copy complexobject.cpp from CPython and enable cmath module

from_cpython/CMakeLists.txt

@@ -36,6 +36,7 @@ file(GLOB_RECURSE STDMODULE_SRCS Modules
     bufferedio.c
     bytesio.c
     cache.c
+    cmathmodule.c
     connection.c
     cStringIO.c
     cursor.c
@@ -83,6 +84,7 @@ file(GLOB_RECURSE STDOBJECT_SRCS Objects
     bytes_methods.c
     capsule.c
     cobject.c
+    complexobject.c
     dictproxy.c
     exceptions.c
     floatobject.c

from_cpython/Objects/complexobject.c

+
+/* Complex object implementation */
+
+/* Borrows heavily from floatobject.c */
+
+/* Submitted by Jim Hugunin */
+
+#include "Python.h"
+#include "structmember.h"
+
+#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;
+    }
+}
+
+static PyObject *
+try_complex_special_method(PyObject *op) {
+    PyObject *f;
+    static PyObject *complexstr;
+
+    if (complexstr == NULL) {
+        complexstr = PyString_InternFromString("__complex__");
+        if (complexstr == NULL)
+            return NULL;
+    }
+    if (PyInstance_Check(op)) {
+        f = PyObject_GetAttr(op, complexstr);
+        if (f == NULL) {
+            if (PyErr_ExceptionMatches(PyExc_AttributeError))
+                PyErr_Clear();
+            else
+                return NULL;
+        }
+    }
+    else {
+        f = _PyObject_LookupSpecial(op, "__complex__", &complexstr);
+        if (f == NULL && PyErr_Occurred())
+            return NULL;
+    }
+    if (f != NULL) {
+        PyObject *res = PyObject_CallFunctionObjArgs(f, NULL);
+        Py_DECREF(f);
+        return res;
+    }
+    return NULL;
+}
+
+Py_complex
+PyComplex_AsCComplex(PyObject *op)
+{
+    Py_complex cv;
+    PyObject *newop = 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.;
+
+    newop = try_complex_special_method(op);
+
+    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;
+    }
+    else if (PyErr_Occurred()) {
+        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 PyObject *
+complex_format(PyComplexObject *v, int precision, char format_code)
+{
+    PyObject *result = NULL;
+    Py_ssize_t len;
+
+    /* If these are non-NULL, they'll need to be freed. */
+    char *pre = NULL;
+    char *im = NULL;
+    char *buf = NULL;
+
+    /* These do not need to be freed. re is either an alias
+       for pre or a pointer to a constant.  lead and tail
+       are pointers to constants. */
+    char *re = NULL;
+    char *lead = "";
+    char *tail = "";
+
+    if (v->cval.real == 0. && copysign(1.0, v->cval.real)==1.0) {
+        re = "";
+        im = PyOS_double_to_string(v->cval.imag, format_code,
+                                   precision, 0, NULL);
+        if (!im) {
+            PyErr_NoMemory();
+            goto done;
+        }
+    } else {
+        /* Format imaginary part with sign, real part without */
+        pre = PyOS_double_to_string(v->cval.real, format_code,
+                                    precision, 0, NULL);
+        if (!pre) {
+            PyErr_NoMemory();
+            goto done;
+        }
+        re = pre;
+
+        im = PyOS_double_to_string(v->cval.imag, format_code,
+                                   precision, Py_DTSF_SIGN, NULL);
+        if (!im) {
+            PyErr_NoMemory();
+            goto done;
+        }
+        lead = "(";
+        tail = ")";
+    }
+    /* Alloc the final buffer. Add one for the "j" in the format string,
+       and one for the trailing zero. */
