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python3.2  3.2.2
Classes | Defines | Typedefs | Enumerations | Functions | Variables
floatobject.c File Reference
#include "Python.h"
#include <ctype.h>
#include <float.h>

Go to the source code of this file.

Classes

struct  _floatblock

Defines

#define MAX(x, y)   ((x) < (y) ? (y) : (x))
#define MIN(x, y)   ((x) < (y) ? (x) : (y))
#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))
#define SetIntFlag(flag)   PyStructSequence_SET_ITEM(floatinfo, pos++, PyLong_FromLong(flag))
#define SetDblFlag(flag)   PyStructSequence_SET_ITEM(floatinfo, pos++, PyFloat_FromDouble(flag))
#define CONVERT_TO_DOUBLE(obj, dbl)
#define DOUBLE_IS_ODD_INTEGER(x)   (fmod(fabs(x), 2.0) == 1.0)
#define NDIGITS_MAX   ((int)((DBL_MANT_DIG-DBL_MIN_EXP) * 0.30103))
#define NDIGITS_MIN   (-(int)((DBL_MAX_EXP + 1) * 0.30103))
#define TOHEX_NBITS   DBL_MANT_DIG + 3 - (DBL_MANT_DIG+2)%4
#define HEX_DIGIT(j)
#define INPLACE_UPDATE(obj, call)

Typedefs

typedef struct _floatblock

Enumerations

enum  float_format_type { unknown_format, ieee_big_endian_format, ieee_little_endian_format }

Functions

static PyFloatObjectfill_free_list (void)
double PyFloat_GetMax (void)
double PyFloat_GetMin (void)
 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.")
PyObjectPyFloat_GetInfo (void)
PyObjectPyFloat_FromDouble (double fval)
PyObjectPyFloat_FromString (PyObject *v)
static void float_dealloc (PyFloatObject *op)
double PyFloat_AsDouble (PyObject *op)
static int convert_to_double (PyObject **v, double *dbl)
static PyObjectfloat_repr (PyFloatObject *v)
static PyObjectfloat_richcompare (PyObject *v, PyObject *w, int op)
static Py_hash_t float_hash (PyFloatObject *v)
static PyObjectfloat_add (PyObject *v, PyObject *w)
static PyObjectfloat_sub (PyObject *v, PyObject *w)
static PyObjectfloat_mul (PyObject *v, PyObject *w)
static PyObjectfloat_div (PyObject *v, PyObject *w)
static PyObjectfloat_rem (PyObject *v, PyObject *w)
static PyObjectfloat_divmod (PyObject *v, PyObject *w)
static PyObjectfloat_floor_div (PyObject *v, PyObject *w)
static PyObjectfloat_pow (PyObject *v, PyObject *w, PyObject *z)
static PyObjectfloat_neg (PyFloatObject *v)
static PyObjectfloat_abs (PyFloatObject *v)
static int float_bool (PyFloatObject *v)
static PyObjectfloat_is_integer (PyObject *v)
static PyObjectfloat_trunc (PyObject *v)
static PyObjectdouble_round (double x, int ndigits)
static PyObjectfloat_round (PyObject *v, PyObject *args)
static PyObjectfloat_float (PyObject *v)
static char char_from_hex (int x)
static int hex_from_char (char c)
static PyObjectfloat_hex (PyObject *v)
 PyDoc_STRVAR (float_hex_doc,"float.hex() -> string\n\ \n\ Return a hexadecimal representation of a floating-point number.\n\ >>> (-0.1).hex()\n\ '-0x1.999999999999ap-4'\n\ >>> 3.14159.hex()\n\ '0x1.921f9f01b866ep+1'")
static PyObjectfloat_fromhex (PyObject *cls, PyObject *arg)
 PyDoc_STRVAR (float_fromhex_doc,"float.fromhex(string) -> float\n\ \n\ Create a floating-point number from a hexadecimal string.\n\ >>> float.fromhex('0x1.ffffp10')\n\ 2047.984375\n\ >>> float.fromhex('-0x1p-1074')\n\ -4.9406564584124654e-324")
static PyObjectfloat_as_integer_ratio (PyObject *v, PyObject *unused)
 PyDoc_STRVAR (float_as_integer_ratio_doc,"float.as_integer_ratio() -> (int, int)\n""\n""Returns a pair of integers, whose ratio is exactly equal to the original\n""float and with a positive denominator.\n""Raises OverflowError on infinities and a ValueError on NaNs.\n""\n"">>> (10.0).as_integer_ratio()\n""(10, 1)\n"">>> (0.0).as_integer_ratio()\n""(0, 1)\n"">>> (-.25).as_integer_ratio()\n""(-1, 4)")
static PyObjectfloat_subtype_new (PyTypeObject *type, PyObject *args, PyObject *kwds)
static PyObjectfloat_new (PyTypeObject *type, PyObject *args, PyObject *kwds)
static PyObjectfloat_getnewargs (PyFloatObject *v)
static PyObjectfloat_getformat (PyTypeObject *v, PyObject *arg)
 PyDoc_STRVAR (float_getformat_doc,"float.__getformat__(typestr) -> string\n""\n""You probably don't want to use this function. It exists mainly to be\n""used in Python's test suite.\n""\n""typestr must be 'double' or 'float'. This function returns whichever of\n""'unknown', 'IEEE, big-endian' or 'IEEE, little-endian' best describes the\n""format of floating point numbers used by the C type named by typestr.")
static PyObjectfloat_setformat (PyTypeObject *v, PyObject *args)
 PyDoc_STRVAR (float_setformat_doc,"float.__setformat__(typestr, fmt) -> None\n""\n""You probably don't want to use this function. It exists mainly to be\n""used in Python's test suite.\n""\n""typestr must be 'double' or 'float'. fmt must be one of 'unknown',\n""'IEEE, big-endian' or 'IEEE, little-endian', and in addition can only be\n""one of the latter two if it appears to match the underlying C reality.\n""\n""Overrides the automatic determination of C-level floating point type.\n""This affects how floats are converted to and from binary strings.")
static PyObjectfloat_getzero (PyObject *v, void *closure)
static PyObjectfloat__format__ (PyObject *self, PyObject *args)
 PyDoc_STRVAR (float__format__doc,"float.__format__(format_spec) -> string\n""\n""Formats the float according to format_spec.")
 PyDoc_STRVAR (float_doc,"float(x) -> floating point number\n\ \n\ Convert a string or number to a floating point number, if possible.")
void _PyFloat_Init (void)
int PyFloat_ClearFreeList (void)
void PyFloat_Fini (void)
int _PyFloat_Pack4 (double x, unsigned char *p, int le)
int _PyFloat_Pack8 (double x, unsigned char *p, int le)
double _PyFloat_Unpack4 (const unsigned char *p, int le)
double _PyFloat_Unpack8 (const unsigned char *p, int le)

Variables

static PyFloatBlock * block_list = NULL
static PyFloatObjectfree_list = NULL
static PyTypeObject FloatInfoType
static PyStructSequence_Field floatinfo_fields []
static PyStructSequence_Desc floatinfo_desc
static float_format_type double_format
static float_format_type float_format
static float_format_type detected_double_format
static float_format_type detected_float_format
static PyMethodDef float_methods []
static PyGetSetDef float_getset []
static PyNumberMethods float_as_number
PyTypeObject PyFloat_Type

Class Documentation

struct _floatblock

Definition at line 43 of file floatobject.c.

