floatobject.c

/* Float object implementation */

/* XXX There should be overflow checks here, but it's hard to check
   for any kind of float exception without losing portability. */

#include "Python.h"
#include "structseq.h"

#include <ctype.h>
#include <float.h>

#undef MAX
#undef MIN
#define MAX(x, y) ((x) < (y) ? (y) : (x))
#define MIN(x, y) ((x) < (y) ? (x) : (y))

#ifdef _OSF_SOURCE
/* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
extern int finite(double);
#endif

/* Special free list -- see comments for same code in intobject.c. */
#define BLOCK_SIZE      1000    /* 1K less typical malloc overhead */
#define BHEAD_SIZE      8       /* Enough for a 64-bit pointer */
#define N_FLOATOBJECTS  ((BLOCK_SIZE - BHEAD_SIZE) / sizeof(PyFloatObject))

struct _floatblock {
    struct _floatblock *next;
    PyFloatObject objects[N_FLOATOBJECTS];
};

typedef struct _floatblock PyFloatBlock;

static PyFloatBlock *block_list = NULL;
static PyFloatObject *free_list = NULL;

static PyFloatObject *
fill_free_list(void)
{
    PyFloatObject *p, *q;
    /* XXX Float blocks escape the object heap. Use PyObject_MALLOC ??? */
    p = (PyFloatObject *) PyMem_MALLOC(sizeof(PyFloatBlock));
    if (p == NULL)
        return (PyFloatObject *) PyErr_NoMemory();
    ((PyFloatBlock *)p)->next = block_list;
    block_list = (PyFloatBlock *)p;
    p = &((PyFloatBlock *)p)->objects[0];
    q = p + N_FLOATOBJECTS;
    while (--q > p)
        Py_TYPE(q) = (struct _typeobject *)(q-1);
    Py_TYPE(q) = NULL;
    return p + N_FLOATOBJECTS - 1;
}

double
PyFloat_GetMax(void)
{
    return DBL_MAX;
}

double
PyFloat_GetMin(void)
{
    return DBL_MIN;
}

static PyTypeObject FloatInfoType = {0, 0, 0, 0, 0, 0};

PyDoc_STRVAR(floatinfo__doc__,
"sys.float_info\n\
\n\
A structseq holding information about the float type. It contains low level\n\
information about the precision and internal representation. Please study\n\
your system's :file:`float.h` for more information.");

static PyStructSequence_Field floatinfo_fields[] = {
    {"max",             "DBL_MAX -- maximum representable finite float"},
    {"max_exp",         "DBL_MAX_EXP -- maximum int e such that radix**(e-1) "
                    "is representable"},
    {"max_10_exp",      "DBL_MAX_10_EXP -- maximum int e such that 10**e "
                    "is representable"},
    {"min",             "DBL_MIN -- Minimum positive normalizer float"},
    {"min_exp",         "DBL_MIN_EXP -- minimum int e such that radix**(e-1) "
                    "is a normalized float"},
    {"min_10_exp",      "DBL_MIN_10_EXP -- minimum int e such that 10**e is "
                    "a normalized"},
    {"dig",             "DBL_DIG -- digits"},
    {"mant_dig",        "DBL_MANT_DIG -- mantissa digits"},
    {"epsilon",         "DBL_EPSILON -- Difference between 1 and the next "
                    "representable float"},
    {"radix",           "FLT_RADIX -- radix of exponent"},
    {"rounds",          "FLT_ROUNDS -- addition rounds"},
    {0}
};

static PyStructSequence_Desc floatinfo_desc = {
    "sys.float_info",           /* name */
    floatinfo__doc__,           /* doc */
    floatinfo_fields,           /* fields */
    11
};

PyObject *
PyFloat_GetInfo(void)
{
    PyObject* floatinfo;
    int pos = 0;

    floatinfo = PyStructSequence_New(&FloatInfoType);
    if (floatinfo == NULL) {
        return NULL;
    }

