complex numbers a la Konrad Hinsen

1 files changed, 562 insertions, 0 deletions

diff --git a/Objects/complexobject.c b/Objects/complexobject.c
new file mode 100644
index 0000000..8299b0b
--- /dev/null
+++ b/Objects/complexobject.c
@@ -0,0 +1,562 @@
+/* Complex object implementation */
+
+/* Borrows heavily from floatobject.c */
+
+#ifndef WITHOUT_COMPLEX
+
+#include "allobjects.h"
+#include "modsupport.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
+
+#ifdef HAVE_LIMITS_H
+#include <limits.h>
+#endif
+
+#ifndef LONG_MAX
+#define LONG_MAX 0X7FFFFFFFL
+#endif
+
+#ifndef LONG_MIN
+#define LONG_MIN (-LONG_MAX-1)
+#endif
+
+#ifdef __NeXT__
+#ifdef __sparc__
+/*
+ * This works around a bug in the NS/Sparc 3.3 pre-release
+ * limits.h header file.
+ * 10-Feb-1995 bwarsaw@cnri.reston.va.us
+ */
+#undef LONG_MIN
+#define LONG_MIN (-LONG_MAX-1)
+#endif
+#endif
+
+#if !defined(__STDC__) && !defined(macintosh)
+extern double fmod PROTO((double, double));
+extern double pow PROTO((double, double));
+#endif
+
+
+/* elementary operations on complex numbers */
+
+int c_error;
+static complex c_1 = {1., 0.};
+
+complex c_sum(a,b)
+	complex a,b;
+{
+	complex r;
+	r.real = a.real + b.real;
+	r.imag = a.imag + b.imag;
+	return r;
+}
+
+complex c_diff(a,b)
+	complex a,b;
+{
+	complex r;
+	r.real = a.real - b.real;
+	r.imag = a.imag - b.imag;
+	return r;
+}
+
+complex c_neg(a)
+	complex a;
+{
+	complex r;
+	r.real = -a.real;
+	r.imag = -a.imag;
+	return r;
+}
+
+complex c_prod(a,b)
+	complex a,b;
+{
+	complex r;
+	r.real = a.real*b.real - a.imag*b.imag;
+	r.imag = a.real*b.imag + a.imag*b.real;
+	return r;
+}
+
+complex c_quot(a,b)
+	complex a,b;
+{
+	complex r;
+	double d = b.real*b.real + b.imag*b.imag;
+	if (d == 0.)
+		c_error = 1;
+	r.real = (a.real*b.real + a.imag*b.imag)/d;
+	r.imag = (a.imag*b.real - a.real*b.imag)/d;
+	return r;
+}
+
+complex c_pow(a,b)
+	complex a,b;
+{
+	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.)
+			c_error = 2;
+		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;
+}
+
+complex c_powu(x, n)
+	complex x;
+	long n;
+{
+	complex r = c_1;
+	complex p = x;
+	long mask = 1;
+	while (mask > 0 && n >= mask) {
+		if (n & mask)
+			r = c_prod(r,p);
+		mask <<= 1;
+		p = c_prod(p,p);
+	}
+	return r;
+}
+
+complex c_powi(x, n)
+	complex x;
+	long n;
+{
+	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(complex cval)
+{
+	register complexobject *op = (complexobject *) malloc(sizeof(complexobject));
+	if (op == NULL)
+		return err_nomem();
+	op->ob_type = &Complextype;
+	op->cval = cval;
+	NEWREF(op);
+	return (object *) op;
+}
+
+PyObject *
+PyComplex_FromDoubles(double real, double imag) {
+  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;
+  }
+}
+
+static void
+complex_dealloc(op)
+	object *op;
+{
+	DEL(op);
+}
+
+
+void
+complex_buf_repr(buf, v)
+	char *buf;
+	complexobject *v;
+{
+	if (v->cval.real == 0.)
+		sprintf(buf, "%.12gi", v->cval.imag);
+	else
+		sprintf(buf, "(%.12g%+.12gi)", v->cval.real, v->cval.imag);
+}
+
+static int
+complex_print(v, fp, flags)
+	complexobject *v;
+	FILE *fp;
+	int flags; /* Not used but required by interface */
+{
+	char buf[100];
+	complex_buf_repr(buf, v);
+	fputs(buf, fp);
+	return 0;
+}
+
+static object *
+complex_repr(v)
+	complexobject *v;
+{
+	char buf[100];
+	complex_buf_repr(buf, v);
+	return newstringobject(buf);
+}
+
+static int
+complex_compare(v, w)
+	complexobject *v, *w;
+{
+/* Note: "greater" and "smaller" have no meaning for complex numbers,
+   but Python requires that they be defined nevertheless. */
+	complex i = v->cval;
+	complex 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(v)
+	complexobject *v;
+{
+	double intpart, fractpart;
+	int expo;
+	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) {
+		if (intpart > 0x7fffffffL || -intpart > 0x7fffffffL) {
+			/* Convert to long int and use its hash... */
+			object *w = dnewlongobject(v->cval.real);
+			if (w == NULL)
+				return -1;
+			x = hashobject(w);
+			DECREF(w);
+			return x;
+		}
+		x = (long)intpart;
+	}
+	else {
+		fractpart = frexp(fractpart, &expo);
+		fractpart = fractpart*2147483648.0; /* 2**31 */
+		x = (long) (intpart + fractpart) ^ expo; /* Rather arbitrary */
+	}
+	if (x == -1)
+		x = -2;
+	return x;
+}
+