Collaboration diagram for _floatblock:
Class Members
struct _floatblock * next
PyFloatObject objects

Define Documentation

#define BHEAD_SIZE   8 /* Enough for a 64-bit pointer */

Definition at line 40 of file floatobject.c.

#define BLOCK_SIZE   1000 /* 1K less typical malloc overhead */

Definition at line 39 of file floatobject.c.

#define CONVERT_TO_DOUBLE (   obj,
  dbl 
)
Value:
if (PyFloat_Check(obj))                             \
        dbl = PyFloat_AS_DOUBLE(obj);                   \
    else if (convert_to_double(&(obj), &(dbl)) < 0)     \
        return obj;

Definition at line 284 of file floatobject.c.

#define DOUBLE_IS_ODD_INTEGER (   x)    (fmod(fabs(x), 2.0) == 1.0)

Definition at line 683 of file floatobject.c.

#define HEX_DIGIT (   j)
Value:
hex_from_char(*((j) < fdigits ?            \
                     coeff_end-(j) :                                    \
                     coeff_end-1-(j)))
#define INPLACE_UPDATE (   obj,
  call 
)
Value:
prev = obj; \
    obj = call; \
    Py_DECREF(prev); \
#define MAX (   x,
 
)    ((x) < (y) ? (y) : (x))

Definition at line 14 of file floatobject.c.

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

Definition at line 15 of file floatobject.c.

#define N_FLOATOBJECTS   ((BLOCK_SIZE - BHEAD_SIZE) / sizeof(PyFloatObject))

Definition at line 41 of file floatobject.c.

#define NDIGITS_MAX   ((int)((DBL_MANT_DIG-DBL_MIN_EXP) * 0.30103))
#define NDIGITS_MIN   (-(int)((DBL_MAX_EXP + 1) * 0.30103))
#define SetDblFlag (   flag)    PyStructSequence_SET_ITEM(floatinfo, pos++, PyFloat_FromDouble(flag))
#define SetIntFlag (   flag)    PyStructSequence_SET_ITEM(floatinfo, pos++, PyLong_FromLong(flag))
#define TOHEX_NBITS   DBL_MANT_DIG + 3 - (DBL_MANT_DIG+2)%4

Definition at line 1150 of file floatobject.c.


Typedef Documentation

typedef struct _floatblock

Definition at line 48 of file floatobject.c.


Enumeration Type Documentation

Enumerator:
unknown_format 
ieee_big_endian_format 
ieee_little_endian_format 

Definition at line 1611 of file floatobject.c.


Function Documentation

Definition at line 1892 of file floatobject.c.

{
    /* We attempt to determine if this machine is using IEEE
       floating point formats by peering at the bits of some
       carefully chosen values.  If it looks like we are on an
       IEEE platform, the float packing/unpacking routines can
       just copy bits, if not they resort to arithmetic & shifts
       and masks.  The shifts & masks approach works on all finite
       values, but what happens to infinities, NaNs and signed
       zeroes on packing is an accident, and attempting to unpack
       a NaN or an infinity will raise an exception.

       Note that if we're on some whacked-out platform which uses
       IEEE formats but isn't strictly little-endian or big-
       endian, we will fall back to the portable shifts & masks
       method. */

#if SIZEOF_DOUBLE == 8
    {
        double x = 9006104071832581.0;
        if (memcmp(&x, "\x43\x3f\xff\x01\x02\x03\x04\x05", 8) == 0)
            detected_double_format = ieee_big_endian_format;
        else if (memcmp(&x, "\x05\x04\x03\x02\x01\xff\x3f\x43", 8) == 0)
            detected_double_format = ieee_little_endian_format;
        else
            detected_double_format = unknown_format;
    }
#else
    detected_double_format = unknown_format;
#endif

#if SIZEOF_FLOAT == 4
    {
        float y = 16711938.0;
        if (memcmp(&y, "\x4b\x7f\x01\x02", 4) == 0)
            detected_float_format = ieee_big_endian_format;
        else if (memcmp(&y, "\x02\x01\x7f\x4b", 4) == 0)
            detected_float_format = ieee_little_endian_format;
        else
            detected_float_format = unknown_format;
    }
#else
    detected_float_format = unknown_format;
#endif

    double_format = detected_double_format;
    float_format = detected_float_format;

    /* Init float info */
    if (FloatInfoType.tp_name == 0)
        PyStructSequence_InitType(&FloatInfoType, &floatinfo_desc);
}

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int _PyFloat_Pack4 ( double  x,
unsigned char *  p,
int  le 
)

Definition at line 2044 of file floatobject.c.

{
    if (float_format == unknown_format) {
        unsigned char sign;
        int e;
        double f;
        unsigned int fbits;
        int incr = 1;

        if (le) {
            p += 3;
            incr = -1;
        }

        if (x < 0) {
            sign = 1;
            x = -x;
        }
        else
            sign = 0;

        f = frexp(x, &e);

        /* Normalize f to be in the range [1.0, 2.0) */
        if (0.5 <= f && f < 1.0) {
            f *= 2.0;
            e--;
        }
        else if (f == 0.0)
            e = 0;
        else {
            PyErr_SetString(PyExc_SystemError,
                            "frexp() result out of range");
            return -1;
        }

        if (e >= 128)
            goto Overflow;
        else if (e < -126) {
            /* Gradual underflow */
            f = ldexp(f, 126 + e);
            e = 0;
        }
        else if (!(e == 0 && f == 0.0)) {
            e += 127;
            f -= 1.0; /* Get rid of leading 1 */
        }

        f *= 8388608.0; /* 2**23 */
        fbits = (unsigned int)(f + 0.5); /* Round */
        assert(fbits <= 8388608);
        if (fbits >> 23) {
            /* The carry propagated out of a string of 23 1 bits. */
            fbits = 0;
            ++e;
            if (e >= 255)
                goto Overflow;
        }

        /* First byte */
        *p = (sign << 7) | (e >> 1);
        p += incr;

        /* Second byte */
        *p = (char) (((e & 1) << 7) | (fbits >> 16));
        p += incr;

        /* Third byte */
        *p = (fbits >> 8) & 0xFF;
        p += incr;

        /* Fourth byte */
        *p = fbits & 0xFF;

        /* Done */
        return 0;

    }
    else {
        float y = (float)x;
        const char *s = (char*)&y;
        int i, incr = 1;

        if (Py_IS_INFINITY(y) && !Py_IS_INFINITY(x))
            goto Overflow;

        if ((float_format == ieee_little_endian_format && !le)
            || (float_format == ieee_big_endian_format && le)) {
            p += 3;
            incr = -1;
        }

        for (i = 0; i < 4; i++) {
            *p = *s++;
            p += incr;
        }
        return 0;
    }
  Overflow:
    PyErr_SetString(PyExc_OverflowError,
                    "float too large to pack with f format");
    return -1;
}

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int _PyFloat_Pack8 ( double  x,
unsigned char *  p,
int  le 
)

Definition at line 2149 of file floatobject.c.