#define SetIntFlag(flag) \
    PyStructSequence_SET_ITEM(floatinfo, pos++, PyInt_FromLong(flag))
#define SetDblFlag(flag) \
    PyStructSequence_SET_ITEM(floatinfo, pos++, PyFloat_FromDouble(flag))

    SetDblFlag(DBL_MAX);
    SetIntFlag(DBL_MAX_EXP);
    SetIntFlag(DBL_MAX_10_EXP);
    SetDblFlag(DBL_MIN);
    SetIntFlag(DBL_MIN_EXP);
    SetIntFlag(DBL_MIN_10_EXP);
    SetIntFlag(DBL_DIG);
    SetIntFlag(DBL_MANT_DIG);
    SetDblFlag(DBL_EPSILON);
    SetIntFlag(FLT_RADIX);
    SetIntFlag(FLT_ROUNDS);
#undef SetIntFlag
#undef SetDblFlag

    if (PyErr_Occurred()) {
        Py_CLEAR(floatinfo);
        return NULL;
    }
    return floatinfo;
}

PyObject *
PyFloat_FromDouble(double fval)
{
    register PyFloatObject *op;
    if (free_list == NULL) {
        if ((free_list = fill_free_list()) == NULL)
            return NULL;
    }
    /* Inline PyObject_New */
    op = free_list;
    free_list = (PyFloatObject *)Py_TYPE(op);
    PyObject_INIT(op, &PyFloat_Type);
    op->ob_fval = fval;
    return (PyObject *) op;
}

/**************************************************************************
RED_FLAG 22-Sep-2000 tim
PyFloat_FromString's pend argument is braindead.  Prior to this RED_FLAG,

1.  If v was a regular string, *pend was set to point to its terminating
    null byte.  That's useless (the caller can find that without any
    help from this function!).

2.  If v was a Unicode string, or an object convertible to a character
    buffer, *pend was set to point into stack trash (the auto temp
    vector holding the character buffer).  That was downright dangerous.

Since we can't change the interface of a public API function, pend is
still supported but now *officially* useless:  if pend is not NULL,
*pend is set to NULL.
**************************************************************************/
PyObject *
PyFloat_FromString(PyObject *v, char **pend)
{
    const char *s, *last, *end;
    double x;
    char buffer[256]; /* for errors */
#ifdef Py_USING_UNICODE
    char *s_buffer = NULL;
#endif
    Py_ssize_t len;
    PyObject *result = NULL;

    if (pend)
        *pend = NULL;
    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,
            "float() argument must be a string or a number");
        return NULL;
    }
    last = s + len;

    while (Py_ISSPACE(*s))
        s++;
    /* We don't care about overflow or underflow.  If the platform
     * supports them, infinities and signed zeroes (on underflow) are
     * fine. */
    x = PyOS_string_to_double(s, (char **)&end, NULL);
    if (x == -1.0 && PyErr_Occurred())
        goto error;
    while (Py_ISSPACE(*end))
        end++;
    if (end == last)
        result = PyFloat_FromDouble(x);
    else {
        PyOS_snprintf(buffer, sizeof(buffer),
                      "invalid literal for float(): %.200s", s);
        PyErr_SetString(PyExc_ValueError, buffer);
        result = NULL;
    }

  error:
#ifdef Py_USING_UNICODE
    if (s_buffer)
        PyMem_FREE(s_buffer);
#endif
    return result;
}

static void
float_dealloc(PyFloatObject *op)
{
    if (PyFloat_CheckExact(op)) {
        Py_TYPE(op) = (struct _typeobject *)free_list;
        free_list = op;
    }
    else
        Py_TYPE(op)->tp_free((PyObject *)op);
}

double
PyFloat_AsDouble(PyObject *op)
{
    PyNumberMethods *nb;
    PyFloatObject *fo;
    double val;

