complex math

Modules/cmathmodule.c

+/* Complex math module */
+
+/* much code borrowed from mathmodule.c */
+
+#include "allobjects.h"
+#include "complexobject.h"
+
+#include <errno.h>
+
+#include "mymath.h"
+
+#ifdef i860
+/* Cray APP has bogus definition of HUGE_VAL in <math.h> */
+#undef HUGE_VAL
+#endif
+
+#ifdef HUGE_VAL
+#define CHECK(x) if (errno != 0) ; \
+	else if (-HUGE_VAL <= (x) && (x) <= HUGE_VAL) ; \
+	else errno = ERANGE
+#else
+#define CHECK(x) /* Don't know how to check */
+#endif
+
+#ifndef M_PI
+#define M_PI (3.141592653589793239)
+#endif
+
+/* First, the C functions that do the real work */
+
+/* constants */
+static complex c_1 = {1., 0.};
+static complex c_half = {0.5, 0.};
+static complex c_i = {0., 1.};
+static complex c_i2 = {0., 0.5};
+static complex c_mi = {0., -1.};
+static complex c_pi2 = {M_PI/2., 0.};
+
+/* forward declarations */
+complex c_log();
+complex c_prodi();
+complex c_sqrt();
+
+
+complex c_acos(x)
+	complex x;
+{
+	return c_neg(c_prodi(c_log(c_sum(x,c_prod(c_i,
+		    c_sqrt(c_diff(c_1,c_prod(x,x))))))));
+}
+
+complex c_acosh(x)
+	complex x;
+{
+	return c_log(c_sum(x,c_prod(c_i,
+		    c_sqrt(c_diff(c_1,c_prod(x,x))))));
+}
+
+complex c_asin(x)
+	complex x;
+{
+	return c_neg(c_prodi(c_log(c_sum(c_prod(c_i,x),
+		    c_sqrt(c_diff(c_1,c_prod(x,x)))))));
+}
+
+complex c_asinh(x)
+	complex x;
+{
+	return c_neg(c_log(c_diff(c_sqrt(c_sum(c_1,c_prod(x,x))),x)));
+}
+
+complex c_atan(x)
+	complex x;
+{
+	return c_prod(c_i2,c_log(c_quot(c_sum(c_i,x),c_diff(c_i,x))));
+}
+
+complex c_atanh(x)
+	complex x;
+{
+	return c_prod(c_half,c_log(c_quot(c_sum(c_1,x),c_diff(c_1,x))));
+}
+
+complex c_cos(x)
+	complex x;
+{
+	complex r;
+	r.real = cos(x.real)*cosh(x.imag);
+	r.imag = -sin(x.real)*sinh(x.imag);
+	return r;
+}
+
+complex c_cosh(x)
+	complex x;
+{
+	complex r;
+	r.real = cos(x.imag)*cosh(x.real);
+	r.imag = sin(x.imag)*sinh(x.real);
+	return r;
+}
+
+complex c_exp(x)
+	complex x;
+{
+	complex r;
+	double l = exp(x.real);
+	r.real = l*cos(x.imag);
+	r.imag = l*sin(x.imag);
+	return r;
+}
+
+complex c_log(x)
+	complex x;
+{
+	complex r;
+	double l = hypot(x.real,x.imag);
+	r.imag = atan2(x.imag, x.real);
+	r.real = log(l);
+	return r;
+}
+
+complex c_log10(x)
+	complex x;
+{
+	complex r;
+	double l = hypot(x.real,x.imag);
+	r.imag = atan2(x.imag, x.real)/log(10.);
+	r.real = log10(l);
+	return r;
+}
+
+complex c_prodi(x)
+     complex x;
+{
+	complex r;
+	r.real = -x.imag;
+	r.imag = x.real;
+	return r;
+}
+
+complex c_sin(x)
+	complex x;
+{
+	complex r;
+	r.real = sin(x.real)*cosh(x.imag);
+	r.imag = cos(x.real)*sinh(x.imag);
+	return r;
+}
+
+complex c_sinh(x)
+	complex x;
+{
+	complex r;
+	r.real = cos(x.imag)*sinh(x.real);
+	r.imag = sin(x.imag)*cosh(x.real);
+	return r;
+}
+
+complex c_sqrt(x)
+	complex x;
+{
+	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;
+}
+
+complex c_tan(x)
+	complex x;
+{
+	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;
+}
+
+complex c_tanh(x)
+	complex x;
+{
+	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;
+}
+
+
+/* And now the glue to make them available from Python: */
+
+static object *
+math_error()
+{
+	if (errno == EDOM)
+		err_setstr(ValueError, "math domain error");
+	else if (errno == ERANGE)
+		err_setstr(OverflowError, "math range error");
+	else
+		err_errno(ValueError); /* Unexpected math error */
+	return NULL;
+}
+
+static object *
+math_1(args, func)
+	object *args;
+	complex (*func) FPROTO((complex));
+{
+	complex x;
+	if (!PyArg_ParseTuple(args, "D", &x))
+		return NULL;
+	errno = 0;
+	x = (*func)(x);
+	CHECK(x.real);
+	CHECK(x.imag);
+	if (errno != 0)
+		return math_error();
+	else
+		return newcomplexobject(x);
+}
+
+#define FUNC1(stubname, func) \
+	static object * stubname(self, args) object *self, *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_log, c_log)
+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)
+
+
+static struct methodlist cmath_methods[] = {
+	{"acos", cmath_acos, 1},
+	{"acosh", cmath_acosh, 1},
+	{"asin", cmath_asin, 1},
+	{"asinh", cmath_asinh, 1},
+	{"atan", cmath_atan, 1},
+	{"atanh", cmath_atanh, 1},
+	{"cos", cmath_cos, 1},
+	{"cosh", cmath_cosh, 1},
+	{"exp", cmath_exp, 1},
+	{"log", cmath_log, 1},
+	{"log10", cmath_log10, 1},
+	{"sin", cmath_sin, 1},
+	{"sinh", cmath_sinh, 1},
+	{"sqrt", cmath_sqrt, 1},
+	{"tan", cmath_tan, 1},
+	{"tanh", cmath_tanh, 1},
+	{NULL,		NULL}		/* sentinel */
+};
+
+void
+initcmath()
+{
+	object *m, *d, *v;
+	
+	m = Py_InitModule("cmath", cmath_methods);
+	d = getmoduledict(m);
+	dictinsert(d, "pi", v = newfloatobject(atan(1.0) * 4.0));
+	DECREF(v);
+	dictinsert(d, "e", v = newfloatobject(exp(1.0)));
+	DECREF(v);
+}