{
    if (double_format == unknown_format) {
        unsigned char sign;
        int e;
        double f;
        unsigned int fhi, flo;
        int incr = 1;

        if (le) {
            p += 7;
            incr = -1;
        }

        if (x < 0) {
            sign = 1;
            x = -x;
        }
        else
            sign = 0;

        f = frexp(x, &e);

        /* Normalize f to be in the range [1.0, 2.0) */
        if (0.5 <= f && f < 1.0) {
            f *= 2.0;
            e--;
        }
        else if (f == 0.0)
            e = 0;
        else {
            PyErr_SetString(PyExc_SystemError,
                            "frexp() result out of range");
            return -1;
        }

        if (e >= 1024)
            goto Overflow;
        else if (e < -1022) {
            /* Gradual underflow */
            f = ldexp(f, 1022 + e);
            e = 0;
        }
        else if (!(e == 0 && f == 0.0)) {
            e += 1023;
            f -= 1.0; /* Get rid of leading 1 */
        }

        /* fhi receives the high 28 bits; flo the low 24 bits (== 52 bits) */
        f *= 268435456.0; /* 2**28 */
        fhi = (unsigned int)f; /* Truncate */
        assert(fhi < 268435456);

        f -= (double)fhi;
        f *= 16777216.0; /* 2**24 */
        flo = (unsigned int)(f + 0.5); /* Round */
        assert(flo <= 16777216);
        if (flo >> 24) {
            /* The carry propagated out of a string of 24 1 bits. */
            flo = 0;
            ++fhi;
            if (fhi >> 28) {
                /* And it also progagated out of the next 28 bits. */
                fhi = 0;
                ++e;
                if (e >= 2047)
                    goto Overflow;
            }
        }

        /* First byte */
        *p = (sign << 7) | (e >> 4);
        p += incr;

        /* Second byte */
        *p = (unsigned char) (((e & 0xF) << 4) | (fhi >> 24));
        p += incr;

        /* Third byte */
        *p = (fhi >> 16) & 0xFF;
        p += incr;

        /* Fourth byte */
        *p = (fhi >> 8) & 0xFF;
        p += incr;

        /* Fifth byte */
        *p = fhi & 0xFF;
        p += incr;

        /* Sixth byte */
        *p = (flo >> 16) & 0xFF;
        p += incr;

        /* Seventh byte */
        *p = (flo >> 8) & 0xFF;
        p += incr;

        /* Eighth byte */
        *p = flo & 0xFF;
        p += incr;

        /* Done */
        return 0;

      Overflow:
        PyErr_SetString(PyExc_OverflowError,
                        "float too large to pack with d format");
        return -1;
    }
    else {
        const char *s = (char*)&x;
        int i, incr = 1;

        if ((double_format == ieee_little_endian_format && !le)
            || (double_format == ieee_big_endian_format && le)) {
            p += 7;
            incr = -1;
        }

        for (i = 0; i < 8; i++) {
            *p = *s++;
            p += incr;
        }
        return 0;
    }
}

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double _PyFloat_Unpack4 ( const unsigned char *  p,
int  le 
)

Definition at line 2278 of file floatobject.c.

{
    if (float_format == unknown_format) {
        unsigned char sign;
        int e;
        unsigned int f;
        double x;
        int incr = 1;

        if (le) {
            p += 3;
            incr = -1;
        }

        /* First byte */
        sign = (*p >> 7) & 1;
        e = (*p & 0x7F) << 1;
        p += incr;

        /* Second byte */
        e |= (*p >> 7) & 1;
        f = (*p & 0x7F) << 16;
        p += incr;

        if (e == 255) {
            PyErr_SetString(
                PyExc_ValueError,
                "can't unpack IEEE 754 special value "
                "on non-IEEE platform");
            return -1;
        }

        /* Third byte */
        f |= *p << 8;
        p += incr;

        /* Fourth byte */
        f |= *p;

        x = (double)f / 8388608.0;

        /* XXX This sadly ignores Inf/NaN issues */
        if (e == 0)
            e = -126;
        else {
            x += 1.0;
            e -= 127;
        }
        x = ldexp(x, e);

        if (sign)
            x = -x;

        return x;
    }
    else {
        float x;

        if ((float_format == ieee_little_endian_format && !le)
            || (float_format == ieee_big_endian_format && le)) {
            char buf[4];
            char *d = &buf[3];
            int i;

            for (i = 0; i < 4; i++) {
                *d-- = *p++;
            }
            memcpy(&x, buf, 4);
        }
        else {
            memcpy(&x, p, 4);
        }

        return x;
    }
}

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double _PyFloat_Unpack8 ( const unsigned char *  p,
int  le 
)

Definition at line 2356 of file floatobject.c.

{
    if (double_format == unknown_format) {
        unsigned char sign;
        int e;
        unsigned int fhi, flo;
        double x;
        int incr = 1;

        if (le) {
            p += 7;
            incr = -1;
        }

        /* First byte */
        sign = (*p >> 7) & 1;
        e = (*p & 0x7F) << 4;

        p += incr;

        /* Second byte */
        e |= (*p >> 4) & 0xF;
        fhi = (*p & 0xF) << 24;
        p += incr;

        if (e == 2047) {
            PyErr_SetString(
                PyExc_ValueError,
                "can't unpack IEEE 754 special value "
                "on non-IEEE platform");
            return -1.0;
        }

        /* Third byte */
        fhi |= *p << 16;
        p += incr;

        /* Fourth byte */
        fhi |= *p  << 8;
        p += incr;

        /* Fifth byte */
        fhi |= *p;
        p += incr;

        /* Sixth byte */
        flo = *p << 16;
        p += incr;

        /* Seventh byte */
        flo |= *p << 8;
        p += incr;

        /* Eighth byte */
        flo |= *p;

        x = (double)fhi + (double)flo / 16777216.0; /* 2**24 */
        x /= 268435456.0; /* 2**28 */

        if (e == 0)
            e = -1022;
        else {
            x += 1.0;
            e -= 1023;
        }
        x = ldexp(x, e);

        if (sign)
            x = -x;

        return x;
    }
    else {
        double x;

        if ((double_format == ieee_little_endian_format && !le)
            || (double_format == ieee_big_endian_format && le)) {
            char buf[8];
            char *d = &buf[7];
            int i;

            for (i = 0; i < 8; i++) {
                *d-- = *p++;
            }
            memcpy(&x, buf, 8);
        }
        else {
            memcpy(&x, p, 8);
        }

        return x;
    }
}

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static char char_from_hex ( int  x) [static]

Definition at line 1075 of file floatobject.c.

{
    assert(0 <= x && x < 16);
    return "0123456789abcdef"[x];
}

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static int convert_to_double ( PyObject **  v,
double *  dbl 
) [static]

Definition at line 293 of file floatobject.c.

{
    register PyObject *obj = *v;

    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;
}

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static PyObject* double_round ( double  x,
int  ndigits 
) [static]

Definition at line 915 of file floatobject.c.