    if (op && PyFloat_Check(op))
        return PyFloat_AS_DOUBLE((PyFloatObject*) op);

    if (op == NULL) {
        PyErr_BadArgument();
        return -1;
    }

    if ((nb = Py_TYPE(op)->tp_as_number) == NULL || nb->nb_float == NULL) {
        PyErr_SetString(PyExc_TypeError, "a float is required");
        return -1;
    }

    fo = (PyFloatObject*) (*nb->nb_float) (op);
    if (fo == NULL)
        return -1;
    if (!PyFloat_Check(fo)) {
        Py_DECREF(fo);
        PyErr_SetString(PyExc_TypeError,
                        "nb_float should return float object");
        return -1;
    }

    val = PyFloat_AS_DOUBLE(fo);
    Py_DECREF(fo);

    return val;
}

/* Methods */

/* Macro and helper that convert PyObject obj to a C double and store
   the value in dbl; this replaces the functionality of the coercion
   slot function.  If conversion to double raises an exception, obj is
   set to NULL, and the function invoking this macro returns NULL.  If
   obj is not of float, int or long type, Py_NotImplemented is incref'ed,
   stored in obj, and returned from the function invoking this macro.
*/
#define CONVERT_TO_DOUBLE(obj, dbl)                     \
    if (PyFloat_Check(obj))                             \
        dbl = PyFloat_AS_DOUBLE(obj);                   \
    else if (convert_to_double(&(obj), &(dbl)) < 0)     \
        return obj;

static int
convert_to_double(PyObject **v, double *dbl)
{
    register PyObject *obj = *v;

    if (PyInt_Check(obj)) {
        *dbl = (double)PyInt_AS_LONG(obj);
    }
    else if (PyLong_Check(obj)) {
        *dbl = PyLong_AsDouble(obj);
        if (*dbl == -1.0 && PyErr_Occurred()) {
            *v = NULL;
            return -1;
        }
    }
    else {
        Py_INCREF(Py_NotImplemented);
        *v = Py_NotImplemented;
        return -1;
    }
    return 0;
}

/* XXX PyFloat_AsString and PyFloat_AsReprString are deprecated:
   XXX they pass a char buffer without passing a length.
*/
void
PyFloat_AsString(char *buf, PyFloatObject *v)
{
    char *tmp = PyOS_double_to_string(v->ob_fval, 'g',
                    PyFloat_STR_PRECISION,
                    Py_DTSF_ADD_DOT_0, NULL);
    strcpy(buf, tmp);
    PyMem_Free(tmp);
}

void
PyFloat_AsReprString(char *buf, PyFloatObject *v)
{
    char * tmp = PyOS_double_to_string(v->ob_fval, 'r', 0,
                    Py_DTSF_ADD_DOT_0, NULL);
    strcpy(buf, tmp);
    PyMem_Free(tmp);
}

/* ARGSUSED */
static int
float_print(PyFloatObject *v, FILE *fp, int flags)
{
    char *buf;
    if (flags & Py_PRINT_RAW)
        buf = PyOS_double_to_string(v->ob_fval,
                                    'g', PyFloat_STR_PRECISION,
                                    Py_DTSF_ADD_DOT_0, NULL);
    else
        buf = PyOS_double_to_string(v->ob_fval,
                            'r', 0, Py_DTSF_ADD_DOT_0, NULL);
    Py_BEGIN_ALLOW_THREADS
    fputs(buf, fp);
    Py_END_ALLOW_THREADS
    PyMem_Free(buf);
    return 0;
}

static PyObject *
float_str_or_repr(PyFloatObject *v, int precision, char format_code)
{
    PyObject *result;
    char *buf = PyOS_double_to_string(PyFloat_AS_DOUBLE(v),
                                  format_code, precision,
                                  Py_DTSF_ADD_DOT_0,
                                  NULL);
    if (!buf)
        return PyErr_NoMemory();
    result = PyString_FromString(buf);
    PyMem_Free(buf);
    return result;
}

static PyObject *
float_repr(PyFloatObject *v)
{
    return float_str_or_repr(v, 0, 'r');
}

static PyObject *
float_str(PyFloatObject *v)
{
    return float_str_or_repr(v, PyFloat_STR_PRECISION, 'g');
}

