Changeset 388 for python/vendor/current/Objects/complexobject.c

Timestamp:

Mar 19, 2014, 11:11:30 AM (11 years ago)

Author:

dmik

Message:

python: Update vendor to 2.7.6.

File:

• python/vendor/current/Objects/complexobject.c (modified) (42 diffs)

python/vendor/current/Objects/complexobject.c

@@ -8 +8 @@
 #include "Python.h"
 #include "structmember.h"
-
-#ifdef HAVE_IEEEFP_H
-#include <ieeefp.h>
-#endif
 
 #ifndef WITHOUT_COMPLEX
@@ -28 +24 @@
 */
 
-#define PREC_REPR       17
-#define PREC_STR        12
+#define PREC_REPR       17
+#define PREC_STR        12
 
 /* elementary operations on complex numbers */
@@ -38 +34 @@
 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 r;
+    r.real = a.real + b.real;
+    r.imag = a.imag + b.imag;
+    return r;
 }
 
@@ -47 +43 @@
 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 r;
+    r.real = a.real - b.real;
+    r.imag = a.imag - b.imag;
+    return r;
 }
 
@@ -56 +52 @@
 c_neg(Py_complex a)
 {
-        Py_complex r;
-        r.real = -a.real;
-        r.imag = -a.imag;
-        return r;
+    Py_complex r;
+    r.real = -a.real;
+    r.imag = -a.imag;
+    return r;
 }
 
@@ -65 +61 @@
 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 r;
+    r.real = a.real*b.real - a.imag*b.imag;
+    r.imag = a.real*b.imag + a.imag*b.real;
+    return r;
 }
 
@@ -74 +70 @@
 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;
+    /******************************************************************
+    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;
 }
 
@@ -128 +124 @@
 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;
+    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;
 }
 
@@ -158 +154 @@
 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;
+    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;
 }
 
@@ -174 +170 @@
 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));
+    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));
 
 }
@@ -191 +187 @@
 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;
+    /* 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;
 }
 
@@ -223 +219 @@
 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 *op;
+
+    op = type->tp_alloc(type, 0);
+    if (op != NULL)
+        ((PyComplexObject *)op)->cval = cval;
+    return op;
 }
 
@@ -234 +230 @@
 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;
+    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;
 }
 
@@ -248 +244 @@
 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);
+    Py_complex c;
+    c.real = real;
+    c.imag = imag;
+    return complex_subtype_from_c_complex(type, c);
 }
 
@@ -257 +253 @@
 PyComplex_FromDoubles(double real, double imag)
 {
-        Py_complex c;
-        c.real = real;
-        c.imag = imag;
-        return PyComplex_FromCComplex(c);
+    Py_complex c;
+    c.real = real;
+    c.imag = imag;
+    return PyComplex_FromCComplex(c);
 }
 
@@ -266 +262 @@
 PyComplex_RealAsDouble(PyObject *op)
 {
-        if (PyComplex_Check(op)) {
-                return ((PyComplexObject *)op)->cval.real;
-        }
-        else {
-                return PyFloat_AsDouble(op);
-        }
+    if (PyComplex_Check(op)) {
+        return ((PyComplexObject *)op)->cval.real;
+    }
+    else {
+        return PyFloat_AsDouble(op);
+    }
 }
 
@@ -277 +273 @@
 PyComplex_ImagAsDouble(PyObject *op)
 {
-        if (PyComplex_Check(op)) {
-                return ((PyComplexObject *)op)->cval.imag;
-        }
-        else {
-                return 0.0;
-        }
+    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;
 }
 
@@ -288 +316 @@
 PyComplex_AsCComplex(PyObject *op)
 {
-        Py_complex cv;
-        PyObject *newop = NULL;
-        static PyObject *complex_str = 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.;
-
-        if (complex_str == NULL) {
-                if (!(complex_str = PyString_InternFromString("__complex__")))
-                        return cv;
-        }
-        
-        if (PyInstance_Check(op)) {
-                /* this can go away in python 3000 */
-                if (PyObject_HasAttr(op, complex_str)) {
-                        newop = PyObject_CallMethod(op, "__complex__", NULL);
-                        if (!newop)
-                                return cv;
-                }
-                /* else try __float__ */
-        } else {
-                PyObject *complexfunc;
-                complexfunc = _PyType_Lookup(op->ob_type, complex_str);
-                /* complexfunc is a borrowed reference */
-                if (complexfunc) {
-                        newop = PyObject_CallFunctionObjArgs(complexfunc, op, NULL);
-                        if (!newop)
-                                return cv;
-                }
-        }
-
-        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;
-        }
-        /* 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;
-        }
+    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;
+    }
 }
 
