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floatobject.c
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2354 lines (2081 loc) · 65.2 KB
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/* 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 <ctype.h>
#include <float.h>
#undef MAX
#undef MIN
#define MAX(x, y) ((x) < (y) ? (y) : (x))
#define MIN(x, y) ((x) < (y) ? (x) : (y))
/* Special free list
free_list is a singly-linked list of available PyFloatObjects, linked
via abuse of their ob_type members.
*/
#ifndef PyFloat_MAXFREELIST
#define PyFloat_MAXFREELIST 100
#endif
static int numfree = 0;
static PyFloatObject *free_list = NULL;
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 structseq holding information about the float type. It contains low level\n\
information about the precision and internal representation. Please study\n\
your system's :file:`float.h` for more information.");
static PyStructSequence_Field floatinfo_fields[] = {
{"max", "DBL_MAX -- maximum representable finite float"},
{"max_exp", "DBL_MAX_EXP -- maximum int e such that radix**(e-1) "
"is representable"},
{"max_10_exp", "DBL_MAX_10_EXP -- maximum int e such that 10**e "
"is representable"},
{"min", "DBL_MIN -- Minimum positive normalizer float"},
{"min_exp", "DBL_MIN_EXP -- minimum int e such that radix**(e-1) "
"is a normalized float"},
{"min_10_exp", "DBL_MIN_10_EXP -- minimum int e such that 10**e is "
"a normalized"},
{"dig", "DBL_DIG -- digits"},
{"mant_dig", "DBL_MANT_DIG -- mantissa digits"},
{"epsilon", "DBL_EPSILON -- Difference between 1 and the next "
"representable float"},
{"radix", "FLT_RADIX -- radix of exponent"},
{"rounds", "FLT_ROUNDS -- addition rounds"},
{0}
};
static PyStructSequence_Desc floatinfo_desc = {
"sys.float_info", /* name */
floatinfo__doc__, /* doc */
floatinfo_fields, /* fields */
11
};
PyObject *
PyFloat_GetInfo(void)
{
PyObject* floatinfo;
int pos = 0;
floatinfo = PyStructSequence_New(&FloatInfoType);
if (floatinfo == NULL) {
return NULL;
}
#define SetIntFlag(flag) \
PyStructSequence_SET_ITEM(floatinfo, pos++, 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;
}
PyObject *
PyFloat_FromDouble(double fval)
{
register PyFloatObject *op = free_list;
if (op != NULL) {
free_list = (PyFloatObject *) Py_TYPE(op);
numfree--;
} else {
op = (PyFloatObject*) PyObject_MALLOC(sizeof(PyFloatObject));
if (!op)
return PyErr_NoMemory();
}
/* Inline PyObject_New */
PyObject_INIT(op, &PyFloat_Type);
op->ob_fval = fval;
return (PyObject *) op;
}
PyObject *
PyFloat_FromString(PyObject *v)
{
const char *s, *last, *end;
double x;
PyObject *s_buffer = NULL;
Py_ssize_t len;
PyObject *result = NULL;
if (PyUnicode_Check(v)) {
s_buffer = _PyUnicode_TransformDecimalAndSpaceToASCII(v);
if (s_buffer == NULL)
return NULL;
s = PyUnicode_AsUTF8AndSize(s_buffer, &len);
if (s == NULL) {
Py_DECREF(s_buffer);
return NULL;
}
}
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;
}
static void
float_dealloc(PyFloatObject *op)
{
if (PyFloat_CheckExact(op)) {
if (numfree >= PyFloat_MAXFREELIST) {
PyObject_FREE(op);
return;
}
numfree++;
Py_TYPE(op) = (struct _typeobject *)free_list;
free_list = op;
}
else
Py_TYPE(op)->tp_free((PyObject *)op);
}
double
PyFloat_AsDouble(PyObject *op)
{
PyNumberMethods *nb;
PyFloatObject *fo;
double val;
if (op && PyFloat_Check(op))
return PyFloat_AS_DOUBLE((PyFloatObject*) op);
if (op == NULL) {
PyErr_BadArgument();
return -1;
}
if ((nb = Py_TYPE(op)->tp_as_number) == NULL || nb->nb_float == NULL) {
PyErr_SetString(PyExc_TypeError, "a float is required");
return -1;
}
fo = (PyFloatObject*) (*nb->nb_float) (op);
if (fo == NULL)
return -1;
if (!PyFloat_Check(fo)) {
PyErr_SetString(PyExc_TypeError,
"nb_float should return float object");
return -1;
}
val = PyFloat_AS_DOUBLE(fo);
Py_DECREF(fo);
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)
{
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;
}
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 <= 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 ints 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 or int */
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_RETURN_NOTIMPLEMENTED;
}
static Py_hash_t
float_hash(PyFloatObject *v)
{