/* Comparison is pretty much a nightmare.  When comparing float to float,
 * we do it as straightforwardly (and long-windedly) as conceivable, so
 * that, e.g., Python x == y delivers the same result as the platform
 * C x == y when x and/or y is a NaN.
 * When mixing float with an integer type, there's no good *uniform* approach.
 * Converting the double to an integer obviously doesn't work, since we
 * may lose info from fractional bits.  Converting the integer to a double
 * also has two failure modes:  (1) a long int may trigger overflow (too
 * large to fit in the dynamic range of a C double); (2) even a C long may have
 * more bits than fit in a C double (e.g., on a a 64-bit box long may have
 * 63 bits of precision, but a C double probably has only 53), and then
 * we can falsely claim equality when low-order integer bits are lost by
 * coercion to double.  So this part is painful too.
 */

static PyObject*
float_richcompare(PyObject *v, PyObject *w, int op)
{
    double i, j;
    int r = 0;

    assert(PyFloat_Check(v));
    i = PyFloat_AS_DOUBLE(v);

    /* Switch on the type of w.  Set i and j to doubles to be compared,
     * and op to the richcomp to use.
     */
    if (PyFloat_Check(w))
        j = PyFloat_AS_DOUBLE(w);

    else if (!Py_IS_FINITE(i)) {
        if (PyInt_Check(w) || PyLong_Check(w))
            /* If i is an infinity, its magnitude exceeds any
             * finite integer, so it doesn't matter which int we
             * compare i with.  If i is a NaN, similarly.
             */
            j = 0.0;
        else
            goto Unimplemented;
    }

    else if (PyInt_Check(w)) {
        long jj = PyInt_AS_LONG(w);
        /* In the worst realistic case I can imagine, C double is a
         * Cray single with 48 bits of precision, and long has 64
         * bits.
         */
#if SIZEOF_LONG > 6
        unsigned long abs = (unsigned long)(jj < 0 ? -jj : jj);
        if (abs >> 48) {
            /* Needs more than 48 bits.  Make it take the
             * PyLong path.
             */
            PyObject *result;
            PyObject *ww = PyLong_FromLong(jj);

            if (ww == NULL)
                return NULL;
            result = float_richcompare(v, ww, op);
            Py_DECREF(ww);
            return result;
        }
#endif
        j = (double)jj;
        assert((long)j == jj);
    }

    else if (PyLong_Check(w)) {
        int vsign = i == 0.0 ? 0 : i < 0.0 ? -1 : 1;
        int wsign = _PyLong_Sign(w);
        size_t nbits;
        int exponent;