@@ -350 +358 @@
 complex_dealloc(PyObject *op)
 {
-        op->ob_type->tp_free(op);
-}
-
-
-static void
-complex_to_buf(char *buf, int bufsz, PyComplexObject *v, int precision)
-{
-        char format[32];
-        if (v->cval.real == 0.) {
-                if (!Py_IS_FINITE(v->cval.imag)) {
-                        if (Py_IS_NAN(v->cval.imag))
-                                strncpy(buf, "nan*j", 6);
-                        else if (copysign(1, v->cval.imag) == 1)
-                                strncpy(buf, "inf*j", 6);
-                        else
-                                strncpy(buf, "-inf*j", 7);
-                }
-                else {
-                        PyOS_snprintf(format, sizeof(format), "%%.%ig", precision);
-                        PyOS_ascii_formatd(buf, bufsz - 1, format, v->cval.imag);
-                        strncat(buf, "j", 1);
-                }
-        } else {
-                char re[64], im[64];
-                /* Format imaginary part with sign, real part without */
-                if (!Py_IS_FINITE(v->cval.real)) {
-                        if (Py_IS_NAN(v->cval.real))
-                                strncpy(re, "nan", 4);
-                        /* else if (copysign(1, v->cval.real) == 1) */
-                        else if (v->cval.real > 0)
-                                strncpy(re, "inf", 4);
-                        else
-                                strncpy(re, "-inf", 5);
-                }
-                else {
-                        PyOS_snprintf(format, sizeof(format), "%%.%ig", precision);
-                        PyOS_ascii_formatd(re, sizeof(re), format, v->cval.real);
-                }
-                if (!Py_IS_FINITE(v->cval.imag)) {
-                        if (Py_IS_NAN(v->cval.imag))
-                                strncpy(im, "+nan*", 6);
-                        /* else if (copysign(1, v->cval.imag) == 1) */
-                        else if (v->cval.imag > 0)
-                                strncpy(im, "+inf*", 6);
-                        else
-                                strncpy(im, "-inf*", 6);
-                }
-                else {
-                        PyOS_snprintf(format, sizeof(format), "%%+.%ig", precision);
-                        PyOS_ascii_formatd(im, sizeof(im), format, v->cval.imag);
-                }
-                PyOS_snprintf(buf, bufsz, "(%s%sj)", re, im);
-        }
+    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;
 }
 
@@ -408 +428 @@
 complex_print(PyComplexObject *v, FILE *fp, int flags)
 {
-        char buf[100];
-        complex_to_buf(buf, sizeof(buf), v,
-                       (flags & Py_PRINT_RAW) ? PREC_STR : PREC_REPR);
-        Py_BEGIN_ALLOW_THREADS
-        fputs(buf, fp);
-        Py_END_ALLOW_THREADS
-        return 0;
+    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;
 }
 
@@ -420 +447 @@
 complex_repr(PyComplexObject *v)
 {
-        char buf[100];
-        complex_to_buf(buf, sizeof(buf), v, PREC_REPR);
-        return PyString_FromString(buf);
+    return complex_format(v, 0, 'r');
 }
 
@@ -428 +453 @@
 complex_str(PyComplexObject *v)
 {
-        char buf[100];
-        complex_to_buf(buf, sizeof(buf), v, PREC_STR);
-        return PyString_FromString(buf);
+    return complex_format(v, PyFloat_STR_PRECISION, 'g');
 }
 
