/* 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 "pycore_abstract.h" // _PyNumber_Index()
#include "pycore_dtoa.h" // _Py_dg_dtoa()
#include "pycore_floatobject.h" // _PyFloat_FormatAdvancedWriter()
#include "pycore_initconfig.h" // _PyStatus_OK()
#include "pycore_interp.h" // _Py_float_freelist
#include "pycore_long.h" // _PyLong_GetOne()
#include "pycore_modsupport.h" // _PyArg_NoKwnames()
#include "pycore_object.h" // _PyObject_Init(), _PyDebugAllocatorStats()
#include "pycore_pymath.h" // _PY_SHORT_FLOAT_REPR
#include "pycore_pystate.h" // _PyInterpreterState_GET()
#include "pycore_structseq.h" // _PyStructSequence_FiniBuiltin()
#include // DBL_MAX
#include // strtol()
/*[clinic input]
class float "PyObject *" "&PyFloat_Type"
[clinic start generated code]*/
/*[clinic end generated code: output=da39a3ee5e6b4b0d input=dd0003f68f144284]*/
#include "clinic/floatobject.c.h"
#ifdef WITH_FREELISTS
static struct _Py_float_freelist *
get_float_freelist(void)
{
struct _Py_object_freelists *freelists = _Py_object_freelists_GET();
assert(freelists != NULL);
return &freelists->floats;
}
#endif
double
PyFloat_GetMax(void)
{
return DBL_MAX;
}
double
PyFloat_GetMin(void)
{
return DBL_MIN;
}
static PyTypeObject FloatInfoType;
PyDoc_STRVAR(floatinfo__doc__,
"sys.float_info\n\
\n\
A named tuple 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 normalized 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 float"},
{"dig", "DBL_DIG -- maximum number of decimal digits that "
"can be faithfully represented in a float"},
{"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 -- rounding mode used for arithmetic "
"operations"},
{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 SetFlag(CALL) \
do { \
PyObject *flag = (CALL); \
if (flag == NULL) { \
Py_CLEAR(floatinfo); \
return NULL; \
} \
PyStructSequence_SET_ITEM(floatinfo, pos++, flag); \
} while (0)
#define SetIntFlag(FLAG) SetFlag(PyLong_FromLong((FLAG)))
#define SetDblFlag(FLAG) SetFlag(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
#undef SetFlag
return floatinfo;
}
PyObject *
PyFloat_FromDouble(double fval)
{
PyFloatObject *op;
#ifdef WITH_FREELISTS
struct _Py_float_freelist *float_freelist = get_float_freelist();
op = float_freelist->items;
if (op != NULL) {
float_freelist->items = (PyFloatObject *) Py_TYPE(op);
float_freelist->numfree--;
OBJECT_STAT_INC(from_freelist);
}
else
#endif
{
op = PyObject_Malloc(sizeof(PyFloatObject));
if (!op) {
return PyErr_NoMemory();
}
}
_PyObject_Init((PyObject*)op, &PyFloat_Type);
op->ob_fval = fval;
return (PyObject *) op;
}
static PyObject *
float_from_string_inner(const char *s, Py_ssize_t len, void *obj)
{
double x;
const char *end;
const char *last = s + len;
/* strip leading whitespace */
while (s < last && Py_ISSPACE(*s)) {
s++;
}
if (s == last) {
PyErr_Format(PyExc_ValueError,
"could not convert string to float: "
"%R", obj);
return NULL;
}
/* strip trailing whitespace */
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", obj);
return NULL;
}
else if (x == -1.0 && PyErr_Occurred()) {
return NULL;
}
else {
return PyFloat_FromDouble(x);
}
}
PyObject *
PyFloat_FromString(PyObject *v)
{
const char *s;
PyObject *s_buffer = NULL;
Py_ssize_t len;
Py_buffer view = {NULL, NULL};
PyObject *result = NULL;
if (PyUnicode_Check(v)) {
s_buffer = _PyUnicode_TransformDecimalAndSpaceToASCII(v);
if (s_buffer == NULL)
return NULL;
assert(PyUnicode_IS_ASCII(s_buffer));
/* Simply get a pointer to existing ASCII characters. */
s = PyUnicode_AsUTF8AndSize(s_buffer, &len);
assert(s != NULL);
}
else if (PyBytes_Check(v)) {
s = PyBytes_AS_STRING(v);
len = PyBytes_GET_SIZE(v);
}
else if (PyByteArray_Check(v)) {
s = PyByteArray_AS_STRING(v);
len = PyByteArray_GET_SIZE(v);
}
else if (PyObject_GetBuffer(v, &view, PyBUF_SIMPLE) == 0) {
s = (const char *)view.buf;
