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 = PyUnicode_FromString("__complex__")))
			return cv;
	}

        {
		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 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);
	}
}

static PyObject *
complex_repr(PyComplexObject *v)
{
	char buf[100];
	complex_to_buf(buf, sizeof(buf), v, PREC_REPR);
	return PyUnicode_FromString(buf);
}

static PyObject *
complex_str(PyComplexObject *v)
{
	char buf[100];
	complex_to_buf(buf, sizeof(buf), v, PREC_STR);
	return PyUnicode_FromString(buf);
}

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 (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(PyObject *v, PyObject *w)
{
	Py_complex result;
	Py_complex a, b;
	TO_COMPLEX(v, a);
	TO_COMPLEX(w, b);
	PyFPE_START_PROTECT("complex_add", return 0)
	result = c_sum(a, b);
	PyFPE_END_PROTECT(result)
	return PyComplex_FromCComplex(result);
}

static PyObject *
complex_sub(PyObject *v, PyObject *w)
{
	Py_complex result;
	Py_complex a, b;
	TO_COMPLEX(v, a);
	TO_COMPLEX(w, b);
	PyFPE_START_PROTECT("complex_sub", return 0)
	result = c_diff(a, b);
	PyFPE_END_PROTECT(result)
	return PyComplex_FromCComplex(result);
}

static PyObject *
complex_mul(PyObject *v, PyObject *w)
{
	Py_complex result;
	Py_complex a, b;
	TO_COMPLEX(v, a);
	TO_COMPLEX(w, b);
	PyFPE_START_PROTECT("complex_mul", return 0)
	result = c_prod(a, b);
	PyFPE_END_PROTECT(result)
	return PyComplex_FromCComplex(result);
}

static PyObject *
complex_div(PyObject *v, PyObject *w)
{
	Py_complex quot;
	Py_complex a, b;
	TO_COMPLEX(v, a);
	TO_COMPLEX(w, b);
	PyFPE_START_PROTECT("complex_div", return 0)
	errno = 0;
	quot = c_quot(a, b);
	PyFPE_END_PROTECT(quot)
	if (errno == EDOM) {
		PyErr_SetString(PyExc_ZeroDivisionError, "complex division");
		return NULL;
	}
	return PyComplex_FromCComplex(quot);
}

static PyObject *
complex_remainder(PyObject *v, PyObject *w)
{
	PyErr_SetString(PyExc_TypeError,
			"can't mod complex numbers.");
	return NULL;
}


static PyObject *
complex_divmod(PyObject *v, PyObject *w)
{
	PyErr_SetString(PyExc_TypeError,
			"can't take floor or mod of complex number.");
	return NULL;
}

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(PyObject *v, PyObject *w)
{
	PyErr_SetString(PyExc_TypeError,
			"can't take floor of complex number.");
	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_bool(PyComplexObject *v)
{
	return v->cval.real != 0.0 || v->cval.imag != 0.0;
}

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

	if (op != Py_EQ && op != Py_NE) {
		/* XXX Should eventually return NotImplemented */
		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_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);
}

#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},
	{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_re=0, got_im=0, got_bracket=0, done=0;
	int digit_or_dot;
	int sw_error=0;
	int sign;
	char buffer[256]; /* For errors */
	char s_buffer[256];
	Py_ssize_t len;

	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);
	}
	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 (*s && isspace(Py_CHARMASK(*s)))
		s++;
	if (s[0] == '\0') {
		PyErr_SetString(PyExc_ValueError,
				"complex() arg is an empty string");
		return NULL;
	}
	if (s[0] == '(') {
		/* Skip over possible bracket from repr(). */
		got_bracket = 1;
		s++;
		while (*s && isspace(Py_CHARMASK(*s)))
			s++;
	}

	z = -1.0;
	sign = 1;
	do {

		switch (*s) {

		case '\0':
			if (s-start != len) {
				PyErr_SetString(
					PyExc_ValueError,
					"complex() arg contains a null byte");
				return NULL;
			}
			if(!done) sw_error=1;
			break;

		case ')':
			if (!got_bracket || !(got_re || got_im)) {
				sw_error=1;
				break;
			}
			got_bracket=0;
			done=1;
			s++;
			while (*s && isspace(Py_CHARMASK(*s)))
				s++;
			if (*s) sw_error=1;
			break;

		case '-':
			sign = -1;
				/* Fallthrough */
		case '+':
			if (done)  sw_error=1;
			s++;
			if  (  *s=='\0'||*s=='+'||*s=='-'||*s==')'||
			       isspace(Py_CHARMASK(*s))  )  sw_error=1;
			break;

		case 'J':
		case 'j':
			if (got_im || done) {
				sw_error = 1;
				break;
			}
			if  (z<0.0) {
				y=sign;
			}
			else{
				y=sign*z;
			}
			got_im=1;
			s++;
			if  (*s!='+' && *s!='-' )
				done=1;
			break;

		default:
			if (isspace(Py_CHARMASK(*s))) {
				while (*s && isspace(Py_CHARMASK(*s)))
					s++;
				if (*s && *s != ')')
					sw_error=1;
				else
					done = 1;
				break;
			}
			digit_or_dot =
				(*s=='.' || isdigit(Py_CHARMASK(*s)));
			if  (done||!digit_or_dot) {
				sw_error=1;
				break;
			}
			errno = 0;
			PyFPE_START_PROTECT("strtod", return 0)
				z = PyOS_ascii_strtod(s, &end) ;
			PyFPE_END_PROTECT(z)
				if (errno != 0) {
					PyOS_snprintf(buffer, sizeof(buffer),
					  "float() out of range: %.150s", s);
					PyErr_SetString(
						PyExc_ValueError,
						buffer);
					return NULL;
				}
			s=end;
			if  (*s=='J' || *s=='j') {

				break;
			}
			if  (got_re) {
				sw_error=1;
				break;
			}

				/* accept a real part */
			x=sign*z;
			got_re=1;
			if  (got_im)  done=1;
			z = -1.0;
			sign = 1;
			break;

		}  /* end of switch  */

	} while (s - start < len && !sw_error);

	if (sw_error || got_bracket) {
		PyErr_SetString(PyExc_ValueError,
				"complex() arg is a malformed string");
		return NULL;
	}

	return complex_subtype_from_doubles(type, x, y);
}

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 (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 && 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 = PyUnicode_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_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_bool,			/* nb_bool */
	0,					/* nb_invert */
	0,					/* nb_lshift */
	0,					/* nb_rshift */
	0,					/* nb_and */
	0,					/* nb_xor */
	0,					/* nb_or */
	complex_int,				/* nb_int */
	0,					/* nb_reserved */
	complex_float,				/* nb_float */
	0,					/* nb_inplace_add */
	0,					/* nb_inplace_subtract */
	0,					/* nb_inplace_multiply*/
	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 */
	0,					/* tp_print */
	0,					/* tp_getattr */
	0,					/* tp_setattr */
	0,					/* tp_reserved */
	(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