@@ -436 +459 @@
 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;
+    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)
+    if (PyComplex_Check(obj)) \
+        c = ((PyComplexObject *)(obj))->cval; \
+    else if (to_complex(&(obj), &(c)) < 0) \
+        return (obj)
 
 static int
@@ -469 +492 @@
     pc->real = pc->imag = 0.0;
     if (PyInt_Check(obj)) {
-        pc->real = PyInt_AS_LONG(obj);
-        return 0;
+    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;
+    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;
+    pc->real = PyFloat_AsDouble(obj);
+    return 0;
     }
     Py_INCREF(Py_NotImplemented);
@@ -488 +511 @@
     return -1;
 }
-                
-
-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_classic_div(PyComplexObject *v, PyComplexObject *w)
-{
-        Py_complex quot;
-
-        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(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;
-
-        if (PyErr_Warn(PyExc_DeprecationWarning,
-                       "complex divmod(), // and % are deprecated") < 0)
-                return NULL;
-
-        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;
-
-        if (PyErr_Warn(PyExc_DeprecationWarning,
-                       "complex divmod(), // and % are deprecated") < 0)
-                return NULL;
-
-        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 = PyTuple_Pack(2, d, m);
-        Py_XDECREF(d);
-        Py_XDECREF(m);
-        return z;
+
+
+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;
 }
 
@@ -610 +650 @@
 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(PyComplexObject *v, PyComplexObject *w)
-{
-        PyObject *t, *r;
-        
-        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;
+    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;
 }
 
@@ -667 +708 @@
 complex_neg(PyComplexObject *v)
 {
-        Py_complex neg;
-        neg.real = -v->cval.real;
-        neg.imag = -v->cval.imag;
-        return PyComplex_FromCComplex(neg);
+    Py_complex neg;
+    neg.real = -v->cval.real;
+    neg.imag = -v->cval.imag;
+    return PyComplex_FromCComplex(neg);
 }
 
@@ -676 +717 @@
 complex_pos(PyComplexObject *v)
 {
-        if (PyComplex_CheckExact(v)) {
-                Py_INCREF(v);
-                return (PyObject *)v;
-        }
-        else
-                return PyComplex_FromCComplex(v->cval);
+    if (PyComplex_CheckExact(v)) {
+        Py_INCREF(v);
+        return (PyObject *)v;
+    }
+    else
+        return PyComplex_FromCComplex(v->cval);
 }
 
@@ -687 +728 @@
 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);
+    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);
 }
 
@@ -704 +745 @@
 complex_nonzero(PyComplexObject *v)
 {
-        return v->cval.real != 0.0 || v->cval.imag != 0.0;
+    return v->cval.real != 0.0 || v->cval.imag != 0.0;
 }
 
@@ -710 +751 @@
 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 */
+    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 */
 }
 
@@ -743 +784 @@
 complex_richcompare(PyObject *v, PyObject *w, int op)
 {
-        int c;
-        Py_complex i, j;
-        PyObject *res;
-
-        c = PyNumber_CoerceEx(&v, &w);
-        if (c < 0)
-                return NULL;
-        if (c > 0) {
-                Py_INCREF(Py_NotImplemented);
-                return Py_NotImplemented;
-        }
-        /* Make sure both arguments are complex. */
-        if (!(PyComplex_Check(v) && PyComplex_Check(w))) {
-                Py_DECREF(v);
-                Py_DECREF(w);
-                Py_INCREF(Py_NotImplemented);
-                return Py_NotImplemented;
-        }
-
-        i = ((PyComplexObject *)v)->cval;
-        j = ((PyComplexObject *)w)->cval;
-        Py_DECREF(v);
-        Py_DECREF(w);
-
-        if (op != Py_EQ && op != Py_NE) {
-                PyErr_SetString(PyExc_TypeError,
-                        "no ordering relation is defined for complex numbers");
-                return NULL;
-        }
-
-        if ((i.real == j.real && i.imag == j.imag) == (op == Py_EQ))
-                res = Py_True;
-        else
-                res = Py_False;
-
-        Py_INCREF(res);
-        return res;
+    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;
 }
 
@@ -785 +853 @@
 complex_int(PyObject *v)
 {
-        PyErr_SetString(PyExc_TypeError,
-                   "can't convert complex to int");
-        return NULL;
+    PyErr_SetString(PyExc_TypeError,
+               "can't convert complex to int");
+    return NULL;
 }
 
