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cpython/Objects/complexobject.c

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/***********************************************************
Copyright (c) 2000, BeOpen.com.
Copyright (c) 1995-2000, Corporation for National Research Initiatives.
Copyright (c) 1990-1995, Stichting Mathematisch Centrum.
All rights reserved.
See the file "Misc/COPYRIGHT" for information on usage and
redistribution of this file, and for a DISCLAIMER OF ALL WARRANTIES.
******************************************************************/
/* Complex object implementation */
/* Borrows heavily from floatobject.c */
/* Submitted by Jim Hugunin */
#ifndef WITHOUT_COMPLEX
#include "Python.h"
#ifdef HAVE_LIMITS_H
#include <limits.h>
#endif
/* 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)
{
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;
}
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 = ERANGE;
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));
}
PyObject *
PyComplex_FromCComplex(Py_complex cval)
{
register PyComplexObject *op;
/* PyObject_New is inlined */
op = (PyComplexObject *) PyObject_MALLOC(sizeof(PyComplexObject));
if (op == NULL)
return PyErr_NoMemory();
PyObject_INIT(op, &PyComplex_Type);
op->cval = cval;
return (PyObject *) op;
}
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;
if (PyComplex_Check(op)) {
return ((PyComplexObject *)op)->cval;
}
else {
cv.real = PyFloat_AsDouble(op);
cv.imag = 0.;
return cv;
}
}
static void
complex_dealloc(PyObject *op)
{
PyObject_DEL(op);
}
static void
complex_buf_repr(char *buf, PyComplexObject *v)
{
if (v->cval.real == 0.)
sprintf(buf, "%.12gj", v->cval.imag);
else
sprintf(buf, "(%.12g%+.12gj)", v->cval.real, v->cval.imag);
}
static int
complex_print(PyComplexObject *v, FILE *fp, int flags)
/* flags -- not used but required by interface */
{
char buf[100];
complex_buf_repr(buf, v);
fputs(buf, fp);
return 0;
}
static PyObject *
complex_repr(PyComplexObject *v)
{
char buf[100];
complex_buf_repr(buf, v);
return PyString_FromString(buf);
}
static int
complex_compare(PyComplexObject *v, PyComplexObject *w)
{
/* Note: "greater" and "smaller" have no meaning for complex numbers,
but Python requires that they be defined nevertheless. */
Py_complex i, j;
i = v->cval;
j = w->cval;
if (i.real == j.real && i.imag == j.imag)
return 0;
else if (i.real != j.real)
return (i.real < j.real) ? -1 : 1;
else
return (i.imag < j.imag) ? -1 : 1;
}
static long
complex_hash(PyComplexObject *v)
{
double intpart, fractpart;
long x;
/* This is designed so that Python numbers with the same
value hash to the same value, otherwise comparisons
of mapping keys will turn out weird */
#ifdef MPW /* MPW C modf expects pointer to extended as second argument */
{
extended e;
fractpart = modf(v->cval.real, &e);
intpart = e;
}
#else
fractpart = modf(v->cval.real, &intpart);
#endif
if (fractpart == 0.0 && v->cval.imag == 0.0) {
if (intpart > LONG_MAX || -intpart > LONG_MAX) {
/* Convert to long int and use its hash... */
PyObject *w = PyLong_FromDouble(v->cval.real);
if (w == NULL)
return -1;
x = PyObject_Hash(w);
Py_DECREF(w);
return x;
}
x = (long)intpart;
}
else {
x = _Py_HashDouble(v->cval.real);
if (x == -1)
return -1;
if (v->cval.imag != 0.0) { /* Hash the imaginary part */
/* XXX Note that this hashes complex(x, y)
to the same value as complex(y, x).