+    len = strlen(lead) + strlen(re) + strlen(im) + strlen(tail) + 2;
+    buf = PyMem_Malloc(len);
+    if (!buf) {
+        PyErr_NoMemory();
+        goto done;
+    }
+    PyOS_snprintf(buf, len, "%s%s%sj%s", lead, re, im, tail);
+    result = PyString_FromString(buf);
+  done:
+    PyMem_Free(im);
+    PyMem_Free(pre);
+    PyMem_Free(buf);
+
+    return result;
+}
+
+static int
+complex_print(PyComplexObject *v, FILE *fp, int flags)
+{
+    PyObject *formatv;
+    char *buf;
+    if (flags & Py_PRINT_RAW)
+        formatv = complex_format(v, PyFloat_STR_PRECISION, 'g');
+    else
+        formatv = complex_format(v, 0, 'r');
+    if (formatv == NULL)
+        return -1;
+    buf = PyString_AS_STRING(formatv);
+    Py_BEGIN_ALLOW_THREADS
+    fputs(buf, fp);
+    Py_END_ALLOW_THREADS
+    Py_DECREF(formatv);
+    return 0;
+}
+
+static PyObject *
+complex_repr(PyComplexObject *v)
+{
+    return complex_format(v, 0, 'r');
+}
+
+static PyObject *
+complex_str(PyComplexObject *v)
+{
+    return complex_format(v, PyFloat_STR_PRECISION, 'g');
+}
+
+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(PyObject *v, PyObject *w)
+{
+    Py_complex result;
+    Py_complex a, b;
+    TO_COMPLEX(v, a);
+    TO_COMPLEX(w, b);
+    PyFPE_START_PROTECT("complex_add", return 0)
+    result = c_sum(a, b);
+    PyFPE_END_PROTECT(result)
+    return PyComplex_FromCComplex(result);
+}
+
+static PyObject *
+complex_sub(PyObject *v, PyObject *w)
+{
+    Py_complex result;
+    Py_complex a, b;
+    TO_COMPLEX(v, a);
+    TO_COMPLEX(w, b);;
+    PyFPE_START_PROTECT("complex_sub", return 0)
+    result = c_diff(a, b);
+    PyFPE_END_PROTECT(result)
+    return PyComplex_FromCComplex(result);
+}
+
+static PyObject *
+complex_mul(PyObject *v, PyObject *w)
+{
+    Py_complex result;
+    Py_complex a, b;
+    TO_COMPLEX(v, a);
+    TO_COMPLEX(w, b);
+    PyFPE_START_PROTECT("complex_mul", return 0)
+    result = c_prod(a, b);
+    PyFPE_END_PROTECT(result)
+    return PyComplex_FromCComplex(result);
+}
+
+static PyObject *
+complex_div(PyObject *v, PyObject *w)
+{
+    Py_complex quot;
+    Py_complex a, b;
+    TO_COMPLEX(v, a);
+    TO_COMPLEX(w, b);
+    PyFPE_START_PROTECT("complex_div", return 0)
+    errno = 0;
+    quot = c_quot(a, b);
+    PyFPE_END_PROTECT(quot)
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ZeroDivisionError, "complex division by zero");
+        return NULL;
+    }
+    return PyComplex_FromCComplex(quot);
+}
+
+static PyObject *
+complex_classic_div(PyObject *v, PyObject *w)
+{
+    Py_complex quot;
+    Py_complex a, b;
+    TO_COMPLEX(v, a);
+    TO_COMPLEX(w, b);
+    if (Py_DivisionWarningFlag >= 2 &&
+        PyErr_Warn(PyExc_DeprecationWarning,
+                   "classic complex division") < 0)
+        return NULL;
+
+    PyFPE_START_PROTECT("complex_classic_div", return 0)
+    errno = 0;
+    quot = c_quot(a, b);
+    PyFPE_END_PROTECT(quot)
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ZeroDivisionError, "complex division by zero");
+        return NULL;
+    }
+    return PyComplex_FromCComplex(quot);
+}
+
+static PyObject *
+complex_remainder(PyObject *v, PyObject *w)
+{
+    Py_complex div, mod;
+    Py_complex a, b;
+    TO_COMPLEX(v, a);
+    TO_COMPLEX(w, b);
+    if (PyErr_Warn(PyExc_DeprecationWarning,
+                   "complex divmod(), // and % are deprecated") < 0)
+        return NULL;
+
+    errno = 0;
+    div = c_quot(a, b); /* 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(a, c_prod(b, div));
