diff options
Diffstat (limited to 'AppPkg/Applications/Python/Python-2.7.10/Objects/floatobject.c')
| -rw-r--r-- | AppPkg/Applications/Python/Python-2.7.10/Objects/floatobject.c | 2708 |
1 files changed, 2708 insertions, 0 deletions
diff --git a/AppPkg/Applications/Python/Python-2.7.10/Objects/floatobject.c b/AppPkg/Applications/Python/Python-2.7.10/Objects/floatobject.c new file mode 100644 index 0000000000..41db7a9b12 --- /dev/null +++ b/AppPkg/Applications/Python/Python-2.7.10/Objects/floatobject.c @@ -0,0 +1,2708 @@ +
+/* Float object implementation */
+
+/* XXX There should be overflow checks here, but it's hard to check
+ for any kind of float exception without losing portability. */
+
+#include "Python.h"
+#include "structseq.h"
+
+#include <ctype.h>
+#include <float.h>
+
+#undef MAX
+#undef MIN
+#define MAX(x, y) ((x) < (y) ? (y) : (x))
+#define MIN(x, y) ((x) < (y) ? (x) : (y))
+
+#ifdef _OSF_SOURCE
+/* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
+extern int finite(double);
+#endif
+
+/* Special free list -- see comments for same code in intobject.c. */
+#define BLOCK_SIZE 1000 /* 1K less typical malloc overhead */
+#define BHEAD_SIZE 8 /* Enough for a 64-bit pointer */
+#define N_FLOATOBJECTS ((BLOCK_SIZE - BHEAD_SIZE) / sizeof(PyFloatObject))
+
+struct _floatblock {
+ struct _floatblock *next;
+ PyFloatObject objects[N_FLOATOBJECTS];
+};
+
+typedef struct _floatblock PyFloatBlock;
+
+static PyFloatBlock *block_list = NULL;
+static PyFloatObject *free_list = NULL;
+
+static PyFloatObject *
+fill_free_list(void)
+{
+ PyFloatObject *p, *q;
+ /* XXX Float blocks escape the object heap. Use PyObject_MALLOC ??? */
+ p = (PyFloatObject *) PyMem_MALLOC(sizeof(PyFloatBlock));
+ if (p == NULL)
+ return (PyFloatObject *) PyErr_NoMemory();
+ ((PyFloatBlock *)p)->next = block_list;
+ block_list = (PyFloatBlock *)p;
+ p = &((PyFloatBlock *)p)->objects[0];
+ q = p + N_FLOATOBJECTS;
+ while (--q > p)
+ Py_TYPE(q) = (struct _typeobject *)(q-1);
+ Py_TYPE(q) = NULL;
+ return p + N_FLOATOBJECTS - 1;
+}
+
+double
+PyFloat_GetMax(void)
+{
+ return DBL_MAX;
+}
+
+double
+PyFloat_GetMin(void)
+{
+ return DBL_MIN;
+}
+
+static PyTypeObject FloatInfoType = {0, 0, 0, 0, 0, 0};
+
+PyDoc_STRVAR(floatinfo__doc__,
+"sys.float_info\n\
+\n\
+A structseq holding information about the float type. It contains low level\n\
+information about the precision and internal representation. Please study\n\
+your system's :file:`float.h` for more information.");
+
+static PyStructSequence_Field floatinfo_fields[] = {
+ {"max", "DBL_MAX -- maximum representable finite float"},
+ {"max_exp", "DBL_MAX_EXP -- maximum int e such that radix**(e-1) "
+ "is representable"},
+ {"max_10_exp", "DBL_MAX_10_EXP -- maximum int e such that 10**e "
+ "is representable"},
+ {"min", "DBL_MIN -- Minimum positive normalizer float"},
+ {"min_exp", "DBL_MIN_EXP -- minimum int e such that radix**(e-1) "
+ "is a normalized float"},
+ {"min_10_exp", "DBL_MIN_10_EXP -- minimum int e such that 10**e is "
+ "a normalized"},
+ {"dig", "DBL_DIG -- digits"},
+ {"mant_dig", "DBL_MANT_DIG -- mantissa digits"},
+ {"epsilon", "DBL_EPSILON -- Difference between 1 and the next "
+ "representable float"},
+ {"radix", "FLT_RADIX -- radix of exponent"},
+ {"rounds", "FLT_ROUNDS -- addition rounds"},
+ {0}
+};
+
+static PyStructSequence_Desc floatinfo_desc = {
+ "sys.float_info", /* name */
+ floatinfo__doc__, /* doc */
+ floatinfo_fields, /* fields */
+ 11
+};
+
+PyObject *
+PyFloat_GetInfo(void)
+{
+ PyObject* floatinfo;
+ int pos = 0;
+
+ floatinfo = PyStructSequence_New(&FloatInfoType);
+ if (floatinfo == NULL) {
+ return NULL;
+ }
+
+#define SetIntFlag(flag) \
+ PyStructSequence_SET_ITEM(floatinfo, pos++, PyInt_FromLong(flag))
+#define SetDblFlag(flag) \
+ PyStructSequence_SET_ITEM(floatinfo, pos++, PyFloat_FromDouble(flag))
+
+ SetDblFlag(DBL_MAX);
+ SetIntFlag(DBL_MAX_EXP);
+ SetIntFlag(DBL_MAX_10_EXP);
+ SetDblFlag(DBL_MIN);
+ SetIntFlag(DBL_MIN_EXP);
+ SetIntFlag(DBL_MIN_10_EXP);
+ SetIntFlag(DBL_DIG);
+ SetIntFlag(DBL_MANT_DIG);
+ SetDblFlag(DBL_EPSILON);
+ SetIntFlag(FLT_RADIX);
+ SetIntFlag(FLT_ROUNDS);
+#undef SetIntFlag
+#undef SetDblFlag
+
+ if (PyErr_Occurred()) {
+ Py_CLEAR(floatinfo);
+ return NULL;
+ }
+ return floatinfo;
+}
+
+PyObject *
+PyFloat_FromDouble(double fval)
+{
+ register PyFloatObject *op;
+ if (free_list == NULL) {
+ if ((free_list = fill_free_list()) == NULL)
+ return NULL;
+ }
+ /* Inline PyObject_New */
+ op = free_list;
+ free_list = (PyFloatObject *)Py_TYPE(op);
+ PyObject_INIT(op, &PyFloat_Type);
+ op->ob_fval = fval;
+ return (PyObject *) op;
+}
+
+/**************************************************************************
+RED_FLAG 22-Sep-2000 tim
+PyFloat_FromString's pend argument is braindead. Prior to this RED_FLAG,
+
+1. If v was a regular string, *pend was set to point to its terminating
+ null byte. That's useless (the caller can find that without any
+ help from this function!).