        if (vsign != wsign) {
            /* Magnitudes are irrelevant -- the signs alone
             * determine the outcome.
             */
            i = (double)vsign;
            j = (double)wsign;
            goto Compare;
        }
        /* The signs are the same. */
        /* Convert w to a double if it fits.  In particular, 0 fits. */
        nbits = _PyLong_NumBits(w);
        if (nbits == (size_t)-1 && PyErr_Occurred()) {
            /* This long is so large that size_t isn't big enough
             * to hold the # of bits.  Replace with little doubles
             * that give the same outcome -- w is so large that
             * its magnitude must exceed the magnitude of any
             * finite float.
             */
            PyErr_Clear();
            i = (double)vsign;
            assert(wsign != 0);
            j = wsign * 2.0;
            goto Compare;
        }
        if (nbits <= 48) {
            j = PyLong_AsDouble(w);
            /* It's impossible that <= 48 bits overflowed. */
            assert(j != -1.0 || ! PyErr_Occurred());
            goto Compare;
        }
        assert(wsign != 0); /* else nbits was 0 */
        assert(vsign != 0); /* if vsign were 0, then since wsign is
                             * not 0, we would have taken the
                             * vsign != wsign branch at the start */
        /* We want to work with non-negative numbers. */
        if (vsign < 0) {
            /* "Multiply both sides" by -1; this also swaps the
             * comparator.
             */
            i = -i;
            op = _Py_SwappedOp[op];
        }
        assert(i > 0.0);
        (void) frexp(i, &exponent);
        /* exponent is the # of bits in v before the radix point;
         * we know that nbits (the # of bits in w) > 48 at this point
         */
        if (exponent < 0 || (size_t)exponent < nbits) {
            i = 1.0;
            j = 2.0;
            goto Compare;
        }
        if ((size_t)exponent > nbits) {
            i = 2.0;
            j = 1.0;
            goto Compare;
        }
        /* v and w have the same number of bits before the radix
         * point.  Construct two longs that have the same comparison
         * outcome.
         */
        {
            double fracpart;
            double intpart;
            PyObject *result = NULL;
            PyObject *one = NULL;
            PyObject *vv = NULL;
            PyObject *ww = w;

            if (wsign < 0) {
                ww = PyNumber_Negative(w);
                if (ww == NULL)
                    goto Error;
            }
            else
                Py_INCREF(ww);

            fracpart = modf(i, &intpart);
            vv = PyLong_FromDouble(intpart);
            if (vv == NULL)
                goto Error;

            if (fracpart != 0.0) {
                /* Shift left, and or a 1 bit into vv
                 * to represent the lost fraction.
                 */
                PyObject *temp;

                one = PyInt_FromLong(1);
                if (one == NULL)
                    goto Error;

                temp = PyNumber_Lshift(ww, one);
                if (temp == NULL)
                    goto Error;
                Py_DECREF(ww);
                ww = temp;

                temp = PyNumber_Lshift(vv, one);
                if (temp == NULL)
                    goto Error;
                Py_DECREF(vv);
                vv = temp;

                temp = PyNumber_Or(vv, one);
                if (temp == NULL)
                    goto Error;
                Py_DECREF(vv);
                vv = temp;
            }

            r = PyObject_RichCompareBool(vv, ww, op);
            if (r < 0)
                goto Error;
            result = PyBool_FromLong(r);
         Error:
            Py_XDECREF(vv);
            Py_XDECREF(ww);
            Py_XDECREF(one);
            return result;
        }
    } /* else if (PyLong_Check(w)) */

    else        /* w isn't float, int, or long */
        goto Unimplemented;

 Compare:
    PyFPE_START_PROTECT("richcompare", return NULL)
    switch (op) {
    case Py_EQ:
        r = i == j;
        break;
    case Py_NE:
        r = i != j;
        break;
    case Py_LE:
        r = i <= j;
        break;
    case Py_GE:
        r = i >= j;
        break;
    case Py_LT:
        r = i < j;
        break;
    case Py_GT:
        r = i > j;
        break;
    }
    PyFPE_END_PROTECT(r)
    return PyBool_FromLong(r);

 Unimplemented:
    Py_INCREF(Py_NotImplemented);
    return Py_NotImplemented;
}

static long
float_hash(PyFloatObject *v)
{
    return _Py_HashDouble(v->ob_fval);
}

static PyObject *
float_add(PyObject *v, PyObject *w)
{
    double a,b;
    CONVERT_TO_DOUBLE(v, a);
    CONVERT_TO_DOUBLE(w, b);
    PyFPE_START_PROTECT("add", return 0)
    a = a + b;
    PyFPE_END_PROTECT(a)
    return PyFloat_FromDouble(a);
}