return _Py_HashDouble(v->ob_fval);
}
static PyObject *
float_add(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
PyFPE_START_PROTECT("add", return 0)
a = a + b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}
static PyObject *
float_sub(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
PyFPE_START_PROTECT("subtract", return 0)
a = a - b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}
static PyObject *
float_mul(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
PyFPE_START_PROTECT("multiply", return 0)
a = a * b;
PyFPE_END_PROTECT(a)
return PyFloat_FromDouble(a);
}
static PyObject *
float_div(PyObject *v, PyObject *w)
{
double a,b;
CONVERT_TO_DOUBLE(v, a);
CONVERT_TO_DOUBLE(w, b);
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);
}
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");
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);
}
static PyObject *
float_divmod(PyObject *v, PyObject *w)
{
double vx, wx;
double div, mod, floordiv;
CONVERT_TO_DOUBLE(v, vx);
CONVERT_TO_DOUBLE(w, wx);
if (wx == 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()");
return NULL;
}
PyFPE_START_PROTECT("divmod", return 0)
mod = fmod(vx, wx);
/* fmod is typically exact, so vx-mod is *mathematically* an
exact multiple of wx. But this is fp arithmetic, and fp
vx - mod is an approximation; the result is that div may
not be an exact integral value after the division, although
it will always be very close to one.
*/
div = (vx - mod) / wx;
if (mod) {
/* ensure the remainder has the same sign as the denominator */
if ((wx < 0) != (mod < 0)) {
mod += wx;
div -= 1.0;
}
}
else {
/* the remainder is zero, and in the presence of signed zeroes
fmod returns different results across platforms; ensure
it has the same sign as the denominator. */
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);
}
static PyObject *
float_floor_div(PyObject *v, PyObject *w)
{
PyObject *t, *r;
t = float_divmod(v, w);
if (t == NULL || t == Py_NotImplemented)
return t;
assert(PyTuple_CheckExact(t));
r = PyTuple_GET_ITEM(t, 0);
Py_INCREF(r);
Py_DECREF(t);
return r;
}
/* determine whether x is an odd integer or not; assumes that
x is not an infinity or nan. */
#define DOUBLE_IS_ODD_INTEGER(x) (fmod(fabs(x), 2.0) == 1.0)
static PyObject *
float_pow(PyObject *v, PyObject *w, PyObject *z)
{
double iv, iw, ix;
int negate_result = 0;
if ((PyObject *)z != Py_None) {
PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not "
"allowed unless all arguments are integers");
return NULL;
}
CONVERT_TO_DOUBLE(v, iv);
CONVERT_TO_DOUBLE(w, iw);
/* Sort out special cases here instead of relying on pow() */
if (iw == 0) { /* v**0 is 1, even 0**0 */
return PyFloat_FromDouble(1.0);
}
if (Py_IS_NAN(iv)) { /* nan**w = nan, unless w == 0 */
return PyFloat_FromDouble(iv);
}
if (Py_IS_NAN(iw)) { /* v**nan = nan, unless v == 1; 1**nan = 1 */
return PyFloat_FromDouble(iv == 1.0 ? 1.0 : iw);
}
if (Py_IS_INFINITY(iw)) {
/* v**inf is: 0.0 if abs(v) < 1; 1.0 if abs(v) == 1; inf if
* abs(v) > 1 (including case where v infinite)
*
* v**-inf is: inf if abs(v) < 1; 1.0 if abs(v) == 1; 0.0 if
* abs(v) > 1 (including case where v infinite)
*/
iv = fabs(iv);
if (iv == 1.0)
return PyFloat_FromDouble(1.0);
else if ((iw > 0.0) == (iv > 1.0))
return PyFloat_FromDouble(fabs(iw)); /* return inf */
else
return PyFloat_FromDouble(0.0);
}
if (Py_IS_INFINITY(iv)) {
/* (+-inf)**w is: inf for w positive, 0 for w negative; in
* both cases, we need to add the appropriate sign if w is
* an odd integer.
*/
int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
if (iw > 0.0)
return PyFloat_FromDouble(iw_is_odd ? iv : fabs(iv));
else
return PyFloat_FromDouble(iw_is_odd ?
copysign(0.0, iv) : 0.0);
}
if (iv == 0.0) { /* 0**w is: 0 for w positive, 1 for w zero
(already dealt with above), and an error
if w is negative. */
int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
if (iw < 0.0) {
PyErr_SetString(PyExc_ZeroDivisionError,
"0.0 cannot be raised to a "
"negative power");
return NULL;
}
/* use correct sign if iw is odd */
return PyFloat_FromDouble(iw_is_odd ? iv : 0.0);
}
if (iv < 0.0) {
/* Whether this is an error is a mess, and bumps into libm
* bugs so we have to figure it out ourselves.