+
+2. If v was a Unicode string, or an object convertible to a character
+ buffer, *pend was set to point into stack trash (the auto temp
+ vector holding the character buffer). That was downright dangerous.
+
+Since we can't change the interface of a public API function, pend is
+still supported but now *officially* useless: if pend is not NULL,
+*pend is set to NULL.
+**************************************************************************/
+PyObject *
+PyFloat_FromString(PyObject *v, char **pend)
+{
+ const char *s, *last, *end;
+ double x;
+ char buffer[256]; /* for errors */
+#ifdef Py_USING_UNICODE
+ char *s_buffer = NULL;
+#endif
+ Py_ssize_t len;
+ PyObject *result = NULL;
+
+ if (pend)
+ *pend = NULL;
+ if (PyString_Check(v)) {
+ s = PyString_AS_STRING(v);
+ len = PyString_GET_SIZE(v);
+ }
+#ifdef Py_USING_UNICODE
+ else if (PyUnicode_Check(v)) {
+ s_buffer = (char *)PyMem_MALLOC(PyUnicode_GET_SIZE(v)+1);
+ if (s_buffer == NULL)
+ return PyErr_NoMemory();
+ if (PyUnicode_EncodeDecimal(PyUnicode_AS_UNICODE(v),
+ PyUnicode_GET_SIZE(v),
+ s_buffer,
+ NULL))
+ goto error;
+ s = s_buffer;
+ len = strlen(s);
+ }
+#endif
+ else if (PyObject_AsCharBuffer(v, &s, &len)) {
+ PyErr_SetString(PyExc_TypeError,
+ "float() argument must be a string or a number");
+ return NULL;
+ }
+ last = s + len;
+
+ while (Py_ISSPACE(*s))
+ s++;
+ /* We don't care about overflow or underflow. If the platform
+ * supports them, infinities and signed zeroes (on underflow) are
+ * fine. */
+ x = PyOS_string_to_double(s, (char **)&end, NULL);
+ if (x == -1.0 && PyErr_Occurred())
+ goto error;
+ while (Py_ISSPACE(*end))
+ end++;
+ if (end == last)
+ result = PyFloat_FromDouble(x);
+ else {
+ PyOS_snprintf(buffer, sizeof(buffer),
+ "invalid literal for float(): %.200s", s);
+ PyErr_SetString(PyExc_ValueError, buffer);
+ result = NULL;
+ }
+
+ error:
+#ifdef Py_USING_UNICODE
+ if (s_buffer)
+ PyMem_FREE(s_buffer);
+#endif
+ return result;
+}
+
+static void
+float_dealloc(PyFloatObject *op)
+{
+ if (PyFloat_CheckExact(op)) {
+ Py_TYPE(op) = (struct _typeobject *)free_list;
+ free_list = op;
+ }
+ else
+ Py_TYPE(op)->tp_free((PyObject *)op);
+}
+
+double
+PyFloat_AsDouble(PyObject *op)
+{
+ PyNumberMethods *nb;
+ PyFloatObject *fo;
+ double val;
+
+ if (op && PyFloat_Check(op))
+ return PyFloat_AS_DOUBLE((PyFloatObject*) op);
+
+ if (op == NULL) {
+ PyErr_BadArgument();
+ return -1;
+ }
+
+ if ((nb = Py_TYPE(op)->tp_as_number) == NULL || nb->nb_float == NULL) {
+ PyErr_SetString(PyExc_TypeError, "a float is required");
+ return -1;
+ }
+
+ fo = (PyFloatObject*) (*nb->nb_float) (op);
+ if (fo == NULL)
+ return -1;
+ if (!PyFloat_Check(fo)) {
+ Py_DECREF(fo);
+ PyErr_SetString(PyExc_TypeError,
+ "nb_float should return float object");
+ return -1;
+ }
+
+ val = PyFloat_AS_DOUBLE(fo);
+ Py_DECREF(fo);
+
+ return val;
+}
+
+/* Methods */
+
+/* Macro and helper that convert PyObject obj to a C double and store
+ the value in dbl; this replaces the functionality of the coercion
+ slot function. If conversion to double raises an exception, obj is
+ set to NULL, and the function invoking this macro returns NULL. If
+ obj is not of float, int or long type, Py_NotImplemented is incref'ed,
+ stored in obj, and returned from the function invoking this macro.