                                    {

    double rounded;
    Py_ssize_t buflen, mybuflen=100;
    char *buf, *buf_end, shortbuf[100], *mybuf=shortbuf;
    int decpt, sign;
    PyObject *result = NULL;

    /* round to a decimal string */
    buf = _Py_dg_dtoa(x, 3, ndigits, &decpt, &sign, &buf_end);
    if (buf == NULL) {
        PyErr_NoMemory();
        return NULL;
    }

    /* Get new buffer if shortbuf is too small.  Space needed <= buf_end -
    buf + 8: (1 extra for '0', 1 for sign, 5 for exp, 1 for '\0').  */
    buflen = buf_end - buf;
    if (buflen + 8 > mybuflen) {
        mybuflen = buflen+8;
        mybuf = (char *)PyMem_Malloc(mybuflen);
        if (mybuf == NULL) {
            PyErr_NoMemory();
            goto exit;
        }
    }
    /* copy buf to mybuf, adding exponent, sign and leading 0 */
    PyOS_snprintf(mybuf, mybuflen, "%s0%se%d", (sign ? "-" : ""),
                  buf, decpt - (int)buflen);

    /* and convert the resulting string back to a double */
    errno = 0;
    rounded = _Py_dg_strtod(mybuf, NULL);
    if (errno == ERANGE && fabs(rounded) >= 1.)
        PyErr_SetString(PyExc_OverflowError,
                        "rounded value too large to represent");
    else
        result = PyFloat_FromDouble(rounded);

    /* done computing value;  now clean up */
    if (mybuf != shortbuf)
        PyMem_Free(mybuf);
  exit:
    _Py_dg_freedtoa(buf);
    return result;
}

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static PyFloatObject* fill_free_list ( void  ) [static]

Definition at line 54 of file floatobject.c.

{
    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;
}

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static PyObject* float__format__ ( PyObject self,
PyObject args 
) [static]

Definition at line 1745 of file floatobject.c.

{
    PyObject *format_spec;

    if (!PyArg_ParseTuple(args, "U:__format__", &format_spec))
        return NULL;
    return _PyFloat_FormatAdvanced(self,
                                   PyUnicode_AS_UNICODE(format_spec),
                                   PyUnicode_GET_SIZE(format_spec));
}

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static PyObject* float_abs ( PyFloatObject v) [static]

Definition at line 816 of file floatobject.c.

{
    return PyFloat_FromDouble(fabs(v->ob_fval));
}

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static PyObject* float_add ( PyObject v,
PyObject w 
) [static]

Definition at line 537 of file floatobject.c.

{
    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);
}

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static PyObject* float_as_integer_ratio ( PyObject v,
PyObject unused 
) [static]

Definition at line 1468 of file floatobject.c.

{
    double self;
    double float_part;
    int exponent;
    int i;

    PyObject *prev;
    PyObject *py_exponent = NULL;
    PyObject *numerator = NULL;
    PyObject *denominator = NULL;
    PyObject *result_pair = NULL;
    PyNumberMethods *long_methods = PyLong_Type.tp_as_number;

#define INPLACE_UPDATE(obj, call) \
    prev = obj; \
    obj = call; \
    Py_DECREF(prev); \

    CONVERT_TO_DOUBLE(v, self);

    if (Py_IS_INFINITY(self)) {
      PyErr_SetString(PyExc_OverflowError,
                      "Cannot pass infinity to float.as_integer_ratio.");
      return NULL;
    }
    if (Py_IS_NAN(self)) {
      PyErr_SetString(PyExc_ValueError,
                      "Cannot pass NaN to float.as_integer_ratio.");
      return NULL;
    }

    PyFPE_START_PROTECT("as_integer_ratio", goto error);
    float_part = frexp(self, &exponent);        /* self == float_part * 2**exponent exactly */
    PyFPE_END_PROTECT(float_part);

    for (i=0; i<300 && float_part != floor(float_part) ; i++) {
        float_part *= 2.0;
        exponent--;
    }
    /* self == float_part * 2**exponent exactly and float_part is integral.
       If FLT_RADIX != 2, the 300 steps may leave a tiny fractional part
       to be truncated by PyLong_FromDouble(). */

    numerator = PyLong_FromDouble(float_part);
    if (numerator == NULL) goto error;

    /* fold in 2**exponent */
    denominator = PyLong_FromLong(1);
    py_exponent = PyLong_FromLong(labs((long)exponent));
    if (py_exponent == NULL) goto error;
    INPLACE_UPDATE(py_exponent,
                   long_methods->nb_lshift(denominator, py_exponent));
    if (py_exponent == NULL) goto error;
    if (exponent > 0) {
        INPLACE_UPDATE(numerator,
                       long_methods->nb_multiply(numerator, py_exponent));
        if (numerator == NULL) goto error;
    }
    else {
        Py_DECREF(denominator);
        denominator = py_exponent;
        py_exponent = NULL;
    }

    result_pair = PyTuple_Pack(2, numerator, denominator);

#undef INPLACE_UPDATE
error:
    Py_XDECREF(py_exponent);
    Py_XDECREF(denominator);
    Py_XDECREF(numerator);
    return result_pair;
}

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static int float_bool ( PyFloatObject v) [static]

Definition at line 822 of file floatobject.c.

{
    return v->ob_fval != 0.0;
}
static void float_dealloc ( PyFloatObject op) [static]

Definition at line 233 of file floatobject.c.

{
    if (PyFloat_CheckExact(op)) {
        Py_TYPE(op) = (struct _typeobject *)free_list;
        free_list = op;
    }
    else
        Py_TYPE(op)->tp_free((PyObject *)op);
}
static PyObject* float_div ( PyObject v,
PyObject w 
) [static]

Definition at line 573 of file floatobject.c.

{
    double a,b;
    CONVERT_TO_DOUBLE(v, a);
    CONVERT_TO_DOUBLE(w, b);
    if (b == 0.0) {
        PyErr_SetString(PyExc_ZeroDivisionError,
                        "float division by zero");
        return NULL;
    }
    PyFPE_START_PROTECT("divide", return 0)
    a = a / b;
    PyFPE_END_PROTECT(a)
    return PyFloat_FromDouble(a);
}

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static PyObject* float_divmod ( PyObject v,
PyObject w 
) [static]

Definition at line 620 of file floatobject.c.

{
    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. */
        mod = copysign(0.0, wx);
    }
    /* 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 */
        floordiv = copysign(0.0, vx / wx); /* zero w/ sign of vx/wx */
    }
    PyFPE_END_PROTECT(floordiv)
    return Py_BuildValue("(dd)", floordiv, mod);
}

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static PyObject* float_float ( PyObject v) [static]

Definition at line 1063 of file floatobject.c.

{
    if (PyFloat_CheckExact(v))
        Py_INCREF(v);
    else
        v = PyFloat_FromDouble(((PyFloatObject *)v)->ob_fval);
    return v;
}

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static PyObject* float_floor_div ( PyObject v,
PyObject w 
) [static]

Definition at line 667 of file floatobject.c.

{
    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;
}

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static PyObject* float_fromhex ( PyObject cls,
PyObject arg 
) [static]

Definition at line 1217 of file floatobject.c.