@@ -793 +861 @@
 complex_long(PyObject *v)
 {
-        PyErr_SetString(PyExc_TypeError,
-                   "can't convert complex to long");
-        return NULL;
+    PyErr_SetString(PyExc_TypeError,
+               "can't convert complex to long");
+    return NULL;
 }
 
@@ -801 +869 @@
 complex_float(PyObject *v)
 {
-        PyErr_SetString(PyExc_TypeError,
-                   "can't convert complex to float");
-        return NULL;
+    PyErr_SetString(PyExc_TypeError,
+               "can't convert complex to float");
+    return NULL;
 }
 
@@ -809 +877 @@
 complex_conjugate(PyObject *self)
 {
-        Py_complex c;
-        c = ((PyComplexObject *)self)->cval;
-        c.imag = -c.imag;
-        return PyComplex_FromCComplex(c);
+    Py_complex c;
+    c = ((PyComplexObject *)self)->cval;
+    c.imag = -c.imag;
+    return PyComplex_FromCComplex(c);
 }
 
@@ -818 +886 @@
 "complex.conjugate() -> complex\n"
 "\n"
-"Returns the complex conjugate of its argument. (3-4j).conjugate() == 3+4j.");
+"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);
+    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;
 }
 
@@ -831 +934 @@
 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)));
+    Py_complex c;
+    c = ((PyComplexObject *)self)->cval;
+    return PyBool_FromLong((long)(Py_IS_FINITE(c.real) &&
+                                  Py_IS_FINITE(c.imag)));
 }
 
@@ -844 +947 @@
 
 static PyMethodDef complex_methods[] = {
-        {"conjugate",   (PyCFunction)complex_conjugate, METH_NOARGS,
-         complex_conjugate_doc},
+    {"conjugate",       (PyCFunction)complex_conjugate, METH_NOARGS,
+     complex_conjugate_doc},
 #if 0
-        {"is_finite",   (PyCFunction)complex_is_finite, METH_NOARGS,
-         complex_is_finite_doc},
+    {"is_finite",       (PyCFunction)complex_is_finite, METH_NOARGS,
+     complex_is_finite_doc},
 #endif
-        {"__getnewargs__",      (PyCFunction)complex_getnewargs,        METH_NOARGS},
-        {NULL,          NULL}           /* sentinel */
+    {"__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},
+    {"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},
 };
 