+*/
+#define CONVERT_TO_DOUBLE(obj, dbl) \
+ if (PyFloat_Check(obj)) \
+ dbl = PyFloat_AS_DOUBLE(obj); \
+ else if (convert_to_double(&(obj), &(dbl)) < 0) \
+ return obj;
+
+static int
+convert_to_double(PyObject **v, double *dbl)
+{
+ register PyObject *obj = *v;
+
+ if (PyInt_Check(obj)) {
+ *dbl = (double)PyInt_AS_LONG(obj);
+ }
+ else if (PyLong_Check(obj)) {
+ *dbl = PyLong_AsDouble(obj);
+ if (*dbl == -1.0 && PyErr_Occurred()) {
+ *v = NULL;
+ return -1;
+ }
+ }
+ else {
+ Py_INCREF(Py_NotImplemented);
+ *v = Py_NotImplemented;
+ return -1;
+ }
+ return 0;
+}
+
+/* XXX PyFloat_AsString and PyFloat_AsReprString are deprecated:
+ XXX they pass a char buffer without passing a length.
+*/
+void
+PyFloat_AsString(char *buf, PyFloatObject *v)
+{
+ char *tmp = PyOS_double_to_string(v->ob_fval, 'g',
+ PyFloat_STR_PRECISION,
+ Py_DTSF_ADD_DOT_0, NULL);
+ strcpy(buf, tmp);
+ PyMem_Free(tmp);
+}
+
+void
+PyFloat_AsReprString(char *buf, PyFloatObject *v)
+{
+ char * tmp = PyOS_double_to_string(v->ob_fval, 'r', 0,
+ Py_DTSF_ADD_DOT_0, NULL);
+ strcpy(buf, tmp);
+ PyMem_Free(tmp);
+}
+
+/* ARGSUSED */
+static int
+float_print(PyFloatObject *v, FILE *fp, int flags)
+{
+ char *buf;
+ if (flags & Py_PRINT_RAW)
+ buf = PyOS_double_to_string(v->ob_fval,
+ 'g', PyFloat_STR_PRECISION,
+ Py_DTSF_ADD_DOT_0, NULL);
+ else
+ buf = PyOS_double_to_string(v->ob_fval,
+ 'r', 0, Py_DTSF_ADD_DOT_0, NULL);
+ Py_BEGIN_ALLOW_THREADS
+ fputs(buf, fp);
+ Py_END_ALLOW_THREADS
+ PyMem_Free(buf);
+ return 0;
+}
+
+static PyObject *
+float_str_or_repr(PyFloatObject *v, int precision, char format_code)
+{
+ PyObject *result;
+ char *buf = PyOS_double_to_string(PyFloat_AS_DOUBLE(v),
+ format_code, precision,
+ Py_DTSF_ADD_DOT_0,
+ NULL);
+ if (!buf)
+ return PyErr_NoMemory();
+ result = PyString_FromString(buf);
+ PyMem_Free(buf);
+ return result;
+}
+
+static PyObject *
+float_repr(PyFloatObject *v)
+{
+ return float_str_or_repr(v, 0, 'r');
+}
+
+static PyObject *
+float_str(PyFloatObject *v)
+{
+ return float_str_or_repr(v, PyFloat_STR_PRECISION, 'g');
+}
+
+/* Comparison is pretty much a nightmare. When comparing float to float,
+ * we do it as straightforwardly (and long-windedly) as conceivable, so
+ * that, e.g., Python x == y delivers the same result as the platform
+ * C x == y when x and/or y is a NaN.
+ * When mixing float with an integer type, there's no good *uniform* approach.
+ * Converting the double to an integer obviously doesn't work, since we
+ * may lose info from fractional bits. Converting the integer to a double
+ * also has two failure modes: (1) a long int may trigger overflow (too
+ * large to fit in the dynamic range of a C double); (2) even a C long may have
+ * more bits than fit in a C double (e.g., on a a 64-bit box long may have
+ * 63 bits of precision, but a C double probably has only 53), and then
+ * we can falsely claim equality when low-order integer bits are lost by
+ * coercion to double. So this part is painful too.
+ */
+
+static PyObject*
+float_richcompare(PyObject *v, PyObject *w, int op)
+{
+ double i, j;
+ int r = 0;
+
+ assert(PyFloat_Check(v));
+ i = PyFloat_AS_DOUBLE(v);
+
+ /* Switch on the type of w. Set i and j to doubles to be compared,
+ * and op to the richcomp to use.
+ */
+ if (PyFloat_Check(w))
+ j = PyFloat_AS_DOUBLE(w);
+
+ else if (!Py_IS_FINITE(i)) {
+ if (PyInt_Check(w) || PyLong_Check(w))
+ /* If i is an infinity, its magnitude exceeds any
+ * finite integer, so it doesn't matter which int we
+ * compare i with. If i is a NaN, similarly.
+ */
+ j = 0.0;
+ else
+ goto Unimplemented;
+ }
+
+ else if (PyInt_Check(w)) {
+ long jj = PyInt_AS_LONG(w);
+ /* In the worst realistic case I can imagine, C double is a
+ * Cray single with 48 bits of precision, and long has 64
+ * bits.
+ */
+#if SIZEOF_LONG > 6
+ unsigned long abs = (unsigned long)(jj < 0 ? -jj : jj);
+ if (abs >> 48) {
+ /* Needs more than 48 bits. Make it take the
+ * PyLong path.