len = view.len;
/* Copy to NUL-terminated buffer. */
s_buffer = PyBytes_FromStringAndSize(s, len);
if (s_buffer == NULL) {
PyBuffer_Release(&view);
return NULL;
}
s = PyBytes_AS_STRING(s_buffer);
}
else {
PyErr_Format(PyExc_TypeError,
"float() argument must be a string or a real number, not '%.200s'",
Py_TYPE(v)->tp_name);
return NULL;
}
result = _Py_string_to_number_with_underscores(s, len, "float", v, v,
float_from_string_inner);
PyBuffer_Release(&view);
Py_XDECREF(s_buffer);
return result;
}
void
_PyFloat_ExactDealloc(PyObject *obj)
{
assert(PyFloat_CheckExact(obj));
PyFloatObject *op = (PyFloatObject *)obj;
#ifdef WITH_FREELISTS
struct _Py_float_freelist *float_freelist = get_float_freelist();
if (float_freelist->numfree >= PyFloat_MAXFREELIST || float_freelist->numfree < 0) {
PyObject_Free(op);
return;
}
float_freelist->numfree++;
Py_SET_TYPE(op, (PyTypeObject *)float_freelist->items);
float_freelist->items = op;
OBJECT_STAT_INC(to_freelist);
#else
PyObject_Free(op);
#endif
}
static void
float_dealloc(PyObject *op)
{
assert(PyFloat_Check(op));
#ifdef WITH_FREELISTS
if (PyFloat_CheckExact(op)) {
_PyFloat_ExactDealloc(op);
}
else
#endif
{
Py_TYPE(op)->tp_free(op);
}
}
double
PyFloat_AsDouble(PyObject *op)
{
PyNumberMethods *nb;
PyObject *res;
double val;
if (op == NULL) {
PyErr_BadArgument();
return -1;
}
if (PyFloat_Check(op)) {
return PyFloat_AS_DOUBLE(op);
}
nb = Py_TYPE(op)->tp_as_number;
if (nb == NULL || nb->nb_float == NULL) {
if (nb && nb->nb_index) {
PyObject *res = _PyNumber_Index(op);
if (!res) {
return -1;
}
double val = PyLong_AsDouble(res);
Py_DECREF(res);
return val;
}
PyErr_Format(PyExc_TypeError, "must be real number, not %.50s",
Py_TYPE(op)->tp_name);
return -1;
}
res = (*nb->nb_float) (op);
if (res == NULL) {
return -1;
}
if (!PyFloat_CheckExact(res)) {
if (!PyFloat_Check(res)) {
PyErr_Format(PyExc_TypeError,
"%.50s.__float__ returned non-float (type %.50s)",
Py_TYPE(op)->tp_name, Py_TYPE(res)->tp_name);
Py_DECREF(res);
return -1;
}
if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
"%.50s.__float__ returned non-float (type %.50s). "
"The ability to return an instance of a strict subclass of float "
"is deprecated, and may be removed in a future version of Python.",
Py_TYPE(op)->tp_name, Py_TYPE(res)->tp_name)) {
Py_DECREF(res);
return -1;
}
}
val = PyFloat_AS_DOUBLE(res);
Py_DECREF(res);
return val;
}
/* Macro and helper that convert PyObject obj to a C double and store
the value in dbl. 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 or int 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;
/* Methods */
static int
convert_to_double(PyObject **v, double *dbl)
{
PyObject *obj = *v;
if (PyLong_Check(obj)) {
*dbl = PyLong_AsDouble(obj);
if (*dbl == -1.0 && PyErr_Occurred()) {
*v = NULL;
return -1;
}
}
else {
*v = Py_NewRef(Py_NotImplemented);
return -1;
}
return 0;
}
static PyObject *
float_repr(PyFloatObject *v)
{
PyObject *result;
char *buf;
buf = PyOS_double_to_string(PyFloat_AS_DOUBLE(v),
'r', 0,
Py_DTSF_ADD_DOT_0,
NULL);
if (!buf)
return PyErr_NoMemory();
result = _PyUnicode_FromASCII(buf, strlen(buf));
PyMem_Free(buf);
return result;
}
/* 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) an 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 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 (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 j;
break;
}
return PyBool_FromLong(r);
Unimplemented:
Py_RETURN_NOTIMPLEMENTED;
}
static Py_hash_t
float_hash(PyFloatObject *v)
{
return _Py_HashDouble((PyObject *)v, v->ob_fval);
}
static PyObject *
float_add(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
a = a + b;
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);
a = a - b;
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);
a = a * b;
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);