{
    PyObject *result_as_float, *result;
    double x;
    long exp, top_exp, lsb, key_digit;
    char *s, *coeff_start, *s_store, *coeff_end, *exp_start, *s_end;
    int half_eps, digit, round_up, negate=0;
    Py_ssize_t length, ndigits, fdigits, i;

    /*
     * For the sake of simplicity and correctness, we impose an artificial
     * limit on ndigits, the total number of hex digits in the coefficient
     * The limit is chosen to ensure that, writing exp for the exponent,
     *
     *   (1) if exp > LONG_MAX/2 then the value of the hex string is
     *   guaranteed to overflow (provided it's nonzero)
     *
     *   (2) if exp < LONG_MIN/2 then the value of the hex string is
     *   guaranteed to underflow to 0.
     *
     *   (3) if LONG_MIN/2 <= exp <= LONG_MAX/2 then there's no danger of
     *   overflow in the calculation of exp and top_exp below.
     *
     * More specifically, ndigits is assumed to satisfy the following
     * inequalities:
     *
     *   4*ndigits <= DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2
     *   4*ndigits <= LONG_MAX/2 + 1 - DBL_MAX_EXP
     *
     * If either of these inequalities is not satisfied, a ValueError is
     * raised.  Otherwise, write x for the value of the hex string, and
     * assume x is nonzero.  Then
     *
     *   2**(exp-4*ndigits) <= |x| < 2**(exp+4*ndigits).
     *
     * Now if exp > LONG_MAX/2 then:
     *
     *   exp - 4*ndigits >= LONG_MAX/2 + 1 - (LONG_MAX/2 + 1 - DBL_MAX_EXP)
     *                    = DBL_MAX_EXP
     *
     * so |x| >= 2**DBL_MAX_EXP, which is too large to be stored in C
     * double, so overflows.  If exp < LONG_MIN/2, then
     *
     *   exp + 4*ndigits <= LONG_MIN/2 - 1 + (
     *                      DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2)
     *                    = DBL_MIN_EXP - DBL_MANT_DIG - 1
     *
     * and so |x| < 2**(DBL_MIN_EXP-DBL_MANT_DIG-1), hence underflows to 0
     * when converted to a C double.
     *
     * It's easy to show that if LONG_MIN/2 <= exp <= LONG_MAX/2 then both
     * exp+4*ndigits and exp-4*ndigits are within the range of a long.
     */

    s = _PyUnicode_AsStringAndSize(arg, &length);
    if (s == NULL)
        return NULL;
    s_end = s + length;

    /********************
     * Parse the string *
     ********************/

    /* leading whitespace */
    while (Py_ISSPACE(*s))
        s++;

    /* infinities and nans */
    x = _Py_parse_inf_or_nan(s, &coeff_end);
    if (coeff_end != s) {
        s = coeff_end;
        goto finished;
    }

    /* optional sign */
    if (*s == '-') {
        s++;
        negate = 1;
    }
    else if (*s == '+')
        s++;

    /* [0x] */
    s_store = s;
    if (*s == '0') {
        s++;
        if (*s == 'x' || *s == 'X')
            s++;
        else
            s = s_store;
    }

    /* coefficient: <integer> [. <fraction>] */
    coeff_start = s;
    while (hex_from_char(*s) >= 0)
        s++;
    s_store = s;
    if (*s == '.') {
        s++;
        while (hex_from_char(*s) >= 0)
            s++;
        coeff_end = s-1;
    }
    else
        coeff_end = s;

    /* ndigits = total # of hex digits; fdigits = # after point */
    ndigits = coeff_end - coeff_start;
    fdigits = coeff_end - s_store;
    if (ndigits == 0)
        goto parse_error;
    if (ndigits > MIN(DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2,
                      LONG_MAX/2 + 1 - DBL_MAX_EXP)/4)
        goto insane_length_error;

    /* [p <exponent>] */
    if (*s == 'p' || *s == 'P') {
        s++;
        exp_start = s;
        if (*s == '-' || *s == '+')
            s++;
        if (!('0' <= *s && *s <= '9'))
            goto parse_error;
        s++;
        while ('0' <= *s && *s <= '9')
            s++;
        exp = strtol(exp_start, NULL, 10);
    }
    else
        exp = 0;

/* for 0 <= j < ndigits, HEX_DIGIT(j) gives the jth most significant digit */
#define HEX_DIGIT(j) hex_from_char(*((j) < fdigits ?            \
                     coeff_end-(j) :                                    \
                     coeff_end-1-(j)))

    /*******************************************
     * Compute rounded value of the hex string *
     *******************************************/

    /* Discard leading zeros, and catch extreme overflow and underflow */
    while (ndigits > 0 && HEX_DIGIT(ndigits-1) == 0)
        ndigits--;
    if (ndigits == 0 || exp < LONG_MIN/2) {
        x = 0.0;
        goto finished;
    }
    if (exp > LONG_MAX/2)
        goto overflow_error;

    /* Adjust exponent for fractional part. */
    exp = exp - 4*((long)fdigits);

    /* top_exp = 1 more than exponent of most sig. bit of coefficient */
    top_exp = exp + 4*((long)ndigits - 1);
    for (digit = HEX_DIGIT(ndigits-1); digit != 0; digit /= 2)
        top_exp++;

    /* catch almost all nonextreme cases of overflow and underflow here */
    if (top_exp < DBL_MIN_EXP - DBL_MANT_DIG) {
        x = 0.0;
        goto finished;
    }
    if (top_exp > DBL_MAX_EXP)
        goto overflow_error;

    /* lsb = exponent of least significant bit of the *rounded* value.
       This is top_exp - DBL_MANT_DIG unless result is subnormal. */
    lsb = MAX(top_exp, (long)DBL_MIN_EXP) - DBL_MANT_DIG;

    x = 0.0;
    if (exp >= lsb) {
        /* no rounding required */
        for (i = ndigits-1; i >= 0; i--)
            x = 16.0*x + HEX_DIGIT(i);
        x = ldexp(x, (int)(exp));
        goto finished;
    }
    /* rounding required.  key_digit is the index of the hex digit
       containing the first bit to be rounded away. */
    half_eps = 1 << (int)((lsb - exp - 1) % 4);
    key_digit = (lsb - exp - 1) / 4;
    for (i = ndigits-1; i > key_digit; i--)
        x = 16.0*x + HEX_DIGIT(i);
    digit = HEX_DIGIT(key_digit);
    x = 16.0*x + (double)(digit & (16-2*half_eps));

    /* round-half-even: round up if bit lsb-1 is 1 and at least one of
       bits lsb, lsb-2, lsb-3, lsb-4, ... is 1. */
    if ((digit & half_eps) != 0) {
        round_up = 0;
        if ((digit & (3*half_eps-1)) != 0 ||
            (half_eps == 8 && (HEX_DIGIT(key_digit+1) & 1) != 0))
            round_up = 1;
        else
            for (i = key_digit-1; i >= 0; i--)
                if (HEX_DIGIT(i) != 0) {
                    round_up = 1;
                    break;
                }
        if (round_up) {
            x += 2*half_eps;
            if (top_exp == DBL_MAX_EXP &&
                x == ldexp((double)(2*half_eps), DBL_MANT_DIG))
                /* overflow corner case: pre-rounded value <
                   2**DBL_MAX_EXP; rounded=2**DBL_MAX_EXP. */
                goto overflow_error;
        }
    }
    x = ldexp(x, (int)(exp+4*key_digit));

  finished:
    /* optional trailing whitespace leading to the end of the string */
    while (Py_ISSPACE(*s))
        s++;
    if (s != s_end)
        goto parse_error;
    result_as_float = Py_BuildValue("(d)", negate ? -x : x);
    if (result_as_float == NULL)
        return NULL;
    result = PyObject_CallObject(cls, result_as_float);
    Py_DECREF(result_as_float);
    return result;

  overflow_error:
    PyErr_SetString(PyExc_OverflowError,
                    "hexadecimal value too large to represent as a float");
    return NULL;

  parse_error:
    PyErr_SetString(PyExc_ValueError,
                    "invalid hexadecimal floating-point string");
    return NULL;

  insane_length_error:
    PyErr_SetString(PyExc_ValueError,
                    "hexadecimal string too long to convert");
    return NULL;
}

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static PyObject* float_getformat ( PyTypeObject v,
PyObject arg 
) [static]

Definition at line 1619 of file floatobject.c.