+ */
+ PyObject *result;
+ PyObject *ww = PyLong_FromLong(jj);
+
+ if (ww == NULL)
+ return NULL;
+ result = float_richcompare(v, ww, op);
+ Py_DECREF(ww);
+ return result;
+ }
+#endif
+ j = (double)jj;
+ assert((long)j == jj);
+ }
+
+ else if (PyLong_Check(w)) {
+ int vsign = i == 0.0 ? 0 : i < 0.0 ? -1 : 1;
+ int wsign = _PyLong_Sign(w);
+ size_t nbits;
+ int exponent;
+
+ if (vsign != wsign) {
+ /* Magnitudes are irrelevant -- the signs alone
+ * determine the outcome.
+ */
+ i = (double)vsign;
+ j = (double)wsign;
+ goto Compare;
+ }
+ /* The signs are the same. */
+ /* Convert w to a double if it fits. In particular, 0 fits. */
+ nbits = _PyLong_NumBits(w);
+ if (nbits == (size_t)-1 && PyErr_Occurred()) {
+ /* This long is so large that size_t isn't big enough
+ * to hold the # of bits. Replace with little doubles
+ * that give the same outcome -- w is so large that
+ * its magnitude must exceed the magnitude of any
+ * finite float.
+ */
+ PyErr_Clear();
+ i = (double)vsign;
+ assert(wsign != 0);
+ j = wsign * 2.0;
+ goto Compare;
+ }
+ if (nbits <= 48) {
+ j = PyLong_AsDouble(w);
+ /* It's impossible that <= 48 bits overflowed. */
+ assert(j != -1.0 || ! PyErr_Occurred());
+ goto Compare;
+ }
+ assert(wsign != 0); /* else nbits was 0 */
+ assert(vsign != 0); /* if vsign were 0, then since wsign is
+ * not 0, we would have taken the
+ * vsign != wsign branch at the start */
+ /* We want to work with non-negative numbers. */
+ if (vsign < 0) {
+ /* "Multiply both sides" by -1; this also swaps the
+ * comparator.
+ */
+ i = -i;
+ op = _Py_SwappedOp[op];
+ }
+ assert(i > 0.0);
+ (void) frexp(i, &exponent);
+ /* exponent is the # of bits in v before the radix point;
+ * we know that nbits (the # of bits in w) > 48 at this point
+ */
+ if (exponent < 0 || (size_t)exponent < nbits) {
+ i = 1.0;
+ j = 2.0;
+ goto Compare;
+ }
+ if ((size_t)exponent > nbits) {
+ i = 2.0;
+ j = 1.0;
+ goto Compare;
+ }
+ /* v and w have the same number of bits before the radix
+ * point. Construct two longs that have the same comparison
+ * outcome.
+ */
+ {
+ double fracpart;
+ double intpart;
+ PyObject *result = NULL;
+ PyObject *one = NULL;
+ PyObject *vv = NULL;
+ PyObject *ww = w;
+
+ if (wsign < 0) {
+ ww = PyNumber_Negative(w);
+ if (ww == NULL)
+ goto Error;
+ }
+ else
+ Py_INCREF(ww);
+
+ fracpart = modf(i, &intpart);
+ vv = PyLong_FromDouble(intpart);
+ if (vv == NULL)
+ goto Error;
+
+ if (fracpart != 0.0) {
+ /* Shift left, and or a 1 bit into vv
+ * to represent the lost fraction.
+ */
+ PyObject *temp;
+
+ one = PyInt_FromLong(1);
+ if (one == NULL)
+ goto Error;
+
+ temp = PyNumber_Lshift(ww, one);
+ if (temp == NULL)
+ goto Error;
+ Py_DECREF(ww);
+ ww = temp;
+
+ temp = PyNumber_Lshift(vv, one);
+ if (temp == NULL)
+ goto Error;
+ Py_DECREF(vv);
+ vv = temp;
+
+ temp = PyNumber_Or(vv, one);
+ if (temp == NULL)
+ goto Error;
+ Py_DECREF(vv);
+ vv = temp;
+ }
+
+ r = PyObject_RichCompareBool(vv, ww, op);
+ if (r < 0)
+ goto Error;
+ result = PyBool_FromLong(r);
+ Error:
+ Py_XDECREF(vv);
+ Py_XDECREF(ww);
+ Py_XDECREF(one);
+ return result;
+ }
+ } /* else if (PyLong_Check(w)) */
+
+ else /* w isn't float, int, or long */
+ goto Unimplemented;
+
+ Compare:
+ PyFPE_START_PROTECT("richcompare", return NULL)
+ switch (op) {
+ case Py_EQ:
+ r = i == j;
+ break;
+ case Py_NE:
+ r = i != j;
+ break;
+ case Py_LE:
+ r = i <= j;
+ break;
+ case Py_GE:
+ r = i >= j;
+ break;
+ case Py_LT:
+ r = i < j;
+ break;
+ case Py_GT:
+ r = i > j;
+ break;
+ }
+ PyFPE_END_PROTECT(r)
+ return PyBool_FromLong(r);
+
+ Unimplemented:
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+}
+
+static long
+float_hash(PyFloatObject *v)
+{
+ return _Py_HashDouble(v->ob_fval);
+}
+
+static PyObject *
+float_add(PyObject *v, PyObject *w)
+{
+ double a,b;
+ CONVERT_TO_DOUBLE(v, a);
+ CONVERT_TO_DOUBLE(w, b);
+ PyFPE_START_PROTECT("add", return 0)