if (b == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError,
"float division by zero");
return NULL;
}
a = a / b;
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);
if (wx == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError,
"float modulo by zero");
return NULL;
}
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);
}
return PyFloat_FromDouble(mod);
}
static void
_float_div_mod(double vx, double wx, double *floordiv, double *mod)
{
double div;
*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 */
}
}
static PyObject *
float_divmod(PyObject *v, PyObject *w)
{
double vx, wx;
double mod, floordiv;
CONVERT_TO_DOUBLE(v, vx);
CONVERT_TO_DOUBLE(w, wx);
if (wx == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()");
return NULL;
}
_float_div_mod(vx, wx, &floordiv, &mod);
return Py_BuildValue("(dd)", floordiv, mod);
}
static PyObject *
float_floor_div(PyObject *v, PyObject *w)
{
double vx, wx;
double mod, floordiv;
CONVERT_TO_DOUBLE(v, vx);
CONVERT_TO_DOUBLE(w, wx);
if (wx == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError, "float floor division by zero");
return NULL;
}
_float_div_mod(vx, wx, &floordiv, &mod);
return PyFloat_FromDouble(floordiv);
}
/* 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)) {
/* 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;
ix = pow(iv, iw);
_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_bool(PyFloatObject *v)
{
return v->ob_fval != 0.0;
}
/*[clinic input]
float.is_integer
Return True if the float is an integer.
[clinic start generated code]*/
static PyObject *
float_is_integer_impl(PyObject *self)
/*[clinic end generated code: output=7112acf95a4d31ea input=311810d3f777e10d]*/
{
double x = PyFloat_AsDouble(self);
PyObject *o;
if (x == -1.0 && PyErr_Occurred())
return NULL;
if (!Py_IS_FINITE(x))
Py_RETURN_FALSE;
errno = 0;
o = (floor(x) == x) ? Py_True : Py_False;
if (errno != 0) {
PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
PyExc_ValueError);
return NULL;
}
return Py_NewRef(o);
}
/*[clinic input]
float.__trunc__
Return the Integral closest to x between 0 and x.
[clinic start generated code]*/
static PyObject *
float___trunc___impl(PyObject *self)
/*[clinic end generated code: output=dd3e289dd4c6b538 input=591b9ba0d650fdff]*/
{
return PyLong_FromDouble(PyFloat_AS_DOUBLE(self));
}
/*[clinic input]
float.__floor__
Return the floor as an Integral.
[clinic start generated code]*/
static PyObject *
float___floor___impl(PyObject *self)
/*[clinic end generated code: output=e0551dbaea8c01d1 input=77bb13eb12e268df]*/
{
double x = PyFloat_AS_DOUBLE(self);
return PyLong_FromDouble(floor(x));
}
/*[clinic input]
float.__ceil__
Return the ceiling as an Integral.
[clinic start generated code]*/
static PyObject *
float___ceil___impl(PyObject *self)
/*[clinic end generated code: output=a2fd8858f73736f9 input=79e41ae94aa0a516]*/
{
double x = PyFloat_AS_DOUBLE(self);
return PyLong_FromDouble(ceil(x));
}
/* double_round: rounds a finite double to the closest multiple of
10**-ndigits; here ndigits is within reasonable bounds (typically, -308 Py_MIN(DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2,
LONG_MAX/2 + 1 - DBL_MAX_EXP)/4)
goto insane_length_error;
/* [p ] */
if (*s == 'p' || *s == 'P') {
s++;
exp_start = s;
if (*s == '-' || *s == '+')
s++;
if (!('0' = 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 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 &&
key_digit+1 < ndigits && (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 = PyFloat_FromDouble(negate ? -x : x);
if (type != &PyFloat_Type && result != NULL) {
Py_SETREF(result, PyObject_CallOneArg((PyObject *)type, result));
}
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;
}
/*[clinic input]
float.as_integer_ratio
Return a pair of integers, whose ratio is exactly equal to the original float.