Still better than it used to be :-) */
long y = _Py_HashDouble(v->cval.imag);
if (y == -1)
return -1;
x += y;
}
}
if (x == -1)
x = -2;
return x;
}
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_remainder(PyComplexObject *v, PyComplexObject *w)
{
Py_complex div, mod;
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;
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 = Py_BuildValue("(OO)", d, m);
Py_XDECREF(d);
Py_XDECREF(m);
return z;
}
static PyObject *
complex_pow(PyComplexObject *v, PyObject *w, PyComplexObject *z)
{
Py_complex p;
Py_complex exponent;
long int_exponent;
if ((PyObject *)z!=Py_None) {
PyErr_SetString(PyExc_ValueError, "complex modulo");
return NULL;
}
PyFPE_START_PROTECT("complex_pow", return 0)
errno = 0;
exponent = ((PyComplexObject*)w)->cval;
int_exponent = (long)exponent.real;
if (exponent.imag == 0. && exponent.real == int_exponent)
p = c_powi(v->cval,int_exponent);
else
p = c_pow(v->cval,exponent);
PyFPE_END_PROTECT(p)
if (errno == ERANGE) {
PyErr_SetString(PyExc_ValueError,
"0.0 to a negative or complex power");
return NULL;
}
return PyComplex_FromCComplex(p);
}
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)
{
Py_INCREF(v);
return (PyObject *)v;
}
static PyObject *
complex_abs(PyComplexObject *v)
{
double result;
PyFPE_START_PROTECT("complex_abs", return 0)
result = hypot(v->cval.real,v->cval.imag);
PyFPE_END_PROTECT(result)
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);
*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;
}
return 1; /* Can't do it */
}
static PyObject *
complex_int(PyObject *v)
{
PyErr_SetString(PyExc_TypeError,
"can't convert complex to int; use e.g. int(abs(z))");
return NULL;
}
static PyObject *
complex_long(PyObject *v)
{
PyErr_SetString(PyExc_TypeError,
"can't convert complex to long; use e.g. long(abs(z))");
return NULL;
}
static PyObject *
complex_float(PyObject *v)
{
PyErr_SetString(PyExc_TypeError,
"can't convert complex to float; use e.g. abs(z)");
return NULL;
}
static PyObject *
complex_conjugate(PyObject *self, PyObject *args)
{
Py_complex c;
if (!PyArg_ParseTuple(args, ":conjugate"))
return NULL;
c = ((PyComplexObject *)self)->cval;
c.imag = -c.imag;
return PyComplex_FromCComplex(c);
}
static PyMethodDef complex_methods[] = {
{"conjugate", complex_conjugate, 1},
{NULL, NULL} /* sentinel */
};
static PyObject *
complex_getattr(PyComplexObject *self, char *name)
{
if (strcmp(name, "real") == 0)
return (PyObject *)PyFloat_FromDouble(self->cval.real);
else if (strcmp(name, "imag") == 0)
return (PyObject *)PyFloat_FromDouble(self->cval.imag);
else if (strcmp(name, "__members__") == 0)
return Py_BuildValue("[ss]", "imag", "real");
return Py_FindMethod(complex_methods, (PyObject *)self, name);
}
static PyNumberMethods complex_as_number = {
(binaryfunc)complex_add, /*nb_add*/
(binaryfunc)complex_sub, /*nb_subtract*/
(binaryfunc)complex_mul, /*nb_multiply*/
(binaryfunc)complex_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*/
(coercion)complex_coerce, /*nb_coerce*/
(unaryfunc)complex_int, /*nb_int*/
(unaryfunc)complex_long, /*nb_long*/
(unaryfunc)complex_float, /*nb_float*/
0, /*nb_oct*/
0, /*nb_hex*/
};
PyTypeObject PyComplex_Type = {
PyObject_HEAD_INIT(&PyType_Type)
0,
"complex",
sizeof(PyComplexObject),
0,
(destructor)complex_dealloc, /*tp_dealloc*/
(printfunc)complex_print, /*tp_print*/
(getattrfunc)complex_getattr, /*tp_getattr*/
0, /*tp_setattr*/
(cmpfunc)complex_compare, /*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*/
};
#endif
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