+
+    return PyComplex_FromCComplex(mod);
+}
+
+
+static PyObject *
+complex_divmod(PyObject *v, PyObject *w)
+{
+    Py_complex div, mod;
+    PyObject *d, *m, *z;
+    Py_complex a, b;
+    TO_COMPLEX(v, a);
+    TO_COMPLEX(w, b);
+    if (PyErr_Warn(PyExc_DeprecationWarning,
+                   "complex divmod(), // and % are deprecated") < 0)
+        return NULL;
+
+    errno = 0;
+    div = c_quot(a, b); /* 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(a, c_prod(b, div));
+    d = PyComplex_FromCComplex(div);
+    m = PyComplex_FromCComplex(mod);
+    z = PyTuple_Pack(2, d, m);
+    Py_XDECREF(d);
+    Py_XDECREF(m);
+    return z;
+}
+
+static PyObject *
+complex_pow(PyObject *v, PyObject *w, PyObject *z)
+{
+    Py_complex p;
+    Py_complex exponent;
+    long int_exponent;
+    Py_complex a, b;
+    TO_COMPLEX(v, a);
+    TO_COMPLEX(w, b);
+    if (z!=Py_None) {
+        PyErr_SetString(PyExc_ValueError, "complex modulo");
+        return NULL;
+    }
+    PyFPE_START_PROTECT("complex_pow", return 0)
+    errno = 0;
+    exponent = b;
+    int_exponent = (long)exponent.real;
+    if (exponent.imag == 0. && exponent.real == int_exponent)
+        p = c_powi(a,int_exponent);
+    else
+        p = c_pow(a,exponent);
+
+    PyFPE_END_PROTECT(p)
+    Py_ADJUST_ERANGE2(p.real, p.imag);
+    if (errno == EDOM) {
+        PyErr_SetString(PyExc_ZeroDivisionError,
+                        "0.0 to a negative or complex power");
+        return NULL;
+    }
+    else if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "complex exponentiation");
+        return NULL;
+    }
+    return PyComplex_FromCComplex(p);
+}
+
+static PyObject *
+complex_int_div(PyObject *v, PyObject *w)
+{
+    PyObject *t, *r;
+    Py_complex a, b;
+    TO_COMPLEX(v, a);
+    TO_COMPLEX(w, b);
+    if (PyErr_Warn(PyExc_DeprecationWarning,
+                   "complex divmod(), // and % are deprecated") < 0)
+        return NULL;
+
+    t = complex_divmod(v, w);
+    if (t != NULL) {
+        r = PyTuple_GET_ITEM(t, 0);
+        Py_INCREF(r);
+        Py_DECREF(t);
+        return r;
+    }
+    return NULL;
+}
+
+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)
+{
+    if (PyComplex_CheckExact(v)) {
+        Py_INCREF(v);
+        return (PyObject *)v;
+    }
+    else
+        return PyComplex_FromCComplex(v->cval);
+}
+
+static PyObject *
+complex_abs(PyComplexObject *v)
+{
+    double result;
+
+    PyFPE_START_PROTECT("complex_abs", return 0)
+    result = c_abs(v->cval);
+    PyFPE_END_PROTECT(result)
+
+    if (errno == ERANGE) {
+        PyErr_SetString(PyExc_OverflowError,
+                        "absolute value too large");
+        return NULL;
+    }
+    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);
+        if (cval.real == -1.0 && PyErr_Occurred())
+            return -1;
+        *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;
+    }
+    else if (PyComplex_Check(*pw)) {
+        Py_INCREF(*pv);
+        Py_INCREF(*pw);
+        return 0;
+    }
+    return 1; /* Can't do it */
+}
+
+static PyObject *
+complex_richcompare(PyObject *v, PyObject *w, int op)
+{
+    PyObject *res;
+    Py_complex i;
+    int equal;
+
+    if (op != Py_EQ && op != Py_NE) {
+        /* for backwards compatibility, comparisons with non-numbers return
+         * NotImplemented.  Only comparisons with core numeric types raise
+         * TypeError.