The ratio is in lowest terms and has a positive denominator. Raise
OverflowError on infinities and a ValueError on NaNs.
>>> (10.0).as_integer_ratio()
(10, 1)
>>> (0.0).as_integer_ratio()
(0, 1)
>>> (-.25).as_integer_ratio()
(-1, 4)
[clinic start generated code]*/
static PyObject *
float_as_integer_ratio_impl(PyObject *self)
/*[clinic end generated code: output=65f25f0d8d30a712 input=d5ba7765655d75bd]*/
{
double self_double;
double float_part;
int exponent;
int i;
PyObject *py_exponent = NULL;
PyObject *numerator = NULL;
PyObject *denominator = NULL;
PyObject *result_pair = NULL;
PyNumberMethods *long_methods = PyLong_Type.tp_as_number;
CONVERT_TO_DOUBLE(self, self_double);
if (Py_IS_INFINITY(self_double)) {
PyErr_SetString(PyExc_OverflowError,
"cannot convert Infinity to integer ratio");
return NULL;
}
if (Py_IS_NAN(self_double)) {
PyErr_SetString(PyExc_ValueError,
"cannot convert NaN to integer ratio");
return NULL;
}
float_part = frexp(self_double, &exponent); /* self_double == float_part * 2**exponent exactly */
for (i=0; i 0) {
Py_SETREF(numerator,
long_methods->nb_lshift(numerator, py_exponent));
if (numerator == NULL)
goto error;
}
else {
Py_SETREF(denominator,
long_methods->nb_lshift(denominator, py_exponent));
if (denominator == NULL)
goto error;
}
result_pair = PyTuple_Pack(2, numerator, denominator);
error:
Py_XDECREF(py_exponent);
Py_XDECREF(denominator);
Py_XDECREF(numerator);
return result_pair;
}
static PyObject *
float_subtype_new(PyTypeObject *type, PyObject *x);
/*[clinic input]
@classmethod
float.__new__ as float_new
x: object(c_default="NULL") = 0
/
Convert a string or number to a floating-point number, if possible.
[clinic start generated code]*/
static PyObject *
float_new_impl(PyTypeObject *type, PyObject *x)
/*[clinic end generated code: output=ccf1e8dc460ba6ba input=55909f888aa0c8a6]*/
{
if (type != &PyFloat_Type) {
if (x == NULL) {
x = _PyLong_GetZero();
}
return float_subtype_new(type, x); /* Wimp out */
}
if (x == NULL) {
return PyFloat_FromDouble(0.0);
}
/* 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);
}
/* Wimpy, slow approach to tp_new calls for subtypes of float:
first create a regular float from whatever arguments we got,
then allocate a subtype instance and initialize its ob_fval
from the regular float. The regular float is then thrown away.
*/
static PyObject *
float_subtype_new(PyTypeObject *type, PyObject *x)
{
PyObject *tmp, *newobj;
assert(PyType_IsSubtype(type, &PyFloat_Type));
tmp = float_new_impl(&PyFloat_Type, x);
if (tmp == NULL)
return NULL;
assert(PyFloat_Check(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;
}
static PyObject *
float_vectorcall(PyObject *type, PyObject * const*args,
size_t nargsf, PyObject *kwnames)
{
if (!_PyArg_NoKwnames("float", kwnames)) {
return NULL;
}
Py_ssize_t nargs = PyVectorcall_NARGS(nargsf);
if (!_PyArg_CheckPositional("float", nargs, 0, 1)) {
return NULL;
}
PyObject *x = nargs >= 1 ? args[0] : NULL;
return float_new_impl(_PyType_CAST(type), x);
}
/*[clinic input]
float.__getnewargs__
[clinic start generated code]*/
static PyObject *
float___getnewargs___impl(PyObject *self)
/*[clinic end generated code: output=873258c9d206b088 input=002279d1d77891e6]*/
{
return Py_BuildValue("(d)", ((PyFloatObject *)self)->ob_fval);
}
/* this is for the benefit of the pack/unpack routines below */
typedef enum _py_float_format_type float_format_type;
#define unknown_format _py_float_format_unknown
#define ieee_big_endian_format _py_float_format_ieee_big_endian
#define ieee_little_endian_format _py_float_format_ieee_little_endian
#define float_format (_PyRuntime.float_state.float_format)
#define double_format (_PyRuntime.float_state.double_format)
/*[clinic input]
@classmethod
float.__getformat__
typestr: str
Must be 'double' or 'float'.