static PyObject *
float_sub(PyObject *v, PyObject *w)
{
    double a,b;
    CONVERT_TO_DOUBLE(v, a);
    CONVERT_TO_DOUBLE(w, b);
    PyFPE_START_PROTECT("subtract", return 0)
    a = a - b;
    PyFPE_END_PROTECT(a)
    return PyFloat_FromDouble(a);
}

static PyObject *
float_mul(PyObject *v, PyObject *w)
{
    double a,b;
    CONVERT_TO_DOUBLE(v, a);
    CONVERT_TO_DOUBLE(w, b);
    PyFPE_START_PROTECT("multiply", return 0)
    a = a * b;
    PyFPE_END_PROTECT(a)
    return PyFloat_FromDouble(a);
}

static PyObject *
float_div(PyObject *v, PyObject *w)
{
    double a,b;
    CONVERT_TO_DOUBLE(v, a);
    CONVERT_TO_DOUBLE(w, b);
#ifdef Py_NAN
    if (b == 0.0) {
        PyErr_SetString(PyExc_ZeroDivisionError,
                        "float division by zero");
        return NULL;
    }
#endif
    PyFPE_START_PROTECT("divide", return 0)
    a = a / b;
    PyFPE_END_PROTECT(a)
    return PyFloat_FromDouble(a);
}

static PyObject *
float_classic_div(PyObject *v, PyObject *w)
{
    double a,b;
    CONVERT_TO_DOUBLE(v, a);
    CONVERT_TO_DOUBLE(w, b);
    if (Py_DivisionWarningFlag >= 2 &&
        PyErr_Warn(PyExc_DeprecationWarning, "classic float division") < 0)
        return NULL;
#ifdef Py_NAN
    if (b == 0.0) {
        PyErr_SetString(PyExc_ZeroDivisionError,
                        "float division by zero");
        return NULL;
    }
#endif
    PyFPE_START_PROTECT("divide", return 0)
    a = a / b;
    PyFPE_END_PROTECT(a)
    return PyFloat_FromDouble(a);
}

static PyObject *
float_rem(PyObject *v, PyObject *w)
{
    double vx, wx;
    double mod;
    CONVERT_TO_DOUBLE(v, vx);
    CONVERT_TO_DOUBLE(w, wx);
#ifdef Py_NAN
    if (wx == 0.0) {
        PyErr_SetString(PyExc_ZeroDivisionError,
                        "float modulo");
        return NULL;
    }
#endif
    PyFPE_START_PROTECT("modulo", return 0)
    mod = fmod(vx, wx);
    if (mod) {
        /* ensure the remainder has the same sign as the denominator */
        if ((wx < 0) != (mod < 0)) {
            mod += wx;
        }
    }
    else {
        /* the remainder is zero, and in the presence of signed zeroes
           fmod returns different results across platforms; ensure
           it has the same sign as the denominator; we'd like to do
           "mod = wx * 0.0", but that may get optimized away */
        mod *= mod;  /* hide "mod = +0" from optimizer */
        if (wx < 0.0)
            mod = -mod;
    }
    PyFPE_END_PROTECT(mod)
    return PyFloat_FromDouble(mod);
}