@@ -865 +970 @@
 complex_subtype_from_string(PyTypeObject *type, PyObject *v)
 {
-        const char *s, *start;
-        char *end;
-        double x=0.0, y=0.0, z;
-        int got_re=0, got_im=0, got_bracket=0, done=0;
-        int digit_or_dot;
-        int sw_error=0;
-        int sign;
-        char buffer[256]; /* For errors */
+    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[256];
+    char *s_buffer = NULL;
 #endif
-        Py_ssize_t len;
-
-        if (PyString_Check(v)) {
-                s = PyString_AS_STRING(v);
-                len = PyString_GET_SIZE(v);
-        }
+    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)) {
-                if (PyUnicode_GET_SIZE(v) >= (Py_ssize_t)sizeof(s_buffer)) {
-                        PyErr_SetString(PyExc_ValueError,
-                                 "complex() literal too large to convert");
-                        return NULL;
-                }
-                if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v),
-                                            PyUnicode_GET_SIZE(v),
-                                            s_buffer,
-                                            NULL))
-                        return NULL;
-                s = s_buffer;
-                len = strlen(s);
-        }
+    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 (*s && isspace(Py_CHARMASK(*s)))
-                s++;
-        if (s[0] == '\0') {
-                PyErr_SetString(PyExc_ValueError,
-                                "complex() arg is an empty string");
-                return NULL;
-        }
-        if (s[0] == '(') {
-                /* Skip over possible bracket from repr(). */
-                got_bracket = 1;
-                s++;
-                while (*s && isspace(Py_CHARMASK(*s)))
-                        s++;
-        }
-
-        z = -1.0;
-        sign = 1;
-        do {
-
-                switch (*s) {
-
-                case '\0':
-                        if (s-start != len) {
-                                PyErr_SetString(
-                                        PyExc_ValueError,
-                                        "complex() arg contains a null byte");
-                                return NULL;
-                        }
-                        if(!done) sw_error=1;
-                        break;
-
-                case ')':
-                        if (!got_bracket || !(got_re || got_im)) {
-                                sw_error=1;
-                                break;
-                        }
-                        got_bracket=0;
-                        done=1;
-                        s++;
-                        while (*s && isspace(Py_CHARMASK(*s)))
-                                s++;
-                        if (*s) sw_error=1;
-                        break;
-
-                case '-':
-                        sign = -1;
-                                /* Fallthrough */
-                case '+':
-                        if (done)  sw_error=1;
-                        s++;
-                        if  (  *s=='\0'||*s=='+'||*s=='-'||*s==')'||
-                               isspace(Py_CHARMASK(*s))  )  sw_error=1;
-                        break;
-
-                case 'J':
-                case 'j':
-                        if (got_im || done) {
-                                sw_error = 1;
-                                break;
-                        }
-                        if  (z<0.0) {
-                                y=sign;
-                        }
-                        else{
-                                y=sign*z;
-                        }
-                        got_im=1;
-                        s++;
-                        if  (*s!='+' && *s!='-' )
-                                done=1;
-                        break;
-
-                default:
-                        if (isspace(Py_CHARMASK(*s))) {
-                                while (*s && isspace(Py_CHARMASK(*s)))
-                                        s++;
-                                if (*s && *s != ')')
-                                        sw_error=1;
-                                else
-                                        done = 1;
-                                break;
-                        }
-                        digit_or_dot =
-                                (*s=='.' || isdigit(Py_CHARMASK(*s)));
-                        if  (done||!digit_or_dot) {
-                                sw_error=1;
-                                break;
-                        }
-                        errno = 0;
-                        PyFPE_START_PROTECT("strtod", return 0)
-                        z = PyOS_ascii_strtod(s, &end) ;
-                        PyFPE_END_PROTECT(z)
-                        if (errno == ERANGE && fabs(z) >= 1.0) {
-                                PyOS_snprintf(buffer, sizeof(buffer),
-                                        "float() out of range: %.150s", s);
-                                PyErr_SetString(
-                                        PyExc_ValueError,
-                                        buffer);
-                                return NULL;
-                        }
-                        s=end;
-                        if  (*s=='J' || *s=='j') {
-
-                                break;
-                        }
-                        if  (got_re) {
-                                sw_error=1;
-                                break;
-                        }
-
-                                /* accept a real part */
-                        x=sign*z;
-                        got_re=1;
-                        if  (got_im)  done=1;
-                        z = -1.0;
-                        sign = 1;
-                        break;
-
-                }  /* end of switch  */
-
-        } while (s - start < len && !sw_error);
-
-        if (sw_error || got_bracket) {
-                PyErr_SetString(PyExc_ValueError,
-                                "complex() arg is a malformed string");
-                return NULL;
-        }
-
-        return complex_subtype_from_doubles(type, x, y);
+    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;
 }
 
@@ -1040 +1131 @@
 complex_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
 {
-        PyObject *r, *i, *tmp, *f;
-        PyNumberMethods *nbr, *nbi = NULL;
-        Py_complex cr, ci;
-        int own_r = 0;
-        int cr_is_complex = 0;
-        int ci_is_complex = 0;
-        static PyObject *complexstr;
-        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;
-        }
-
-        /* XXX Hack to support classes with __complex__ method */
-        if (complexstr == NULL) {
-                complexstr = PyString_InternFromString("__complex__");
-                if (complexstr == NULL)
-                        return NULL;
-        }
-        f = PyObject_GetAttr(r, complexstr);
-        if (f == NULL)
-                PyErr_Clear();
-        else {
-                PyObject *args = PyTuple_New(0);
-                if (args == NULL)
-                        return NULL;
-                r = PyEval_CallObject(f, args);
-                Py_DECREF(args);
-                Py_DECREF(f);
-                if (r == NULL)
-                        return NULL;
-                own_r = 1;
-        }
-        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);
+    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);
 }
 
@@ -1189 +1268 @@
 
 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 */
+    (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_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 */
+    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 */
 };