/
You probably don't want to use this function.
It exists mainly to be used in Python's test suite.
This function returns whichever of 'unknown', 'IEEE, big-endian' or
'IEEE, little-endian' best describes the format of floating-point
numbers used by the C type named by typestr.
[clinic start generated code]*/
static PyObject *
float___getformat___impl(PyTypeObject *type, const char *typestr)
/*[clinic end generated code: output=2bfb987228cc9628 input=933cc4bdcf8fa8d3]*/
{
float_format_type r;
if (strcmp(typestr, "double") == 0) {
r = double_format;
}
else if (strcmp(typestr, "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:
PyErr_SetString(PyExc_RuntimeError,
"insane float_format or double_format");
return NULL;
}
}
static PyObject *
float_getreal(PyObject *v, void *closure)
{
return float_float(v);
}
static PyObject *
float_getimag(PyObject *v, void *closure)
{
return PyFloat_FromDouble(0.0);
}
/*[clinic input]
float.__format__
format_spec: unicode
/
Formats the float according to format_spec.
[clinic start generated code]*/
static PyObject *
float___format___impl(PyObject *self, PyObject *format_spec)
/*[clinic end generated code: output=b260e52a47eade56 input=2ece1052211fd0e6]*/
{
_PyUnicodeWriter writer;
int ret;
_PyUnicodeWriter_Init(&writer);
ret = _PyFloat_FormatAdvancedWriter(
&writer,
self,
format_spec, 0, PyUnicode_GET_LENGTH(format_spec));
if (ret == -1) {
_PyUnicodeWriter_Dealloc(&writer);
return NULL;
}
return _PyUnicodeWriter_Finish(&writer);
}
static PyMethodDef float_methods[] = {
FLOAT_CONJUGATE_METHODDEF
FLOAT___TRUNC___METHODDEF
FLOAT___FLOOR___METHODDEF
FLOAT___CEIL___METHODDEF
FLOAT___ROUND___METHODDEF
FLOAT_AS_INTEGER_RATIO_METHODDEF
FLOAT_FROMHEX_METHODDEF
FLOAT_HEX_METHODDEF
FLOAT_IS_INTEGER_METHODDEF
FLOAT___GETNEWARGS___METHODDEF
FLOAT___GETFORMAT___METHODDEF
FLOAT___FORMAT___METHODDEF
{NULL, NULL} /* sentinel */
};
static PyGetSetDef float_getset[] = {
{"real",
float_getreal, (setter)NULL,
"the real part of a complex number",
NULL},
{"imag",
float_getimag, (setter)NULL,
"the imaginary part of a complex number",
NULL},
{NULL} /* Sentinel */
};
static PyNumberMethods float_as_number = {
float_add, /* nb_add */
float_sub, /* nb_subtract */
float_mul, /* nb_multiply */
float_rem, /* nb_remainder */
float_divmod, /* nb_divmod */
float_pow, /* nb_power */
(unaryfunc)float_neg, /* nb_negative */
float_float, /* nb_positive */
(unaryfunc)float_abs, /* nb_absolute */
(inquiry)float_bool, /* nb_bool */
0, /* nb_invert */
0, /* nb_lshift */
0, /* nb_rshift */
0, /* nb_and */
0, /* nb_xor */
0, /* nb_or */
float___trunc___impl, /* nb_int */
0, /* nb_reserved */
float_float, /* nb_float */
0, /* nb_inplace_add */
0, /* nb_inplace_subtract */
0, /* nb_inplace_multiply */
0, /* nb_inplace_remainder */
0, /* nb_inplace_power */