+         */
+        if (PyInt_Check(w) || PyLong_Check(w) ||
+            PyFloat_Check(w) || PyComplex_Check(w)) {
+            PyErr_SetString(PyExc_TypeError,
+                            "no ordering relation is defined "
+                            "for complex numbers");
+            return NULL;
+        }
+        goto Unimplemented;
+    }
+
+    assert(PyComplex_Check(v));
+    TO_COMPLEX(v, i);
+
+    if (PyInt_Check(w) || PyLong_Check(w)) {
+        /* Check for 0.0 imaginary part first to avoid the rich
+         * comparison when possible.
+         */
+        if (i.imag == 0.0) {
+            PyObject *j, *sub_res;
+            j = PyFloat_FromDouble(i.real);
+            if (j == NULL)
+                return NULL;
+
+            sub_res = PyObject_RichCompare(j, w, op);
+            Py_DECREF(j);
+            return sub_res;
+        }
+        else {
+            equal = 0;
+        }
+    }
+    else if (PyFloat_Check(w)) {
+        equal = (i.real == PyFloat_AsDouble(w) && i.imag == 0.0);
+    }
+    else if (PyComplex_Check(w)) {
+        Py_complex j;
+
+        TO_COMPLEX(w, j);
+        equal = (i.real == j.real && i.imag == j.imag);
+    }
+    else {
+        goto Unimplemented;
+    }
+
+    if (equal == (op == Py_EQ))
+         res = Py_True;
+    else
+         res = Py_False;
+
+    Py_INCREF(res);
+    return res;
+
+  Unimplemented:
+    Py_INCREF(Py_NotImplemented);
+    return Py_NotImplemented;
+}
+
+static PyObject *
+complex_int(PyObject *v)
+{
+    PyErr_SetString(PyExc_TypeError,
+               "can't convert complex to int");
+    return NULL;
+}
+
+static PyObject *
+complex_long(PyObject *v)
+{
+    PyErr_SetString(PyExc_TypeError,
+               "can't convert complex to long");
+    return NULL;
+}
+
+static PyObject *
+complex_float(PyObject *v)
+{
+    PyErr_SetString(PyExc_TypeError,
+               "can't convert complex to float");
+    return NULL;
+}
+
+static PyObject *
+complex_conjugate(PyObject *self)
+{
+    Py_complex c;
+    c = ((PyComplexObject *)self)->cval;
+    c.imag = -c.imag;
+    return PyComplex_FromCComplex(c);
+}
+
+PyDoc_STRVAR(complex_conjugate_doc,
+"complex.conjugate() -> complex\n"
+"\n"
+"Return the complex conjugate of its argument. (3-4j).conjugate() == 3+4j.");
+
+static PyObject *
+complex_getnewargs(PyComplexObject *v)
+{
+    Py_complex c = v->cval;
+    return Py_BuildValue("(dd)", c.real, c.imag);
+}
+
+PyDoc_STRVAR(complex__format__doc,
+"complex.__format__() -> str\n"
+"\n"
+"Convert to a string according to format_spec.");
+
+static PyObject *
+complex__format__(PyObject* self, PyObject* args)
+{
+    PyObject *format_spec;
+
+    if (!PyArg_ParseTuple(args, "O:__format__", &format_spec))
+    return NULL;
+    if (PyBytes_Check(format_spec))
+    return _PyComplex_FormatAdvanced(self,
+                                     PyBytes_AS_STRING(format_spec),
+                                     PyBytes_GET_SIZE(format_spec));
+    if (PyUnicode_Check(format_spec)) {
+    /* Convert format_spec to a str */
+    PyObject *result;
+    PyObject *str_spec = PyObject_Str(format_spec);
+
+    if (str_spec == NULL)
+        return NULL;
+
+    result = _PyComplex_FormatAdvanced(self,
+                                       PyBytes_AS_STRING(str_spec),