static PyObject *
float_divmod(PyObject *v, PyObject *w)
{
    double vx, wx;
    double div, mod, floordiv;
    CONVERT_TO_DOUBLE(v, vx);
    CONVERT_TO_DOUBLE(w, wx);
    if (wx == 0.0) {
        PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()");
        return NULL;
    }
    PyFPE_START_PROTECT("divmod", return 0)
    mod = fmod(vx, wx);
    /* fmod is typically exact, so vx-mod is *mathematically* an
       exact multiple of wx.  But this is fp arithmetic, and fp
       vx - mod is an approximation; the result is that div may
       not be an exact integral value after the division, although
       it will always be very close to one.
    */
    div = (vx - mod) / wx;
    if (mod) {
        /* ensure the remainder has the same sign as the denominator */
        if ((wx < 0) != (mod < 0)) {
            mod += wx;
            div -= 1.0;
        }
    }
    else {
        /* the remainder is zero, and in the presence of signed zeroes
           fmod returns different results across platforms; ensure
           it has the same sign as the denominator; we'd like to do
           "mod = wx * 0.0", but that may get optimized away */
        mod *= mod;  /* hide "mod = +0" from optimizer */
        if (wx < 0.0)
            mod = -mod;
    }
    /* snap quotient to nearest integral value */
    if (div) {
        floordiv = floor(div);
        if (div - floordiv > 0.5)
            floordiv += 1.0;
    }
    else {
        /* div is zero - get the same sign as the true quotient */
        div *= div;             /* hide "div = +0" from optimizers */
        floordiv = div * vx / wx; /* zero w/ sign of vx/wx */
    }
    PyFPE_END_PROTECT(floordiv)
    return Py_BuildValue("(dd)", floordiv, mod);
}

static PyObject *
float_floor_div(PyObject *v, PyObject *w)
{
    PyObject *t, *r;

    t = float_divmod(v, w);
    if (t == NULL || t == Py_NotImplemented)
        return t;
    assert(PyTuple_CheckExact(t));
    r = PyTuple_GET_ITEM(t, 0);
    Py_INCREF(r);
    Py_DECREF(t);
    return r;
}

/* determine whether x is an odd integer or not;  assumes that
   x is not an infinity or nan. */
#define DOUBLE_IS_ODD_INTEGER(x) (fmod(fabs(x), 2.0) == 1.0)

static PyObject *
float_pow(PyObject *v, PyObject *w, PyObject *z)
{
    double iv, iw, ix;
    int negate_result = 0;

    if ((PyObject *)z != Py_None) {
        PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not "
            "allowed unless all arguments are integers");
        return NULL;
    }

    CONVERT_TO_DOUBLE(v, iv);
    CONVERT_TO_DOUBLE(w, iw);

    /* Sort out special cases here instead of relying on pow() */
    if (iw == 0) {              /* v**0 is 1, even 0**0 */
        return PyFloat_FromDouble(1.0);
    }
    if (Py_IS_NAN(iv)) {        /* nan**w = nan, unless w == 0 */
        return PyFloat_FromDouble(iv);
    }
    if (Py_IS_NAN(iw)) {        /* v**nan = nan, unless v == 1; 1**nan = 1 */
        return PyFloat_FromDouble(iv == 1.0 ? 1.0 : iw);
    }
    if (Py_IS_INFINITY(iw)) {
        /* v**inf is: 0.0 if abs(v) < 1; 1.0 if abs(v) == 1; inf if
         *     abs(v) > 1 (including case where v infinite)
         *
         * v**-inf is: inf if abs(v) < 1; 1.0 if abs(v) == 1; 0.0 if
         *     abs(v) > 1 (including case where v infinite)
         */
        iv = fabs(iv);
        if (iv == 1.0)
            return PyFloat_FromDouble(1.0);
        else if ((iw > 0.0) == (iv > 1.0))
            return PyFloat_FromDouble(fabs(iw)); /* return inf */
        else
            return PyFloat_FromDouble(0.0);
    }
    if (Py_IS_INFINITY(iv)) {
        /* (+-inf)**w is: inf for w positive, 0 for w negative; in
         *     both cases, we need to add the appropriate sign if w is
         *     an odd integer.
         */
        int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
        if (iw > 0.0)
            return PyFloat_FromDouble(iw_is_odd ? iv : fabs(iv));
        else
            return PyFloat_FromDouble(iw_is_odd ?
                                      copysign(0.0, iv) : 0.0);
    }
    if (iv == 0.0) {  /* 0**w is: 0 for w positive, 1 for w zero
                         (already dealt with above), and an error
                         if w is negative. */
        int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
        if (iw < 0.0) {
            PyErr_SetString(PyExc_ZeroDivisionError,
                            "0.0 cannot be raised to a "
                            "negative power");
            return NULL;
        }
        /* use correct sign if iw is odd */
        return PyFloat_FromDouble(iw_is_odd ? iv : 0.0);
    }