{
    char* s;
    float_format_type r;

    if (!PyUnicode_Check(arg)) {
        PyErr_Format(PyExc_TypeError,
         "__getformat__() argument must be string, not %.500s",
                         Py_TYPE(arg)->tp_name);
        return NULL;
    }
    s = _PyUnicode_AsString(arg);
    if (s == NULL)
        return NULL;
    if (strcmp(s, "double") == 0) {
        r = double_format;
    }
    else if (strcmp(s, "float") == 0) {
        r = float_format;
    }
    else {
        PyErr_SetString(PyExc_ValueError,
                        "__getformat__() argument 1 must be "
                        "'double' or 'float'");
        return NULL;
    }

    switch (r) {
    case unknown_format:
        return PyUnicode_FromString("unknown");
    case ieee_little_endian_format:
        return PyUnicode_FromString("IEEE, little-endian");
    case ieee_big_endian_format:
        return PyUnicode_FromString("IEEE, big-endian");
    default:
        Py_FatalError("insane float_format or double_format");
        return NULL;
    }
}

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static PyObject* float_getnewargs ( PyFloatObject v) [static]

Definition at line 1604 of file floatobject.c.

{
    return Py_BuildValue("(d)", v->ob_fval);
}

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static PyObject* float_getzero ( PyObject v,
void closure 
) [static]

Definition at line 1739 of file floatobject.c.

{
    return PyFloat_FromDouble(0.0);
}

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static Py_hash_t float_hash ( PyFloatObject v) [static]

Definition at line 531 of file floatobject.c.

{
    return _Py_HashDouble(v->ob_fval);
}

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static PyObject* float_hex ( PyObject v) [static]

Definition at line 1153 of file floatobject.c.

{
    double x, m;
    int e, shift, i, si, esign;
    /* Space for 1+(TOHEX_NBITS-1)/4 digits, a decimal point, and the
       trailing NUL byte. */
    char s[(TOHEX_NBITS-1)/4+3];

    CONVERT_TO_DOUBLE(v, x);

    if (Py_IS_NAN(x) || Py_IS_INFINITY(x))
        return float_repr((PyFloatObject *)v);

    if (x == 0.0) {
        if (copysign(1.0, x) == -1.0)
            return PyUnicode_FromString("-0x0.0p+0");
        else
            return PyUnicode_FromString("0x0.0p+0");
    }

    m = frexp(fabs(x), &e);
    shift = 1 - MAX(DBL_MIN_EXP - e, 0);
    m = ldexp(m, shift);
    e -= shift;

    si = 0;
    s[si] = char_from_hex((int)m);
    si++;
    m -= (int)m;
    s[si] = '.';
    si++;
    for (i=0; i < (TOHEX_NBITS-1)/4; i++) {
        m *= 16.0;
        s[si] = char_from_hex((int)m);
        si++;
        m -= (int)m;
    }
    s[si] = '\0';

    if (e < 0) {
        esign = (int)'-';
        e = -e;
    }
    else
        esign = (int)'+';

    if (x < 0.0)
        return PyUnicode_FromFormat("-0x%sp%c%d", s, esign, e);
    else
        return PyUnicode_FromFormat("0x%sp%c%d", s, esign, e);
}

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static PyObject* float_is_integer ( PyObject v) [static]

Definition at line 828 of file floatobject.c.

{
    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;
}

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static PyObject* float_mul ( PyObject v,
PyObject w 
) [static]

Definition at line 561 of file floatobject.c.

{
    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);
}

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static PyObject* float_neg ( PyFloatObject v) [static]

Definition at line 810 of file floatobject.c.

{
    return PyFloat_FromDouble(-v->ob_fval);
}

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static PyObject* float_new ( PyTypeObject type,
PyObject args,
PyObject kwds 
) [static]

Definition at line 1562 of file floatobject.c.

{
    PyObject *x = Py_False; /* Integer zero */
    static char *kwlist[] = {"x", 0};

    if (type != &PyFloat_Type)
        return float_subtype_new(type, args, kwds); /* Wimp out */
    if (!PyArg_ParseTupleAndKeywords(args, kwds, "|O:float", kwlist, &x))
        return NULL;
    /* If it's a string, but not a string subclass, use
       PyFloat_FromString. */
    if (PyUnicode_CheckExact(x))
        return PyFloat_FromString(x);
    return PyNumber_Float(x);
}

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static PyObject* float_pow ( PyObject v,
PyObject w,
PyObject z 
) [static]

Definition at line 686 of file floatobject.c.

{
    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)) {
            /* Negative numbers raised to fractional powers
             * become complex.
             */
            return PyComplex_Type.tp_as_number->nb_power(v, w, z);
        }
        /* 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);
}

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static PyObject* float_rem ( PyObject v,
PyObject w 
) [static]

Definition at line 590 of file floatobject.c.

{
    double vx, wx;
    double mod;
    CONVERT_TO_DOUBLE(v, vx);
    CONVERT_TO_DOUBLE(w, wx);
    if (wx == 0.0) {
        PyErr_SetString(PyExc_ZeroDivisionError,
                        "float modulo");
        return NULL;
    }
    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. */
        mod = copysign(0.0, wx);
    }
    PyFPE_END_PROTECT(mod)
    return PyFloat_FromDouble(mod);
}

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static PyObject* float_repr ( PyFloatObject v) [static]

Definition at line 313 of file floatobject.c.

{
    PyObject *result;
    char *buf = PyOS_double_to_string(PyFloat_AS_DOUBLE(v),
                                      'r', 0,
                                      Py_DTSF_ADD_DOT_0,
                                      NULL);
    if (!buf)
        return PyErr_NoMemory();
    result = PyUnicode_FromString(buf);
    PyMem_Free(buf);
    return result;
}

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static PyObject* float_richcompare ( PyObject v,
PyObject w,
int  op 
) [static]

Definition at line 343 of file floatobject.c.

{
    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 (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 (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 = PyLong_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;
}

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static PyObject* float_round ( PyObject v,
PyObject args 
) [static]

Definition at line 1017 of file floatobject.c.