+static object *
+complex_add(v, w)
+	complexobject *v;
+	complexobject *w;
+{
+	return newcomplexobject(c_sum(v->cval,w->cval));
+}
+
+static object *
+complex_sub(v, w)
+	complexobject *v;
+	complexobject *w;
+{
+	return newcomplexobject(c_diff(v->cval,w->cval));
+}
+
+static object *
+complex_mul(v, w)
+	complexobject *v;
+	complexobject *w;
+{
+	return newcomplexobject(c_prod(v->cval,w->cval));
+}
+
+static object *
+complex_div(v, w)
+	complexobject *v;
+	complexobject *w;
+{
+	complex quot;
+	c_error = 0;
+	quot = c_quot(v->cval,w->cval);
+	if (c_error == 1) {
+		err_setstr(ZeroDivisionError, "float division");
+		return NULL;
+	}
+	return newcomplexobject(quot);
+}
+
+
+static object *
+complex_pow(v, w, z)
+	complexobject *v;
+	object *w;
+	complexobject *z;
+{
+	complex p;
+	complex exponent;
+	long int_exponent;
+
+ 	if ((object *)z!=None) {
+		err_setstr(ValueError, "complex modulo");
+		return NULL;
+	}
+
+	c_error = 0;
+	exponent = ((complexobject*)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);
+
+	if (c_error == 2) {
+		err_setstr(ValueError, "0.0 to a negative or complex power");
+		return NULL;
+	}
+
+	return newcomplexobject(p);
+}
+
+static object *
+complex_neg(v)
+	complexobject *v;
+{
+	complex neg;
+	neg.real = -v->cval.real;
+	neg.imag = -v->cval.imag;
+	return newcomplexobject(neg);
+}
+
+static object *
+complex_pos(v)
+	complexobject *v;
+{
+	INCREF(v);
+	return (object *)v;
+}
+
+static object *
+complex_abs(v)
+	complexobject *v;
+{
+	return newfloatobject(hypot(v->cval.real,v->cval.imag));
+}
+
+static int
+complex_nonzero(v)
+	complexobject *v;
+{
+	return v->cval.real != 0.0 && v->cval.imag != 0.0;
+}
+
+static int
+complex_coerce(pv, pw)
+	object **pv;
+	object **pw;
+{
+	complex cval;
+	cval.imag = 0.;
+	if (is_intobject(*pw)) {
+		cval.real = (double)getintvalue(*pw);
+		*pw = newcomplexobject(cval);
+		INCREF(*pv);
+		return 0;
+	}
+	else if (is_longobject(*pw)) {
+		cval.real = dgetlongvalue(*pw);
+		*pw = newcomplexobject(cval);
+		INCREF(*pv);
+		return 0;
+	}
+	else if (is_floatobject(*pw)) {
+		cval.real = getfloatvalue(*pw);
+		*pw = newcomplexobject(cval);
+		INCREF(*pv);
+		return 0;
+	}
+	return 1; /* Can't do it */
+}
+
+static object *
+complex_int(v)
+	object *v;
+{
+	double x = ((complexobject *)v)->cval.real;
+	if (x < 0 ? (x = ceil(x)) < (double)LONG_MIN
+	          : (x = floor(x)) > (double)LONG_MAX) {
+		err_setstr(OverflowError, "float too large to convert");
+		return NULL;
+	}
+	return newintobject((long)x);
+}
+
+static object *
+complex_long(v)
+	object *v;
+{
+	double x = ((complexobject *)v)->cval.real;
+	return dnewlongobject(x);
+}
+
+static object *
+complex_float(v)
+	object *v;
+{
+	double x = ((complexobject *)v)->cval.real;
+	return newfloatobject(x);
+}
+
+
+static object *
+complex_new(self, args)
+	object *self;
+	object *args;
+{
+	int n;
+	complex cval;
+
+	cval.imag = 0.;
+	if (!PyArg_ParseTuple(args, "d|d", &cval.real, &cval.imag))
+		return NULL;
+	return newcomplexobject(cval);
+}
+
+static object *
+complex_conjugate(self)
+	object *self;
+{
+	complex c = ((complexobject *)self)->cval;
+	c.imag = -c.imag;
+	return newcomplexobject(c);
+}
+
+static PyMethodDef complex_methods[] = {
+	{"conjugate",	(PyCFunction)complex_conjugate,	1},
+	{NULL,		NULL}		/* sentinel */
+};
+
+
+static object *
+complex_getattr(self, name)
+	complexobject *self;
+	char *name;
+{
+	complex cval;
+	if (strcmp(name, "real") == 0)
+		return (object *)newfloatobject(self->cval.real);
+	else if (strcmp(name, "imag") == 0)
+		return (object *)newfloatobject(self->cval.imag);
+	else if (strcmp(name, "conj") == 0) {
+		cval.real = self->cval.real;
+		cval.imag = -self->cval.imag;
+		return (object *)newcomplexobject(cval);
+	}
+	return findmethod(complex_methods, (object *)self, name);
+}
+
+static number_methods complex_as_number = {
+	(binaryfunc)complex_add, /*nb_add*/
+	(binaryfunc)complex_sub, /*nb_subtract*/
+	(binaryfunc)complex_mul, /*nb_multiply*/
+	(binaryfunc)complex_div, /*nb_divide*/
+	0,		/*nb_remainder*/
+	0,		/*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*/
+};
+
+typeobject Complextype = {
+	OB_HEAD_INIT(&Typetype)
+	0,
+	"complex",
+	sizeof(complexobject),
+	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