/* Complex math module */ /* much code borrowed from mathmodule.c */ #include "Python.h" #ifndef M_PI#define M_PI (3.141592653589793239)#endif /* First, the C functions that do the real work */ /* constants */static Py_complex c_one = {1., 0.};static Py_complex c_half = {0.5, 0.};static Py_complex c_i = {0., 1.};static Py_complex c_halfi = {0., 0.5}; /* forward declarations */static Py_complex c_log(Py_complex);static Py_complex c_prodi(Py_complex);static Py_complex c_sqrt(Py_complex);static PyObject * math_error(void);  static Py_complexc_acos(Py_complex x){	return c_neg(c_prodi(c_log(c_sum(x,c_prod(c_i,		    c_sqrt(c_diff(c_one,c_prod(x,x))))))));} PyDoc_STRVAR(c_acos_doc,"acos(x)\n""\n""Return the arc cosine of x.");  static Py_complexc_acosh(Py_complex x){	Py_complex z;	z = c_sqrt(c_half);	z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x,c_one)),				  c_sqrt(c_diff(x,c_one)))));	return c_sum(z, z);} PyDoc_STRVAR(c_acosh_doc,"acosh(x)\n""\n""Return the hyperbolic arccosine of x.");  static Py_complexc_asin(Py_complex x){	/* -i * log[(sqrt(1-x**2) + i*x] */	const Py_complex squared = c_prod(x, x);	const Py_complex sqrt_1_minus_x_sq = c_sqrt(c_diff(c_one, squared));        return c_neg(c_prodi(c_log(        		c_sum(sqrt_1_minus_x_sq, c_prodi(x))		    )       )     );} PyDoc_STRVAR(c_asin_doc,"asin(x)\n""\n""Return the arc sine of x.");  static Py_complexc_asinh(Py_complex x){	Py_complex z;	z = c_sqrt(c_half);	z = c_log(c_prod(z, c_sum(c_sqrt(c_sum(x, c_i)),				  c_sqrt(c_diff(x, c_i)))));	return c_sum(z, z);} PyDoc_STRVAR(c_asinh_doc,"asinh(x)\n""\n""Return the hyperbolic arc sine of x.");  static Py_complexc_atan(Py_complex x){	return c_prod(c_halfi,c_log(c_quot(c_sum(c_i,x),c_diff(c_i,x))));} PyDoc_STRVAR(c_atan_doc,"atan(x)\n""\n""Return the arc tangent of x.");  static Py_complexc_atanh(Py_complex x){	return c_prod(c_half,c_log(c_quot(c_sum(c_one,x),c_diff(c_one,x))));} PyDoc_STRVAR(c_atanh_doc,"atanh(x)\n""\n""Return the hyperbolic arc tangent of x.");  static Py_complexc_cos(Py_complex x){	Py_complex r;	r.real = cos(x.real)*cosh(x.imag);	r.imag = -sin(x.real)*sinh(x.imag);	return r;} PyDoc_STRVAR(c_cos_doc,"cos(x)\n""n""Return the cosine of x.");  static Py_complexc_cosh(Py_complex x){	Py_complex r;	r.real = cos(x.imag)*cosh(x.real);	r.imag = sin(x.imag)*sinh(x.real);	return r;} PyDoc_STRVAR(c_cosh_doc,"cosh(x)\n""n""Return the hyperbolic cosine of x.");  static Py_complexc_exp(Py_complex x){	Py_complex r;	double l = exp(x.real);	r.real = l*cos(x.imag);	r.imag = l*sin(x.imag);	return r;} PyDoc_STRVAR(c_exp_doc,"exp(x)\n""\n""Return the exponential value e**x.");  static Py_complexc_log(Py_complex x){	Py_complex r;	double l = hypot(x.real,x.imag);	r.imag = atan2(x.imag, x.real);	r.real = log(l);	return r;}  static Py_complexc_log10(Py_complex x){	Py_complex r;	double l = hypot(x.real,x.imag);	r.imag = atan2(x.imag, x.real)/log(10.);	r.real = log10(l);	return r;} PyDoc_STRVAR(c_log10_doc,"log10(x)\n""\n""Return the base-10 logarithm of x.");  /* internal function not available from Python */static Py_complexc_prodi(Py_complex x){	Py_complex r;	r.real = -x.imag;	r.imag = x.real;	return r;}  static Py_complexc_sin(Py_complex x){	Py_complex r;	r.real = sin(x.real) * cosh(x.imag);	r.imag = cos(x.real) * sinh(x.imag);	return r;} PyDoc_STRVAR(c_sin_doc,"sin(x)\n""\n""Return the sine of x.");  static Py_complexc_sinh(Py_complex x){	Py_complex r;	r.real = cos(x.imag) * sinh(x.real);	r.imag = sin(x.imag) * cosh(x.real);	return r;} PyDoc_STRVAR(c_sinh_doc,"sinh(x)\n""\n""Return the hyperbolic sine of x.");  static Py_complexc_sqrt(Py_complex x){	Py_complex r;	double s,d;	if (x.real == 0. && x.imag == 0.)		