/* 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 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 int

complex_print(PyComplexObject *v, FILE *fp, int flags)

{

	char buf[100];

	complex_to_buf(buf, sizeof(buf), v,

		       (flags & Py_PRINT_RAW) ? PREC_STR : PREC_REPR);

	Py_BEGIN_ALLOW_THREADS

	fputs(buf, fp);

	Py_END_ALLOW_THREADS

	return 0;

}

static PyObject *

complex_repr(PyComplexObject *v)

{

	char buf[100];

	complex_to_buf(buf, sizeof(buf), v, PREC_REPR);

	return PyString_FromString(buf);

}

static PyObject *

complex_str(PyComplexObject *v)

{

	char buf[100];

	complex_to_buf(buf, sizeof(buf), v, PREC_STR);

	return PyString_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 (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;