+ a = a + b;
+ PyFPE_END_PROTECT(a)
+ return PyFloat_FromDouble(a);
+}
+
+static PyObject *
+float_sub(PyObject *v, PyObject *w)
+{
+ double a,b;
+ CONVERT_TO_DOUBLE(v, a);
+ CONVERT_TO_DOUBLE(w, b);
+ PyFPE_START_PROTECT("subtract", return 0)
+ a = a - b;
+ PyFPE_END_PROTECT(a)
+ return PyFloat_FromDouble(a);
+}
+
+static PyObject *
+float_mul(PyObject *v, PyObject *w)
+{
+ double a,b;
+ CONVERT_TO_DOUBLE(v, a);
+ CONVERT_TO_DOUBLE(w, b);
+ PyFPE_START_PROTECT("multiply", return 0)
+ a = a * b;
+ PyFPE_END_PROTECT(a)
+ return PyFloat_FromDouble(a);
+}
+
+static PyObject *
+float_div(PyObject *v, PyObject *w)
+{
+ double a,b;
+ CONVERT_TO_DOUBLE(v, a);
+ CONVERT_TO_DOUBLE(w, b);
+#ifdef Py_NAN
+ if (b == 0.0) {
+ PyErr_SetString(PyExc_ZeroDivisionError,
+ "float division by zero");
+ return NULL;
+ }
+#endif
+ PyFPE_START_PROTECT("divide", return 0)
+ a = a / b;
+ PyFPE_END_PROTECT(a)
+ return PyFloat_FromDouble(a);
+}
+
+static PyObject *
+float_classic_div(PyObject *v, PyObject *w)
+{
+ double a,b;
+ CONVERT_TO_DOUBLE(v, a);
+ CONVERT_TO_DOUBLE(w, b);
+ if (Py_DivisionWarningFlag >= 2 &&
+ PyErr_Warn(PyExc_DeprecationWarning, "classic float division") < 0)
+ return NULL;
+#ifdef Py_NAN
+ if (b == 0.0) {
+ PyErr_SetString(PyExc_ZeroDivisionError,
+ "float division by zero");
+ return NULL;
+ }
+#endif
+ PyFPE_START_PROTECT("divide", return 0)
+ a = a / b;
+ PyFPE_END_PROTECT(a)
+ return PyFloat_FromDouble(a);
+}
+
+static PyObject *
+float_rem(PyObject *v, PyObject *w)
+{
+ double vx, wx;
+ double mod;
+ CONVERT_TO_DOUBLE(v, vx);
+ CONVERT_TO_DOUBLE(w, wx);
+#ifdef Py_NAN
+ if (wx == 0.0) {
+ PyErr_SetString(PyExc_ZeroDivisionError,
+ "float modulo");
+ return NULL;
+ }
+#endif
+ PyFPE_START_PROTECT("modulo", return 0)
+ mod = fmod(vx, wx);
+ if (mod) {
+ /* ensure the remainder has the same sign as the denominator */
+ if ((wx < 0) != (mod < 0)) {
+ mod += wx;
+ }
+ }
+ else {
+ /* the remainder is zero, and in the presence of signed zeroes
+ fmod returns different results across platforms; ensure
+ it has the same sign as the denominator; we'd like to do
+ "mod = wx * 0.0", but that may get optimized away */
+ mod *= mod; /* hide "mod = +0" from optimizer */
+ if (wx < 0.0)
+ mod = -mod;
+ }
+ PyFPE_END_PROTECT(mod)
+ return PyFloat_FromDouble(mod);
+}
+
+static PyObject *
+float_divmod(PyObject *v, PyObject *w)
+{
+ double vx, wx;
+ double div, mod, floordiv;
+ CONVERT_TO_DOUBLE(v, vx);
+ CONVERT_TO_DOUBLE(w, wx);
+ if (wx == 0.0) {
+ PyErr_SetString(PyExc_ZeroDivisionError, "float divmod()");
+ return NULL;
+ }
+ PyFPE_START_PROTECT("divmod", return 0)
+ mod = fmod(vx, wx);
+ /* fmod is typically exact, so vx-mod is *mathematically* an
+ exact multiple of wx. But this is fp arithmetic, and fp
+ vx - mod is an approximation; the result is that div may
+ not be an exact integral value after the division, although
+ it will always be very close to one.
+ */
+ div = (vx - mod) / wx;
+ if (mod) {
+ /* ensure the remainder has the same sign as the denominator */
+ if ((wx < 0) != (mod < 0)) {
+ mod += wx;
+ div -= 1.0;
+ }
+ }
+ else {
+ /* the remainder is zero, and in the presence of signed zeroes
+ fmod returns different results across platforms; ensure
+ it has the same sign as the denominator; we'd like to do
+ "mod = wx * 0.0", but that may get optimized away */
+ mod *= mod; /* hide "mod = +0" from optimizer */
+ if (wx < 0.0)
+ mod = -mod;
+ }
+ /* snap quotient to nearest integral value */
+ if (div) {
+ floordiv = floor(div);
+ if (div - floordiv > 0.5)
+ floordiv += 1.0;
+ }
+ else {
+ /* div is zero - get the same sign as the true quotient */
+ div *= div; /* hide "div = +0" from optimizers */
+ floordiv = div * vx / wx; /* zero w/ sign of vx/wx */
+ }
+ PyFPE_END_PROTECT(floordiv)
+ return Py_BuildValue("(dd)", floordiv, mod);
+}
+
+static PyObject *