{
    double x, rounded;
    PyObject *o_ndigits = NULL;
    Py_ssize_t ndigits;

    x = PyFloat_AsDouble(v);
    if (!PyArg_ParseTuple(args, "|O", &o_ndigits))
        return NULL;
    if (o_ndigits == NULL) {
        /* single-argument round: round to nearest integer */
        rounded = round(x);
        if (fabs(x-rounded) == 0.5)
            /* halfway case: round to even */
            rounded = 2.0*round(x/2.0);
        return PyLong_FromDouble(rounded);
    }

    /* interpret second argument as a Py_ssize_t; clips on overflow */
    ndigits = PyNumber_AsSsize_t(o_ndigits, NULL);
    if (ndigits == -1 && PyErr_Occurred())
        return NULL;

    /* nans and infinities round to themselves */
    if (!Py_IS_FINITE(x))
        return PyFloat_FromDouble(x);

    /* Deal with extreme values for ndigits. For ndigits > NDIGITS_MAX, x
       always rounds to itself.  For ndigits < NDIGITS_MIN, x always
       rounds to +-0.0.  Here 0.30103 is an upper bound for log10(2). */
#define NDIGITS_MAX ((int)((DBL_MANT_DIG-DBL_MIN_EXP) * 0.30103))
#define NDIGITS_MIN (-(int)((DBL_MAX_EXP + 1) * 0.30103))
    if (ndigits > NDIGITS_MAX)
        /* return x */
        return PyFloat_FromDouble(x);
    else if (ndigits < NDIGITS_MIN)
        /* return 0.0, but with sign of x */
        return PyFloat_FromDouble(0.0*x);
    else
        /* finite x, and ndigits is not unreasonably large */
        return double_round(x, (int)ndigits);
#undef NDIGITS_MAX
#undef NDIGITS_MIN
}

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static PyObject* float_setformat ( PyTypeObject v,
PyObject args 
) [static]

Definition at line 1670 of file floatobject.c.

{
    char* typestr;
    char* format;
    float_format_type f;
    float_format_type detected;
    float_format_type *p;

    if (!PyArg_ParseTuple(args, "ss:__setformat__", &typestr, &format))
        return NULL;

    if (strcmp(typestr, "double") == 0) {
        p = &double_format;
        detected = detected_double_format;
    }
    else if (strcmp(typestr, "float") == 0) {
        p = &float_format;
        detected = detected_float_format;
    }
    else {
        PyErr_SetString(PyExc_ValueError,
                        "__setformat__() argument 1 must "
                        "be 'double' or 'float'");
        return NULL;
    }

    if (strcmp(format, "unknown") == 0) {
        f = unknown_format;
    }
    else if (strcmp(format, "IEEE, little-endian") == 0) {
        f = ieee_little_endian_format;
    }
    else if (strcmp(format, "IEEE, big-endian") == 0) {
        f = ieee_big_endian_format;
    }
    else {
        PyErr_SetString(PyExc_ValueError,
                        "__setformat__() argument 2 must be "
                        "'unknown', 'IEEE, little-endian' or "
                        "'IEEE, big-endian'");
        return NULL;

    }

    if (f != unknown_format && f != detected) {
        PyErr_Format(PyExc_ValueError,
                     "can only set %s format to 'unknown' or the "
                     "detected platform value", typestr);
        return NULL;
    }

    *p = f;
    Py_RETURN_NONE;
}

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static PyObject* float_sub ( PyObject v,
PyObject w 
) [static]

Definition at line 549 of file floatobject.c.

{
    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);
}

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static PyObject * float_subtype_new ( PyTypeObject type,
PyObject args,
PyObject kwds 
) [static]

Definition at line 1584 of file floatobject.c.

{
    PyObject *tmp, *newobj;

    assert(PyType_IsSubtype(type, &PyFloat_Type));
    tmp = float_new(&PyFloat_Type, args, kwds);
    if (tmp == NULL)
        return NULL;
    assert(PyFloat_CheckExact(tmp));
    newobj = type->tp_alloc(type, 0);
    if (newobj == NULL) {
        Py_DECREF(tmp);
        return NULL;
    }
    ((PyFloatObject *)newobj)->ob_fval = ((PyFloatObject *)tmp)->ob_fval;
    Py_DECREF(tmp);
    return newobj;
}

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static PyObject* float_trunc ( PyObject v) [static]

Definition at line 880 of file floatobject.c.

{
    double x = PyFloat_AsDouble(v);
    double wholepart;           /* integral portion of x, rounded toward 0 */

    (void)modf(x, &wholepart);
    /* Try to get out cheap if this fits in a Python int.  The attempt
     * to cast to long must be protected, as C doesn't define what
     * happens if the double is too big to fit in a long.  Some rare
     * systems raise an exception then (RISCOS was mentioned as one,
     * and someone using a non-default option on Sun also bumped into
     * that).  Note that checking for >= and <= LONG_{MIN,MAX} would
     * still be vulnerable:  if a long has more bits of precision than
     * a double, casting MIN/MAX to double may yield an approximation,
     * and if that's rounded up, then, e.g., wholepart=LONG_MAX+1 would
     * yield true from the C expression wholepart<=LONG_MAX, despite
     * that wholepart is actually greater than LONG_MAX.
     */
    if (LONG_MIN < wholepart && wholepart < LONG_MAX) {
        const long aslong = (long)wholepart;
        return PyLong_FromLong(aslong);
    }
    return PyLong_FromDouble(wholepart);
}

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static int hex_from_char ( char  c) [static]

Definition at line 1082 of file floatobject.c.

                      {
    int x;
    switch(c) {
    case '0':
        x = 0;
        break;
    case '1':
        x = 1;
        break;
    case '2':
        x = 2;
        break;
    case '3':
        x = 3;
        break;
    case '4':
        x = 4;
        break;
    case '5':
        x = 5;
        break;
    case '6':
        x = 6;
        break;
    case '7':
        x = 7;
        break;
    case '8':
        x = 8;
        break;
    case '9':
        x = 9;
        break;
    case 'a':
    case 'A':
        x = 10;
        break;
    case 'b':
    case 'B':
        x = 11;
        break;
    case 'c':
    case 'C':
        x = 12;
        break;
    case 'd':
    case 'D':
        x = 13;
        break;
    case 'e':
    case 'E':
        x = 14;
        break;
    case 'f':
    case 'F':
        x = 15;
        break;
    default:
        x = -1;
        break;
    }
    return x;
}

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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."   
)
PyDoc_STRVAR ( float_hex_doc  ,
"float.hex() -> string\n\\n\Return a hexadecimal representation of a floating-point number.\n\>>  ,
(-0.1).hex()\n\'-0x1.999999999999ap-4'\n>>  ,
3.14159.hex()\n\'0x1.921f9f01b866ep+1'"   
)
PyDoc_STRVAR ( float_fromhex_doc  ,
"float.fromhex(string) -> float\n\\n\Create a floating-point number from a hexadecimal string.\n\>>  ,
float.fromhex('0x1.ffffp10')\n\2047.984375\n>>  ,
float.fromhex('-0x1p-1074')\n\-4.9406564584124654e-324"   
)
PyDoc_STRVAR ( float_as_integer_ratio_doc  ,
"float.as_integer_ratio() -> (int, int)\n""\n""Returns a pair of  integers,
whose ratio is exactly equal to the original\n""float and with a positive denominator.\n""Raises OverflowError on infinities and a ValueError on NaNs.\n""\n"">>  ,
(10.0).as_integer_ratio()\n""(10, 1)\n"">>  ,
(0.0).as_integer_ratio()\n""(0, 1)\n"">>  ,
(-.25).as_integer_ratio()\n""(-1, 4)"   
)
PyDoc_STRVAR ( float_getformat_doc  ,
"float.__getformat__(typestr) -> string\n""\n""You probably don't want to use this function. It exists mainly to be\n""used in Python's test suite.\n""\n""typestr must be 'double' or 'float'. This function returns whichever of\n""'unknown'  ,
IEEE,
big-endian'or '  IEEE,
little-endian'best describes the\n""format of floating point numbers used by the C type named by typestr."   
)
PyDoc_STRVAR ( float_setformat_doc  ,
"float.__setformat__(typestr, fmt) -> None\n""\n""You probably don't want to use this function. It exists mainly to be\n""used in Python's test suite.\n""\n""typestr must be 'double' or 'float'. fmt must be one of 'unknown'  ,
\n""'  IEEE,
big-endian'or '  IEEE,
little-endian'  ,
and in addition can only be\n""one of the latter two if it appears to match the underlying C reality.\n""\n""Overrides the automatic determination of C-level floating point type.\n""This affects how floats are converted to and from binary strings."   
)
PyDoc_STRVAR ( float__format__doc  ,
"float.__format__(format_spec) -> string\n""\n""Formats the float according to format_spec."   
)
PyDoc_STRVAR ( float_doc  ,
"float(x) -> floating point number\n\\n\Convert a string or number to a floating point  number,
if possible."   
)
double PyFloat_AsDouble ( PyObject op)