r = x;	else {		s = sqrt(0.5*(fabs(x.real) + hypot(x.real,x.imag)));		d = 0.5*x.imag/s;		if (x.real > 0.) {			r.real = s;			r.imag = d;		}		else if (x.imag >= 0.) {			r.real = d;			r.imag = s;		}		else {			r.real = -d;			r.imag = -s;		}	}	return r;} PyDoc_STRVAR(c_sqrt_doc,"sqrt(x)\n""\n""Return the square root of x.");  static Py_complexc_tan(Py_complex x){	Py_complex r;	double sr,cr,shi,chi;	double rs,is,rc,ic;	double d;	sr = sin(x.real);	cr = cos(x.real);	shi = sinh(x.imag);	chi = cosh(x.imag);	rs = sr * chi;	is = cr * shi;	rc = cr * chi;	ic = -sr * shi;	d = rc*rc + ic * ic;	r.real = (rs*rc + is*ic) / d;	r.imag = (is*rc - rs*ic) / d;	return r;} PyDoc_STRVAR(c_tan_doc,"tan(x)\n""\n""Return the tangent of x.");  static Py_complexc_tanh(Py_complex x){	Py_complex r;	double si,ci,shr,chr;	double rs,is,rc,ic;	double d;	si = sin(x.imag);	ci = cos(x.imag);	shr = sinh(x.real);	chr = cosh(x.real);	rs = ci * shr;	is = si * chr;	rc = ci * chr;	ic = si * shr;	d = rc*rc + ic*ic;	r.real = (rs*rc + is*ic) / d;	r.imag = (is*rc - rs*ic) / d;	return r;} PyDoc_STRVAR(c_tanh_doc,"tanh(x)\n""\n""Return the hyperbolic tangent of x."); static PyObject *cmath_log(PyObject *self, PyObject *args){	Py_complex x;	Py_complex y; 	if (!PyArg_ParseTuple(args, "D|D", &x, &y))		return NULL; 	errno = 0;	PyFPE_START_PROTECT("complex function", return 0)	x = c_log(x);	if (PyTuple_GET_SIZE(args) == 2)		x = c_quot(x, c_log(y));	PyFPE_END_PROTECT(x)	if (errno != 0)		return math_error();	Py_ADJUST_ERANGE2(x.real, x.imag);	return PyComplex_FromCComplex(x);} PyDoc_STRVAR(cmath_log_doc,"log(x[, base]) -> the logarithm of x to the given base.\n\If the base not specified, returns the natural logarithm (base e) of x.");  /* And now the glue to make them available from Python: */ static PyObject *math_error(void){	if (errno == EDOM)		PyErr_SetString(PyExc_ValueError, "math domain error");	else if (errno == ERANGE)		PyErr_SetString(PyExc_OverflowError, "math range error");	else    /* Unexpected math error */		PyErr_SetFromErrno(PyExc_ValueError);	return NULL;} static PyObject *math_1(PyObject *args, Py_complex (*func)(Py_complex)){	Py_complex x;	if (!PyArg_ParseTuple(args, "D", &x))		return NULL;	errno = 0;	PyFPE_START_PROTECT("complex function", return 0)	x = (*func)(x);	PyFPE_END_PROTECT(x)	Py_ADJUST_ERANGE2(x.real, x.imag);	if (errno != 0)		return math_error();	else		return PyComplex_FromCComplex(x);} #define FUNC1(stubname, func) \	static PyObject * stubname(PyObject *self, PyObject *args) { \		return math_1(args, func); \	} FUNC1(cmath_acos, c_acos)FUNC1(cmath_acosh, c_acosh)FUNC1(cmath_asin, c_asin)FUNC1(cmath_asinh, c_asinh)FUNC1(cmath_atan, c_atan)FUNC1(cmath_atanh, c_atanh)FUNC1(cmath_cos, c_cos)FUNC1(cmath_cosh, c_cosh)FUNC1(cmath_exp, c_exp)FUNC1(cmath_log10, c_log10)FUNC1(cmath_sin, c_sin)FUNC1(cmath_sinh, c_sinh)FUNC1(cmath_sqrt, c_sqrt)FUNC1(cmath_tan, c_tan)FUNC1(cmath_tanh, c_tanh)  PyDoc_STRVAR(module_doc,"This module is always available. It provides access to mathematical\n""functions for complex numbers."); static PyMethodDef cmath_methods[] = {	{"acos",   cmath_acos,  METH_VARARGS, c_acos_doc},	{"acosh",  cmath_acosh, METH_VARARGS, c_acosh_doc},	{"asin",   cmath_asin,  METH_VARARGS, c_asin_doc},	{"asinh",  cmath_asinh, METH_VARARGS, c_asinh_doc},	{"atan",   cmath_atan,  METH_VARARGS, c_atan_doc},	{"atanh",  cmath_atanh, METH_VARARGS, c_atanh_doc},	{"cos",    cmath_cos,   METH_VARARGS, c_cos_doc},	{"cosh",   cmath_cosh,  METH_VARARGS, c_cosh_doc},	{"exp",    cmath_exp,   METH_VARARGS, c_exp_doc},	{"log",    cmath_log,   METH_VARARGS, cmath_log_doc},	{"log10",  cmath_log10, METH_VARARGS, c_log10_doc},	{"sin",    cmath_sin,   METH_VARARGS, c_sin_doc},	{"sinh",   cmath_sinh,  METH_VARARGS, c_sinh_doc},	{"sqrt",   cmath_sqrt,  METH_VARARGS, c_sqrt_doc},	{"tan",    cmath_tan,   METH_VARARGS, c_tan_doc},	{"tanh",   cmath_tanh,  METH_VARARGS, c_tanh_doc},	{NULL,		NULL}		/* sentinel */}; PyMODINIT_FUNCinitcmath(void){	PyObject *m; 	m = Py_InitModule3("cmath", cmath_methods, module_doc);	if (m == NULL)		return; 	PyModule_AddObject(m, "pi",                           PyFloat_FromDouble(atan(1.0) * 4.0));	PyModule_AddObject(m, "e", PyFloat_FromDouble(exp(1.0)));}