+                                       PyBytes_GET_SIZE(str_spec));
+
+    Py_DECREF(str_spec);
+    return result;
+    }
+    PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode");
+    return NULL;
+}
+
+#if 0
+static PyObject *
+complex_is_finite(PyObject *self)
+{
+    Py_complex c;
+    c = ((PyComplexObject *)self)->cval;
+    return PyBool_FromLong((long)(Py_IS_FINITE(c.real) &&
+                                  Py_IS_FINITE(c.imag)));
+}
+
+PyDoc_STRVAR(complex_is_finite_doc,
+"complex.is_finite() -> bool\n"
+"\n"
+"Returns True if the real and the imaginary part is finite.");
+#endif
+
+static PyMethodDef complex_methods[] = {
+    {"conjugate",       (PyCFunction)complex_conjugate, METH_NOARGS,
+     complex_conjugate_doc},
+#if 0
+    {"is_finite",       (PyCFunction)complex_is_finite, METH_NOARGS,
+     complex_is_finite_doc},
+#endif
+    {"__getnewargs__",          (PyCFunction)complex_getnewargs,        METH_NOARGS},
+    {"__format__",          (PyCFunction)complex__format__,
+                                       METH_VARARGS, complex__format__doc},
+    {NULL,              NULL}           /* sentinel */
+};
+
+static PyMemberDef complex_members[] = {
+    {"real", T_DOUBLE, offsetof(PyComplexObject, cval.real), READONLY,
+     "the real part of a complex number"},
+    {"imag", T_DOUBLE, offsetof(PyComplexObject, cval.imag), READONLY,
+     "the imaginary part of a complex number"},
+    {0},
+};
+
+static PyObject *
+complex_subtype_from_string(PyTypeObject *type, PyObject *v)
+{
+    const char *s, *start;
+    char *end;
+    double x=0.0, y=0.0, z;
+    int got_bracket=0;
+#ifdef Py_USING_UNICODE
+    char *s_buffer = NULL;
+#endif
+    Py_ssize_t len;
+
+    if (PyString_Check(v)) {
+        s = PyString_AS_STRING(v);
+        len = PyString_GET_SIZE(v);
+    }
+#ifdef Py_USING_UNICODE
+    else if (PyUnicode_Check(v)) {
+        s_buffer = (char *)PyMem_MALLOC(PyUnicode_GET_SIZE(v)+1);
+        if (s_buffer == NULL)
+            return PyErr_NoMemory();
+        if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v),
+                                    PyUnicode_GET_SIZE(v),
+                                    s_buffer,
+                                    NULL))
+            goto error;
+        s = s_buffer;
+        len = strlen(s);
+    }
+#endif
+    else if (PyObject_AsCharBuffer(v, &s, &len)) {
+        PyErr_SetString(PyExc_TypeError,
+                        "complex() arg is not a string");
+        return NULL;
+    }
+
+    /* position on first nonblank */
+    start = s;
+    while (Py_ISSPACE(*s))
+        s++;
+    if (*s == '(') {
+        /* Skip over possible bracket from repr(). */
+        got_bracket = 1;
+        s++;
+        while (Py_ISSPACE(*s))
+            s++;
+    }
+
+    /* a valid complex string usually takes one of the three forms:
+
+         <float>                  - real part only
+         <float>j                 - imaginary part only
+         <float><signed-float>j   - real and imaginary parts
+
+       where <float> represents any numeric string that's accepted by the
+       float constructor (including 'nan', 'inf', 'infinity', etc.), and
+       <signed-float> is any string of the form <float> whose first
+       character is '+' or '-'.