Definition at line 244 of file floatobject.c.

{
    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)) {
        PyErr_SetString(PyExc_TypeError,
                        "nb_float should return float object");
        return -1;
    }

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

    return val;
}

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Definition at line 1946 of file floatobject.c.

{
    PyFloatObject *p;
    PyFloatBlock *list, *next;
    int i;
    int u;                      /* remaining unfreed floats per block */
    int freelist_size = 0;

    list = block_list;
    block_list = NULL;
    free_list = NULL;
    while (list != NULL) {
        u = 0;
        for (i = 0, p = &list->objects[0];
             i < N_FLOATOBJECTS;
             i++, p++) {
            if (PyFloat_CheckExact(p) && Py_REFCNT(p) != 0)
                u++;
        }
        next = list->next;
        if (u) {
            list->next = block_list;
            block_list = list;
            for (i = 0, p = &list->objects[0];
                 i < N_FLOATOBJECTS;
                 i++, p++) {
                if (!PyFloat_CheckExact(p) ||
                    Py_REFCNT(p) == 0) {
                    Py_TYPE(p) = (struct _typeobject *)
                        free_list;
                    free_list = p;
                }
            }
        }
        else {
            PyMem_FREE(list);
        }
        freelist_size += u;
        list = next;
    }
    return freelist_size;
}

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Definition at line 1990 of file floatobject.c.

{
    PyFloatObject *p;
    PyFloatBlock *list;
    int i;
    int u;                      /* total unfreed floats per block */

    u = PyFloat_ClearFreeList();

    if (!Py_VerboseFlag)
        return;
    fprintf(stderr, "# cleanup floats");
    if (!u) {
        fprintf(stderr, "\n");
    }
    else {
        fprintf(stderr,
            ": %d unfreed float%s\n",
            u, u == 1 ? "" : "s");
    }
    if (Py_VerboseFlag > 1) {
        list = block_list;
        while (list != NULL) {
            for (i = 0, p = &list->objects[0];
                 i < N_FLOATOBJECTS;
                 i++, p++) {
                if (PyFloat_CheckExact(p) &&
                    Py_REFCNT(p) != 0) {
                    char *buf = PyOS_double_to_string(
                        PyFloat_AS_DOUBLE(p), 'r',
                        0, 0, NULL);
                    if (buf) {
                        /* XXX(twouters) cast
                           refcount to long
                           until %zd is
                           universally
                           available
                        */
                        fprintf(stderr,
                 "#   <float at %p, refcnt=%ld, val=%s>\n",
                                    p, (long)Py_REFCNT(p), buf);
                                    PyMem_Free(buf);
                            }
                }
            }
            list = list->next;
        }
    }
}

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PyObject* PyFloat_FromDouble ( double  fval)

Definition at line 157 of file floatobject.c.

{
    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;
}

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Definition at line 173 of file floatobject.c.

{
    const char *s, *last, *end;
    double x;
    PyObject *s_buffer = NULL;
    Py_ssize_t len;
    PyObject *result = NULL;

    if (PyUnicode_Check(v)) {
        Py_ssize_t i, buflen = PyUnicode_GET_SIZE(v);
        Py_UNICODE *bufptr;
        s_buffer = PyUnicode_TransformDecimalToASCII(
            PyUnicode_AS_UNICODE(v), buflen);
        if (s_buffer == NULL)
            return NULL;
        /* Replace non-ASCII whitespace with ' ' */
        bufptr = PyUnicode_AS_UNICODE(s_buffer);
        for (i = 0; i < buflen; i++) {
            Py_UNICODE ch = bufptr[i];
            if (ch > 127 && Py_UNICODE_ISSPACE(ch))
                bufptr[i] = ' ';
        }
        s = _PyUnicode_AsStringAndSize(s_buffer, &len);
        if (s == NULL) {
            Py_DECREF(s_buffer);
            return NULL;
        }
        last = s + len;
    }
    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;
    /* strip space */
    while (s < last && Py_ISSPACE(*s))
        s++;
    while (s < last - 1 && Py_ISSPACE(last[-1]))
        last--;
    /* 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 (end != last) {
        PyErr_Format(PyExc_ValueError,
                     "could not convert string to float: "
                     "%R", v);
        result = NULL;
    }
    else if (x == -1.0 && PyErr_Occurred())
        result = NULL;
    else
        result = PyFloat_FromDouble(x);

    Py_XDECREF(s_buffer);
    return result;
}

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Definition at line 120 of file floatobject.c.

{
    PyObject* floatinfo;
    int pos = 0;

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

#define SetIntFlag(flag) \
    PyStructSequence_SET_ITEM(floatinfo, pos++, PyLong_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;
}

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double PyFloat_GetMax ( void  )

Definition at line 72 of file floatobject.c.

{
    return DBL_MAX;
}
double PyFloat_GetMin ( void  )

Definition at line 78 of file floatobject.c.

{
    return DBL_MIN;
}

Variable Documentation

PyFloatBlock* block_list = NULL [static]

Definition at line 50 of file floatobject.c.

Definition at line 1616 of file floatobject.c.

Definition at line 1616 of file floatobject.c.

Definition at line 1615 of file floatobject.c.

Definition at line 1814 of file floatobject.c.

Definition at line 1615 of file floatobject.c.

Initial value:
 {
    {"real",
     (getter)float_float, (setter)NULL,
     "the real part of a complex number",
     NULL},
    {"imag",
     (getter)float_getzero, (setter)NULL,
     "the imaginary part of a complex number",
     NULL},
    {NULL}  
}

Definition at line 1796 of file floatobject.c.

Definition at line 1762 of file floatobject.c.

Initial value:
 {
    "sys.float_info",           
    floatinfo__doc__,           
    floatinfo_fields,           
    11
}

Definition at line 112 of file floatobject.c.

Initial value:
 {
    {"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}
}

Definition at line 92 of file floatobject.c.

Definition at line 83 of file floatobject.c.

Definition at line 51 of file floatobject.c.

Definition at line 1850 of file floatobject.c.