+float_floor_div(PyObject *v, PyObject *w)
+{
+ PyObject *t, *r;
+
+ t = float_divmod(v, w);
+ if (t == NULL || t == Py_NotImplemented)
+ return t;
+ assert(PyTuple_CheckExact(t));
+ r = PyTuple_GET_ITEM(t, 0);
+ Py_INCREF(r);
+ Py_DECREF(t);
+ return r;
+}
+
+/* determine whether x is an odd integer or not; assumes that
+ x is not an infinity or nan. */
+#define DOUBLE_IS_ODD_INTEGER(x) (fmod(fabs(x), 2.0) == 1.0)
+
+static PyObject *
+float_pow(PyObject *v, PyObject *w, PyObject *z)
+{
+ double iv, iw, ix;
+ int negate_result = 0;
+
+ if ((PyObject *)z != Py_None) {
+ PyErr_SetString(PyExc_TypeError, "pow() 3rd argument not "
+ "allowed unless all arguments are integers");
+ return NULL;
+ }
+
+ CONVERT_TO_DOUBLE(v, iv);
+ CONVERT_TO_DOUBLE(w, iw);
+
+ /* Sort out special cases here instead of relying on pow() */
+ if (iw == 0) { /* v**0 is 1, even 0**0 */
+ return PyFloat_FromDouble(1.0);
+ }
+ if (Py_IS_NAN(iv)) { /* nan**w = nan, unless w == 0 */
+ return PyFloat_FromDouble(iv);
+ }
+ if (Py_IS_NAN(iw)) { /* v**nan = nan, unless v == 1; 1**nan = 1 */
+ return PyFloat_FromDouble(iv == 1.0 ? 1.0 : iw);
+ }
+ if (Py_IS_INFINITY(iw)) {
+ /* v**inf is: 0.0 if abs(v) < 1; 1.0 if abs(v) == 1; inf if
+ * abs(v) > 1 (including case where v infinite)
+ *
+ * v**-inf is: inf if abs(v) < 1; 1.0 if abs(v) == 1; 0.0 if
+ * abs(v) > 1 (including case where v infinite)
+ */
+ iv = fabs(iv);
+ if (iv == 1.0)
+ return PyFloat_FromDouble(1.0);
+ else if ((iw > 0.0) == (iv > 1.0))
+ return PyFloat_FromDouble(fabs(iw)); /* return inf */
+ else
+ return PyFloat_FromDouble(0.0);
+ }
+ if (Py_IS_INFINITY(iv)) {
+ /* (+-inf)**w is: inf for w positive, 0 for w negative; in
+ * both cases, we need to add the appropriate sign if w is
+ * an odd integer.
+ */
+ int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
+ if (iw > 0.0)
+ return PyFloat_FromDouble(iw_is_odd ? iv : fabs(iv));
+ else
+ return PyFloat_FromDouble(iw_is_odd ?
+ copysign(0.0, iv) : 0.0);
+ }
+ if (iv == 0.0) { /* 0**w is: 0 for w positive, 1 for w zero
+ (already dealt with above), and an error
+ if w is negative. */
+ int iw_is_odd = DOUBLE_IS_ODD_INTEGER(iw);
+ if (iw < 0.0) {
+ PyErr_SetString(PyExc_ZeroDivisionError,
+ "0.0 cannot be raised to a "
+ "negative power");
+ return NULL;
+ }
+ /* use correct sign if iw is odd */
+ return PyFloat_FromDouble(iw_is_odd ? iv : 0.0);
+ }
+
+ if (iv < 0.0) {
+ /* Whether this is an error is a mess, and bumps into libm
+ * bugs so we have to figure it out ourselves.
+ */
+ if (iw != floor(iw)) {
+ PyErr_SetString(PyExc_ValueError, "negative number "
+ "cannot be raised to a fractional power");
+ return NULL;
+ }
+ /* iw is an exact integer, albeit perhaps a very large
+ * one. Replace iv by its absolute value and remember
+ * to negate the pow result if iw is odd.
+ */
+ iv = -iv;
+ negate_result = DOUBLE_IS_ODD_INTEGER(iw);
+ }
+
+ if (iv == 1.0) { /* 1**w is 1, even 1**inf and 1**nan */
+ /* (-1) ** large_integer also ends up here. Here's an
+ * extract from the comments for the previous
+ * implementation explaining why this special case is
+ * necessary:
+ *
+ * -1 raised to an exact integer should never be exceptional.
+ * Alas, some libms (chiefly glibc as of early 2003) return
+ * NaN and set EDOM on pow(-1, large_int) if the int doesn't
+ * happen to be representable in a *C* integer. That's a
+ * bug.
+ */
+ return PyFloat_FromDouble(negate_result ? -1.0 : 1.0);
+ }
+
+ /* Now iv and iw are finite, iw is nonzero, and iv is
+ * positive and not equal to 1.0. We finally allow
+ * the platform pow to step in and do the rest.
+ */
+ errno = 0;
+ PyFPE_START_PROTECT("pow", return NULL)
+ ix = pow(iv, iw);
+ PyFPE_END_PROTECT(ix)
+ Py_ADJUST_ERANGE1(ix);
+ if (negate_result)
+ ix = -ix;
+
+ if (errno != 0) {
+ /* We don't expect any errno value other than ERANGE, but
+ * the range of libm bugs appears unbounded.
