nb_true_divide */
	0,					/* nb_inplace_floor_divide */
	0,					/* nb_inplace_true_divide */
};

PyTypeObject PyComplex_Type = {
	PyVarObject_HEAD_INIT(&PyType_Type, 0)
	"complex",
	sizeof(PyComplexObject),
	0,
	complex_dealloc,			/* tp_dealloc */
	(printfunc)complex_print,		/* tp_print */
	0,					/* tp_getattr */
	0,					/* tp_setattr */
	0,					/* tp_compare */
	(reprfunc)complex_repr,			/* tp_repr */
	&complex_as_number,    			/* tp_as_number */
	0,					/* tp_as_sequence */
	0,					/* tp_as_mapping */
	(hashfunc)complex_hash, 		/* tp_hash */
	0,					/* tp_call */
	(reprfunc)complex_str,			/* tp_str */
	PyObject_GenericGetAttr,		/* tp_getattro */
	0,					/* tp_setattro */
	0,					/* tp_as_buffer */
	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE, /* tp_flags */
	complex_doc,				/* tp_doc */
	0,					/* tp_traverse */
	0,					/* tp_clear */
	complex_richcompare,			/* tp_richcompare */
	0,					/* tp_weaklistoffset */
	0,					/* tp_iter */
	0,					/* tp_iternext */
	complex_methods,			/* tp_methods */
	complex_members,			/* tp_members */
	0,					/* tp_getset */
	0,					/* tp_base */
	0,					/* tp_dict */
	0,					/* tp_descr_get */
	0,					/* tp_descr_set */
	0,					/* tp_dictoffset */
	0,					/* tp_init */
	PyType_GenericAlloc,			/* tp_alloc */
	complex_new,				/* tp_new */
	PyObject_Del,           		/* tp_free */
};

#endif