+
+       For backwards compatibility, the extra forms
+
+         <float><sign>j
+         <sign>j
+         j
+
+       are also accepted, though support for these forms may be removed from
+       a future version of Python.
+    */
+
+    /* first look for forms starting with <float> */
+    z = PyOS_string_to_double(s, &end, NULL);
+    if (z == -1.0 && PyErr_Occurred()) {
+        if (PyErr_ExceptionMatches(PyExc_ValueError))
+            PyErr_Clear();
+        else
+            goto error;
+    }
+    if (end != s) {
+        /* all 4 forms starting with <float> land here */
+        s = end;
+        if (*s == '+' || *s == '-') {
+            /* <float><signed-float>j | <float><sign>j */
+            x = z;
+            y = PyOS_string_to_double(s, &end, NULL);
+            if (y == -1.0 && PyErr_Occurred()) {
+                if (PyErr_ExceptionMatches(PyExc_ValueError))
+                    PyErr_Clear();
+                else
+                    goto error;
+            }
+            if (end != s)
+                /* <float><signed-float>j */
+                s = end;
+            else {
+                /* <float><sign>j */
+                y = *s == '+' ? 1.0 : -1.0;
+                s++;
+            }
+            if (!(*s == 'j' || *s == 'J'))
+                goto parse_error;
+            s++;
+        }
+        else if (*s == 'j' || *s == 'J') {
+            /* <float>j */
+            s++;
+            y = z;
+        }
+        else
+            /* <float> */
+            x = z;
+    }
+    else {
+        /* not starting with <float>; must be <sign>j or j */
+        if (*s == '+' || *s == '-') {
+            /* <sign>j */
+            y = *s == '+' ? 1.0 : -1.0;
+            s++;
+        }
+        else
+            /* j */
+            y = 1.0;
+        if (!(*s == 'j' || *s == 'J'))
+            goto parse_error;
+        s++;
+    }
+
+    /* trailing whitespace and closing bracket */
+    while (Py_ISSPACE(*s))
+        s++;
+    if (got_bracket) {
+        /* if there was an opening parenthesis, then the corresponding
+           closing parenthesis should be right here */
+        if (*s != ')')
+            goto parse_error;
+        s++;
+        while (Py_ISSPACE(*s))
+            s++;
+    }
+
+    /* we should now be at the end of the string */
+    if (s-start != len)
+        goto parse_error;
+
+
+#ifdef Py_USING_UNICODE
+    if (s_buffer)
+        PyMem_FREE(s_buffer);
+#endif
+    return complex_subtype_from_doubles(type, x, y);
+
+  parse_error:
+    PyErr_SetString(PyExc_ValueError,
+                    "complex() arg is a malformed string");
+  error:
+#ifdef Py_USING_UNICODE
+    if (s_buffer)
+        PyMem_FREE(s_buffer);
+#endif
+    return NULL;
+}
+
+static PyObject *
+complex_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
+{
+    PyObject *r, *i, *tmp;
+    PyNumberMethods *nbr, *nbi = NULL;
+    Py_complex cr, ci;
+    int own_r = 0;
+    int cr_is_complex = 0;
+    int ci_is_complex = 0;
+    static char *kwlist[] = {"real", "imag", 0};
+
+    r = Py_False;
+    i = NULL;
+    if (!PyArg_ParseTupleAndKeywords(args, kwds, "|OO:complex", kwlist,
+                                     &r, &i))
+        return NULL;
+
+    /* Special-case for a single argument when type(arg) is complex. */
+    if (PyComplex_CheckExact(r) && i == NULL &&
+        type == &PyComplex_Type) {
+        /* Note that we can't know whether it's safe to return
+           a complex *subclass* instance as-is, hence the restriction