0, /* nb_inplace_lshift */
0, /* nb_inplace_rshift */
0, /* nb_inplace_and */
0, /* nb_inplace_xor */
0, /* nb_inplace_or */
float_floor_div, /* nb_floor_divide */
float_div, /* nb_true_divide */
0, /* nb_inplace_floor_divide */
0, /* nb_inplace_true_divide */
};
PyTypeObject PyFloat_Type = {
PyVarObject_HEAD_INIT(&PyType_Type, 0)
"float",
sizeof(PyFloatObject),
0,
(destructor)float_dealloc, /* tp_dealloc */
0, /* tp_vectorcall_offset */
0, /* tp_getattr */
0, /* tp_setattr */
0, /* tp_as_async */
(reprfunc)float_repr, /* tp_repr */
&float_as_number, /* tp_as_number */
0, /* tp_as_sequence */
0, /* tp_as_mapping */
(hashfunc)float_hash, /* tp_hash */
0, /* tp_call */
0, /* tp_str */
PyObject_GenericGetAttr, /* tp_getattro */
0, /* tp_setattro */
0, /* tp_as_buffer */
Py_TPFLAGS_DEFAULT | Py_TPFLAGS_BASETYPE |
_Py_TPFLAGS_MATCH_SELF, /* tp_flags */
float_new__doc__, /* tp_doc */
0, /* tp_traverse */
0, /* tp_clear */
float_richcompare, /* tp_richcompare */
0, /* tp_weaklistoffset */
0, /* tp_iter */
0, /* tp_iternext */
float_methods, /* tp_methods */
0, /* tp_members */
float_getset, /* tp_getset */
0, /* tp_base */
0, /* tp_dict */
0, /* tp_descr_get */
0, /* tp_descr_set */
0, /* tp_dictoffset */
0, /* tp_init */
0, /* tp_alloc */
float_new, /* tp_new */
.tp_vectorcall = (vectorcallfunc)float_vectorcall,
};
static void
_init_global_state(void)
{
float_format_type detected_double_format, detected_float_format;
/* 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;
}
void
_PyFloat_InitState(PyInterpreterState *interp)
{
if (!_Py_IsMainInterpreter(interp)) {
return;
}
_init_global_state();
}
PyStatus
_PyFloat_InitTypes(PyInterpreterState *interp)
{
/* Init float info */
if (_PyStructSequence_InitBuiltin(interp, &FloatInfoType,
&floatinfo_desc) < 0)
{
return _PyStatus_ERR("can't init float info type");
}
return _PyStatus_OK();
}
void
_PyFloat_ClearFreeList(struct _Py_object_freelists *freelists, int is_finalization)
{
#ifdef WITH_FREELISTS
struct _Py_float_freelist *state = &freelists->floats;
PyFloatObject *f = state->items;
while (f != NULL) {
PyFloatObject *next = (PyFloatObject*) Py_TYPE(f);
PyObject_Free(f);
f = next;
}
state->items = NULL;
if (is_finalization) {
state->numfree = -1;
}
else {
state->numfree = 0;
}
#endif
}
void
_PyFloat_FiniType(PyInterpreterState *interp)
{
_PyStructSequence_FiniBuiltin(interp, &FloatInfoType);
}
/* Print summary info about the state of the optimized allocator */
void
_PyFloat_DebugMallocStats(FILE *out)
{
#ifdef WITH_FREELISTS
struct _Py_float_freelist *float_freelist = get_float_freelist();
_PyDebugAllocatorStats(out,
"free PyFloatObject",
float_freelist->numfree, sizeof(PyFloatObject));
#endif
}
/*----------------------------------------------------------------------------
* PyFloat_{Pack,Unpack}{2,4,8}. See floatobject.h.