*/
if (iw != floor(iw)) {
/* 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);
}
#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;
}
static PyObject *
float_is_integer(PyObject *v)
{
double x = PyFloat_AsDouble(v);
PyObject *o;
if (x == -1.0 && PyErr_Occurred())
return NULL;
if (!Py_IS_FINITE(x))
Py_RETURN_FALSE;
errno = 0;
PyFPE_START_PROTECT("is_integer", return NULL)
o = (floor(x) == x) ? Py_True : Py_False;
PyFPE_END_PROTECT(x)
if (errno != 0) {
PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
PyExc_ValueError);
return NULL;
}
Py_INCREF(o);
return o;
}
#if 0
static PyObject *
float_is_inf(PyObject *v)
{
double x = PyFloat_AsDouble(v);
if (x == -1.0 && PyErr_Occurred())
return NULL;
return PyBool_FromLong((long)Py_IS_INFINITY(x));
}
static PyObject *
float_is_nan(PyObject *v)
{
double x = PyFloat_AsDouble(v);
if (x == -1.0 && PyErr_Occurred())
return NULL;
return PyBool_FromLong((long)Py_IS_NAN(x));
}
static PyObject *
float_is_finite(PyObject *v)
{
double x = PyFloat_AsDouble(v);
if (x == -1.0 && PyErr_Occurred())
return NULL;
return PyBool_FromLong((long)Py_IS_FINITE(x));
}
#endif
static PyObject *
float_trunc(PyObject *v)
{
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);
}
/* double_round: rounds a finite double to the closest multiple of
10**-ndigits; here ndigits is within reasonable bounds (typically, -308 <=
ndigits <= 323). Returns a Python float, or sets a Python error and
returns NULL on failure (OverflowError and memory errors are possible). */
#ifndef PY_NO_SHORT_FLOAT_REPR
/* version of double_round that uses the correctly-rounded string<->double
conversions from Python/dtoa.c */
static PyObject *
double_round(double x, int ndigits) {
double rounded;
Py_ssize_t buflen, mybuflen=100;
char *buf, *buf_end, shortbuf[100], *mybuf=shortbuf;
int decpt, sign;
PyObject *result = NULL;
_Py_SET_53BIT_PRECISION_HEADER;
/* round to a decimal string */
_Py_SET_53BIT_PRECISION_START;
buf = _Py_dg_dtoa(x, 3, ndigits, &decpt, &sign, &buf_end);
_Py_SET_53BIT_PRECISION_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;
_Py_SET_53BIT_PRECISION_START;
rounded = _Py_dg_strtod(mybuf, NULL);
_Py_SET_53BIT_PRECISION_END;
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;
}
#else /* PY_NO_SHORT_FLOAT_REPR */
/* fallback version, to be used when correctly rounded binary<->decimal
conversions aren't available */
static PyObject *
double_round(double x, int ndigits) {
double pow1, pow2, y, z;
if (ndigits >= 0) {
if (ndigits > 22) {
/* pow1 and pow2 are each safe from overflow, but
pow1*pow2 ~= pow(10.0, ndigits) might overflow */
pow1 = pow(10.0, (double)(ndigits-22));
pow2 = 1e22;
}
else {
pow1 = pow(10.0, (double)ndigits);
pow2 = 1.0;
}
y = (x*pow1)*pow2;
/* if y overflows, then rounded value is exactly x */
if (!Py_IS_FINITE(y))
return PyFloat_FromDouble(x);
}
else {
pow1 = pow(10.0, (double)-ndigits);
pow2 = 1.0; /* unused; silences a gcc compiler warning */
y = x / pow1;
}
z = round(y);
if (fabs(y-z) == 0.5)
/* halfway between two integers; use round-half-even */
z = 2.0*round(y/2.0);
if (ndigits >= 0)
z = (z / pow2) / pow1;
else
z *= pow1;
/* if computation resulted in overflow, raise OverflowError */
if (!Py_IS_FINITE(z)) {
PyErr_SetString(PyExc_OverflowError,
"overflow occurred during round");
return NULL;
}
return PyFloat_FromDouble(z);
}
#endif /* PY_NO_SHORT_FLOAT_REPR */
/* round a Python float v to the closest multiple of 10**-ndigits */
static PyObject *
float_round(PyObject *v, PyObject *args)
{
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 */