+           to exact complexes here.  If either the input or the
+           output is a complex subclass, it will be handled below
+           as a non-orthogonal vector.  */
+        Py_INCREF(r);
+        return r;
+    }
+    if (PyString_Check(r) || PyUnicode_Check(r)) {
+        if (i != NULL) {
+            PyErr_SetString(PyExc_TypeError,
+                            "complex() can't take second arg"
+                            " if first is a string");
+            return NULL;
+        }
+        return complex_subtype_from_string(type, r);
+    }
+    if (i != NULL && (PyString_Check(i) || PyUnicode_Check(i))) {
+        PyErr_SetString(PyExc_TypeError,
+                        "complex() second arg can't be a string");
+        return NULL;
+    }
+
+    tmp = try_complex_special_method(r);
+    if (tmp) {
+        r = tmp;
+        own_r = 1;
+    }
+    else if (PyErr_Occurred()) {
+        return NULL;
+    }
+
+    nbr = r->ob_type->tp_as_number;
+    if (i != NULL)
+        nbi = i->ob_type->tp_as_number;
+    if (nbr == NULL || nbr->nb_float == NULL ||
+        ((i != NULL) && (nbi == NULL || nbi->nb_float == NULL))) {
+        PyErr_SetString(PyExc_TypeError,
+                   "complex() argument must be a string or a number");
+        if (own_r) {
+            Py_DECREF(r);
+        }
+        return NULL;
+    }
+
+    /* If we get this far, then the "real" and "imag" parts should
+       both be treated as numbers, and the constructor should return a
+       complex number equal to (real + imag*1j).
+
+       Note that we do NOT assume the input to already be in canonical
+       form; the "real" and "imag" parts might themselves be complex
+       numbers, which slightly complicates the code below. */
+    if (PyComplex_Check(r)) {
+        /* Note that if r is of a complex subtype, we're only
+           retaining its real & imag parts here, and the return
+           value is (properly) of the builtin complex type. */
+        cr = ((PyComplexObject*)r)->cval;
+        cr_is_complex = 1;
+        if (own_r) {
+            Py_DECREF(r);
+        }
+    }
+    else {
+        /* The "real" part really is entirely real, and contributes
+           nothing in the imaginary direction.
+           Just treat it as a double. */
+        tmp = PyNumber_Float(r);
+        if (own_r) {
+            /* r was a newly created complex number, rather
+               than the original "real" argument. */
+            Py_DECREF(r);
+        }
+        if (tmp == NULL)
+            return NULL;
+        if (!PyFloat_Check(tmp)) {
+            PyErr_SetString(PyExc_TypeError,
+                            "float(r) didn't return a float");
+            Py_DECREF(tmp);
+            return NULL;
+        }
+        cr.real = PyFloat_AsDouble(tmp);
+        cr.imag = 0.0; /* Shut up compiler warning */
+        Py_DECREF(tmp);
+    }
+    if (i == NULL) {
+        ci.real = 0.0;
+    }
+    else if (PyComplex_Check(i)) {
+        ci = ((PyComplexObject*)i)->cval;
+        ci_is_complex = 1;
+    } else {
+        /* The "imag" part really is entirely imaginary, and
+           contributes nothing in the real direction.
+           Just treat it as a double. */
+        tmp = (*nbi->nb_float)(i);
+        if (tmp == NULL)
+            return NULL;
+        ci.real = PyFloat_AsDouble(tmp);
+        Py_DECREF(tmp);
+    }
+    /*  If the input was in canonical form, then the "real" and "imag"
+        parts are real numbers, so that ci.imag and cr.imag are zero.