* To match the NPY_HALF_ROUND_TIES_TO_EVEN behavior in:
* https://github.com/numpy/numpy/blob/master/numpy/core/src/npymath/halffloat.c
* We use:
* bits = (unsigned short)f; Note the truncation
* if ((f - bits > 0.5) || (f - bits == 0.5 && bits % 2)) {
* bits++;
* }
*/
int
PyFloat_Pack2(double x, char *data, int le)
{
unsigned char *p = (unsigned char *)data;
unsigned char sign;
int e;
double f;
unsigned short bits;
int incr = 1;
if (x == 0.0) {
sign = (copysign(1.0, x) == -1.0);
e = 0;
bits = 0;
}
else if (Py_IS_INFINITY(x)) {
sign = (x < 0.0);
e = 0x1f;
bits = 0;
}
else if (Py_IS_NAN(x)) {
/* There are 2046 distinct half-precision NaNs (1022 signaling and
1024 quiet), but there are only two quiet NaNs that don't arise by
quieting a signaling NaN; we get those by setting the topmost bit
of the fraction field and clearing all other fraction bits. We
choose the one with the appropriate sign. */
sign = (copysign(1.0, x) == -1.0);
e = 0x1f;
bits = 512;
}
else {
sign = (x < 0.0);
if (sign) {
x = -x;
}
f = frexp(x, &e);
if (f < 0.5 || f >= 1.0) {
PyErr_SetString(PyExc_SystemError,
"frexp() result out of range");
return -1;
}
/* Normalize f to be in the range [1.0, 2.0) */
f *= 2.0;
e--;
if (e >= 16) {
goto Overflow;
}
else if (e < -25) {
/* |x| < 2**-25. Underflow to zero. */
f = 0.0;
e = 0;
}
else if (e < -14) {
/* |x| < 2**-14. Gradual underflow */
f = ldexp(f, 14 + e);
e = 0;
}
else /* if (!(e == 0 && f == 0.0)) */ {
e += 15;
f -= 1.0; /* Get rid of leading 1 */
}
f *= 1024.0; /* 2**10 */
/* Round to even */
bits = (unsigned short)f; /* Note the truncation */
assert(bits < 1024);
assert(e < 31);
if ((f - bits > 0.5) || ((f - bits == 0.5) && (bits % 2 == 1))) {
++bits;
if (bits == 1024) {
/* The carry propagated out of a string of 10 1 bits. */
bits = 0;
++e;
if (e == 31)
goto Overflow;
}
}
}
bits |= (e 8) & 0xFF);
p += incr;
/* Second byte */
*p = (unsigned char)(bits & 0xFF);
return 0;
Overflow:
PyErr_SetString(PyExc_OverflowError,
"float too large to pack with e format");
return -1;
}
int
PyFloat_Pack4(double x, char *data, int le)
{
unsigned char *p = (unsigned char *)data;
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 = 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 > 23) {
/* The carry propagated out of a string of 23 1 bits. */
fbits = 0;
++e;
if (e >= 255)
goto Overflow;
}
/* First byte */
*p = (sign > 1);
p += incr;
/* Second byte */
*p = (char) (((e & 1) > 16));
p += incr;
/* Third byte */
*p = (fbits >> 8) & 0xFF;
p += incr;
/* Fourth byte */
*p = fbits & 0xFF;
/* Done */
return 0;
}
else {
float y = (float)x;
int i, incr = 1;
if (Py_IS_INFINITY(y) && !Py_IS_INFINITY(x))
goto Overflow;
unsigned char s[sizeof(float)];
memcpy(s, &y, sizeof(float));
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[i];
p += incr;
}
return 0;
}
Overflow:
PyErr_SetString(PyExc_OverflowError,
"float too large to pack with f format");
return -1;
}
int
PyFloat_Pack8(double x, char *data, int le)
{
unsigned char *p = (unsigned char *)data;
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 = 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 > 24) {
/* The carry propagated out of a string of 24 1 bits. */
flo = 0;
++fhi;
if (fhi >> 28) {
/* And it also propagated out of the next 28 bits. */
fhi = 0;
++e;
if (e >= 2047)
goto Overflow;
}
}
/* First byte */
*p = (sign > 4);
p += incr;
/* Second byte */
*p = (unsigned char) (((e & 0xF) > 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 unsigned char *s = (unsigned 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;
}
}
double
PyFloat_Unpack2(const char *data, int le)
{
unsigned char *p = (unsigned char *)data;
unsigned char sign;
int e;
unsigned int f;
double x;
int incr = 1;
if (le) {
p += 1;
incr = -1;
}
/* First byte */
sign = (*p >> 7) & 1;
e = (*p & 0x7C) >> 2;
f = (*p & 0x03) > 7) & 1;
e = (*p & 0x7F) > 7) & 1;
f = (*p & 0x7F) 7) & 1;
e = (*p & 0x7F) > 4) & 0xF;
fhi = (*p & 0xF)