+ */
+ PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
+ PyExc_ValueError);
+ return NULL;
+ }
+ return PyFloat_FromDouble(ix);
+}
+
+#undef DOUBLE_IS_ODD_INTEGER
+
+static PyObject *
+float_neg(PyFloatObject *v)
+{
+ return PyFloat_FromDouble(-v->ob_fval);
+}
+
+static PyObject *
+float_abs(PyFloatObject *v)
+{
+ return PyFloat_FromDouble(fabs(v->ob_fval));
+}
+
+static int
+float_nonzero(PyFloatObject *v)
+{
+ return v->ob_fval != 0.0;
+}
+
+static int
+float_coerce(PyObject **pv, PyObject **pw)
+{
+ if (PyInt_Check(*pw)) {
+ long x = PyInt_AsLong(*pw);
+ *pw = PyFloat_FromDouble((double)x);
+ Py_INCREF(*pv);
+ return 0;
+ }
+ else if (PyLong_Check(*pw)) {
+ double x = PyLong_AsDouble(*pw);
+ if (x == -1.0 && PyErr_Occurred())
+ return -1;
+ *pw = PyFloat_FromDouble(x);
+ Py_INCREF(*pv);
+ return 0;
+ }
+ else if (PyFloat_Check(*pw)) {
+ Py_INCREF(*pv);
+ Py_INCREF(*pw);
+ return 0;
+ }
+ return 1; /* Can't do it */
+}
+
+static PyObject *
+float_is_integer(PyObject *v)
+{
+ double x = PyFloat_AsDouble(v);
+ PyObject *o;
+
+ if (x == -1.0 && PyErr_Occurred())
+ return NULL;
+ if (!Py_IS_FINITE(x))
+ Py_RETURN_FALSE;
+ errno = 0;
+ PyFPE_START_PROTECT("is_integer", return NULL)
+ o = (floor(x) == x) ? Py_True : Py_False;
+ PyFPE_END_PROTECT(x)
+ if (errno != 0) {
+ PyErr_SetFromErrno(errno == ERANGE ? PyExc_OverflowError :
+ PyExc_ValueError);
+ return NULL;
+ }
+ Py_INCREF(o);
+ return o;
+}
+
+#if 0
+static PyObject *
+float_is_inf(PyObject *v)
+{
+ 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 <= LONG_MAX is unsafe: if a long
+ * has more bits of precision than a double, casting LONG_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. However, assuming a two's complement
+ * machine with no trap representation, LONG_MIN will be a power of 2 (and
+ * hence exactly representable as a double), and LONG_MAX = -1-LONG_MIN, so
+ * the comparisons with (double)LONG_MIN below should be safe.
+ */
+ if ((double)LONG_MIN <= wholepart && wholepart < -(double)LONG_MIN) {
+ const long aslong = (long)wholepart;
+ return PyInt_FromLong(aslong);
+ }
+ return PyLong_FromDouble(wholepart);
+}
+
+static PyObject *
+float_long(PyObject *v)
+{
+ double x = PyFloat_AsDouble(v);
+ return PyLong_FromDouble(x);
+}
+
+/* _Py_double_round: rounds a finite nonzero 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 _Py_double_round that uses the correctly-rounded string<->double
+ conversions from Python/dtoa.c */
+
+/* FIVE_POW_LIMIT is the largest k such that 5**k is exactly representable as
+ a double. Since we're using the code in Python/dtoa.c, it should be safe
+ to assume that C doubles are IEEE 754 binary64 format. To be on the safe
+ side, we check this. */
+#if DBL_MANT_DIG == 53
+#define FIVE_POW_LIMIT 22
+#else
+#error "C doubles do not appear to be IEEE 754 binary64 format"
+#endif
+
+PyObject *
+_Py_double_round(double x, int ndigits) {
+
+ double rounded, m;
+ Py_ssize_t buflen, mybuflen=100;
+ char *buf, *buf_end, shortbuf[100], *mybuf=shortbuf;
+ int decpt, sign, val, halfway_case;
+ PyObject *result = NULL;
+ _Py_SET_53BIT_PRECISION_HEADER;
+
+ /* Easy path for the common case ndigits == 0. */
+ if (ndigits == 0) {
+ rounded = round(x);
+ if (fabs(rounded - x) == 0.5)
+ /* halfway between two integers; use round-away-from-zero */
+ rounded = x + (x > 0.0 ? 0.5 : -0.5);
+ return PyFloat_FromDouble(rounded);
+ }
+
+ /* The basic idea is very simple: convert and round the double to a
+ decimal string using _Py_dg_dtoa, then convert that decimal string
+ back to a double with _Py_dg_strtod. There's one minor difficulty:
+ Python 2.x expects round to do round-half-away-from-zero, while
+ _Py_dg_dtoa does round-half-to-even. So we need some way to detect
+ and correct the halfway cases.
+
+ Detection: a halfway value has the form k * 0.5 * 10**-ndigits for
+ some odd integer k. Or in other words, a rational number x is
+ exactly halfway between two multiples of 10**-ndigits if its
+ 2-valuation is exactly -ndigits-1 and its 5-valuation is at least
+ -ndigits. For ndigits >= 0 the latter condition is automatically
+ satisfied for a binary float x, since any such float has
+ nonnegative 5-valuation. For 0 > ndigits >= -22, x needs to be an
+ integral multiple of 5**-ndigits; we can check this using fmod.
+ For -22 > ndigits, there are no halfway cases: 5**23 takes 54 bits
+ to represent exactly, so any odd multiple of 0.5 * 10**n for n >=
+ 23 takes at least 54 bits of precision to represent exactly.
+
+ Correction: a simple strategy for dealing with halfway cases is to
+ (for the halfway cases only) call _Py_dg_dtoa with an argument of
+ ndigits+1 instead of ndigits (thus doing an exact conversion to
+ decimal), round the resulting string manually, and then convert
+ back using _Py_dg_strtod.