    if (iv < 0.0) {
        /* Whether this is an error is a mess, and bumps into libm
         * bugs so we have to figure it out ourselves.
         */
        if (iw != floor(iw)) {
            PyErr_SetString(PyExc_ValueError, "negative number "
                "cannot be raised to a fractional power");
            return NULL;
        }
        /* iw is an exact integer, albeit perhaps a very large
         * one.  Replace iv by its absolute value and remember
         * to negate the pow result if iw is odd.
         */
        iv = -iv;
        negate_result = DOUBLE_IS_ODD_INTEGER(iw);
    }

    if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
        /* (-1) ** large_integer also ends up here.  Here's an
         * extract from the comments for the previous
         * implementation explaining why this special case is
         * necessary:
         *
         * -1 raised to an exact integer should never be exceptional.
         * Alas, some libms (chiefly glibc as of early 2003) return
         * NaN and set EDOM on pow(-1, large_int) if the int doesn't
         * happen to be representable in a *C* integer.  That's a
         * bug.
         */
        return PyFloat_FromDouble(negate_result ? -1.0 : 1.0);
    }

    /* Now iv and iw are finite, iw is nonzero, and iv is
     * positive and not equal to 1.0.  We finally allow
     * the platform pow to step in and do the rest.
     */
    errno = 0;
    PyFPE_START_PROTECT("pow", return NULL)
    ix = pow(iv, iw);
    PyFPE_END_PROTECT(ix)
    Py_ADJUST_ERANGE1(ix);
    if (negate_result)
        ix = -ix;

    if (errno != 0) {
        /* We don't expect any errno value other than ERANGE, but
         * the range of libm bugs appears unbounded.
         */
        PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
                             PyExc_ValueError);
        return NULL;
    }
    return PyFloat_FromDouble(ix);
}

#undef DOUBLE_IS_ODD_INTEGER

static PyObject *
float_neg(PyFloatObject *v)
{
    return PyFloat_FromDouble(-v->ob_fval);
}

static PyObject *
float_abs(PyFloatObject *v)
{
    return PyFloat_FromDouble(fabs(v->ob_fval));
}

static int
float_nonzero(PyFloatObject *v)
{
    return v->ob_fval != 0.0;
}

static int
float_coerce(PyObject **pv, PyObject **pw)
{
    if (PyInt_Check(*pw)) {
        long x = PyInt_AsLong(*pw);
        *pw = PyFloat_FromDouble((double)x);
        Py_INCREF(*pv);
        return 0;
    }
    else if (PyLong_Check(*pw)) {
        double x = PyLong_AsDouble(*pw);
        if (x == -1.0 && PyErr_Occurred())
            return -1;
        *pw = PyFloat_FromDouble(x);
        Py_INCREF(*pv);
        return 0;
    }
    else if (PyFloat_Check(*pw)) {
        Py_INCREF(*pv);
        Py_INCREF(*pw);
        return 0;
    }
    return 1; /* Can't do it */
}

static PyObject *
float_is_integer(PyObject *v)
{
    double x = PyFloat_AsDouble(v);
    PyObject *o;

    if (x == -1.0 && PyErr_Occurred())
        return NULL;
    if (!Py_IS_FINITE(x))
        Py_RETURN_FALSE;
    errno = 0;
    PyFPE_START_PROTECT("is_integer", return NULL)
    o = (floor(x) == x) ? Py_True : Py_False;
    PyFPE_END_PROTECT(x)
    if (errno != 0) {
        PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
                             PyExc_ValueError);
        return NULL;
    }
    Py_INCREF(o);
    return o;
}

#if 0
static PyObject *
float_is_inf(PyObject *v)