+        We need this correction in case they were not real numbers. */
+
+    if (ci_is_complex) {
+        cr.real -= ci.imag;
+    }
+    if (cr_is_complex) {
+        ci.real += cr.imag;
+    }
+    return complex_subtype_from_doubles(type, cr.real, ci.real);
+}
+
+PyDoc_STRVAR(complex_doc,
+"complex(real[, imag]) -> complex number\n"
+"\n"
+"Create a complex number from a real part and an optional imaginary part.\n"
+"This is equivalent to (real + imag*1j) where imag defaults to 0.");
+
+static PyNumberMethods complex_as_number = {
+    (binaryfunc)complex_add,                    /* nb_add */
+    (binaryfunc)complex_sub,                    /* nb_subtract */
+    (binaryfunc)complex_mul,                    /* nb_multiply */
+    (binaryfunc)complex_classic_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 */
+    complex_coerce,                             /* nb_coerce */
+    complex_int,                                /* nb_int */
+    complex_long,                               /* nb_long */
+    complex_float,                              /* nb_float */
+    0,                                          /* nb_oct */
+    0,                                          /* nb_hex */
+    0,                                          /* nb_inplace_add */
+    0,                                          /* nb_inplace_subtract */
+    0,                                          /* nb_inplace_multiply*/
+    0,                                          /* nb_inplace_divide */
+    0,                                          /* nb_inplace_remainder */
+    0,                                          /* nb_inplace_power */
+    0,                                          /* nb_inplace_lshift */
+    0,                                          /* nb_inplace_rshift */
+    0,                                          /* nb_inplace_and */
+    0,                                          /* nb_inplace_xor */
+    0,                                          /* nb_inplace_or */
+    (binaryfunc)complex_int_div,                /* nb_floor_divide */
+    (binaryfunc)complex_div,                    /* nb_true_divide */
+    0,                                          /* nb_inplace_floor_divide */
+    0,                                          /* nb_inplace_true_divide */
+};
+
+PyTypeObject PyComplex_Type = {
+    PyVarObject_HEAD_INIT(&PyType_Type, 0)
+    "complex",
+    sizeof(PyComplexObject),
+    0,
+    complex_dealloc,                            /* tp_dealloc */
+    (printfunc)complex_print,                   /* tp_print */
+    0,                                          /* tp_getattr */
+    0,                                          /* tp_setattr */
+    0,                                          /* 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 */
+    0,                                          /* tp_call */
+    (reprfunc)complex_str,                      /* tp_str */
+    PyObject_GenericGetAttr,                    /* tp_getattro */
+    0,                                          /* tp_setattro */
+    0,                                          /* tp_as_buffer */
+    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
+        Py_TPFLAGS_BASETYPE,                    /* tp_flags */
+    complex_doc,                                /* tp_doc */
+    0,                                          /* tp_traverse */
+    0,                                          /* tp_clear */
+    complex_richcompare,                        /* tp_richcompare */
+    0,                                          /* tp_weaklistoffset */
+    0,                                          /* tp_iter */
+    0,                                          /* tp_iternext */
+    complex_methods,                            /* tp_methods */
+    complex_members,                            /* tp_members */
+    0,                                          /* tp_getset */
+    0,                                          /* tp_base */
+    0,                                          /* tp_dict */
+    0,                                          /* tp_descr_get */
+    0,                                          /* tp_descr_set */
+    0,                                          /* tp_dictoffset */
+    0,                                          /* tp_init */
+    PyType_GenericAlloc,                        /* tp_alloc */
+    complex_new,                                /* tp_new */
+    PyObject_Del,                               /* tp_free */
+};
+
+#endif

from_cpython/setup.py

@@ -39,6 +39,13 @@ def bz2_ext():
             "Modules/bz2module.c",
             ]), libraries = ['bz2'])
 
+@unique
+def cmath_ext():
+    return Extension("cmath", sources = map(relpath, [
+            "Modules/cmathmodule.c",
+            ]))
+
+
 @unique
 def ctypes_ext():
     ext = Extension("_ctypes", sources = map(relpath, [
@@ -144,6 +151,7 @@ ext_modules = [future_builtins_ext(),
                pyexpat_ext(),
                elementtree_ext(),
                bz2_ext(),
+               cmath_ext(),
                ctypes_ext(),
                ctypes_test_ext(),
                grp_ext(),