+ */
+
+ /* nans, infinities and zeros should have already been dealt
+ with by the caller (in this case, builtin_round) */
+ assert(Py_IS_FINITE(x) && x != 0.0);
+
+ /* find 2-valuation val of x */
+ m = frexp(x, &val);
+ while (m != floor(m)) {
+ m *= 2.0;
+ val--;
+ }
+
+ /* determine whether this is a halfway case */
+ if (val == -ndigits-1) {
+ if (ndigits >= 0)
+ halfway_case = 1;
+ else if (ndigits >= -FIVE_POW_LIMIT) {
+ double five_pow = 1.0;
+ int i;
+ for (i=0; i < -ndigits; i++)
+ five_pow *= 5.0;
+ halfway_case = fmod(x, five_pow) == 0.0;
+ }
+ else
+ halfway_case = 0;
+ }
+ else
+ halfway_case = 0;
+
+ /* round to a decimal string; use an extra place for halfway case */
+ _Py_SET_53BIT_PRECISION_START;
+ buf = _Py_dg_dtoa(x, 3, ndigits+halfway_case, &decpt, &sign, &buf_end);
+ _Py_SET_53BIT_PRECISION_END;
+ if (buf == NULL) {
+ PyErr_NoMemory();
+ return NULL;
+ }
+ buflen = buf_end - buf;
+
+ /* in halfway case, do the round-half-away-from-zero manually */
+ if (halfway_case) {
+ int i, carry;
+ /* sanity check: _Py_dg_dtoa should not have stripped
+ any zeros from the result: there should be exactly
+ ndigits+1 places following the decimal point, and
+ the last digit in the buffer should be a '5'.*/
+ assert(buflen - decpt == ndigits+1);
+ assert(buf[buflen-1] == '5');
+
+ /* increment and shift right at the same time. */
+ decpt += 1;
+ carry = 1;
+ for (i=buflen-1; i-- > 0;) {
+ carry += buf[i] - '0';
+ buf[i+1] = carry % 10 + '0';
+ carry /= 10;
+ }
+ buf[0] = carry + '0';
+ }
+
+ /* 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'). */
+ 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;
+}
+
+#undef FIVE_POW_LIMIT
+
+#else /* PY_NO_SHORT_FLOAT_REPR */
+
+/* fallback version, to be used when correctly rounded binary<->decimal
+ conversions aren't available */
+
+PyObject *
+_Py_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-away-from-zero */
+ z = y + copysign(0.5, y);
+
+ 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 */
+
+static PyObject *
+float_float(PyObject *v)
+{
+ if (PyFloat_CheckExact(v))
+ Py_INCREF(v);
+ else
+ v = PyFloat_FromDouble(((PyFloatObject *)v)->ob_fval);
+ return v;
+}
+
+/* turn ASCII hex characters into integer values and vice versa */
+
+static char
+char_from_hex(int x)
+{
+ assert(0 <= x && x < 16);
+ return "0123456789abcdef"[x];
+}
+
+static int
+hex_from_char(char 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;
+}
+
+/* convert a float to a hexadecimal string */
+
+/* TOHEX_NBITS is DBL_MANT_DIG rounded up to the next integer
+ of the form 4k+1. */
+#define TOHEX_NBITS DBL_MANT_DIG + 3 - (DBL_MANT_DIG+2)%4
+
+static PyObject *
+float_hex(PyObject *v)
+{
+ 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_str((PyFloatObject *)v);
+
+ if (x == 0.0) {
+ if (copysign(1.0, x) == -1.0)
+ return PyString_FromString("-0x0.0p+0");
+ else
+ return PyString_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 PyString_FromFormat("-0x%sp%c%d", s, esign, e);
+ else
+ return PyString_FromFormat("0x%sp%c%d", s, esign, e);
+}
+
+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'");
+
+/* Case-insensitive locale-independent string match used for nan and inf
+ detection. t should be lower-case and null-terminated. Return a nonzero
+ result if the first strlen(t) characters of s match t and 0 otherwise. */
+
+static int
+case_insensitive_match(const char *s, const char *t)
+{
+ while(*t && Py_TOLOWER(*s) == *t) {
+ s++;
+ t++;
+ }
+ return *t ? 0 : 1;
+}
+
+/* Convert a hexadecimal string to a float. */
+
+static PyObject *
+float_fromhex(PyObject *cls, PyObject *arg)
+{
+ 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, sign=1;
+ 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.
+ */
+
+ if (PyString_AsStringAndSize(arg, &s, &length))
+ return NULL;
+ s_end = s + length;
+
+ /********************
+ * Parse the string *
+ ********************/
+
+ /* leading whitespace and optional sign */
+ while (Py_ISSPACE(*s))
+ s++;
+ if (*s == '-') {
+ s++;
+ sign = -1;
+ }
+ else if (*s == '+')
+ s++;
+
+ /* infinities and nans */
+ if (*s == 'i' || *s == 'I') {
+ if (!case_insensitive_match(s+1, "nf"))
+ goto parse_error;
+ s += 3;
+ x = Py_HUGE_VAL;
+ if (case_insensitive_match(s, "inity"))
+ s += 5;
+ goto finished;
+ }
+ if (*s == 'n' || *s == 'N') {
+ if (!case_insensitive_match(s+1, "an"))
+ goto parse_error;
+ s += 3;
+ x = Py_NAN;
+ goto finished;
+ }
+
+ /* [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 == 1) {
+ 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)", sign * 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;
+}
+
+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 PyObject *
+float_as_integer_ratio(PyObject *v, PyObject *unused)
+{
+ 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;
+ }
+#ifdef Py_NAN
+ if (Py_IS_NAN(self)) {
+ PyErr_SetString(PyExc_ValueError,
+ "Cannot pass NaN to float.as_integer_ratio.");
+ return NULL;
+ }
+#endif
+
+ 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;
+ }
+
+ /* Returns ints instead of longs where possible */
+ INPLACE_UPDATE(numerator, PyNumber_Int(numerator));
+ if (numerator == NULL) goto error;
+ INPLACE_UPDATE(denominator, PyNumber_Int(denominator));
+ if (denominator == NULL) goto error;
+
+ result_pair = PyTuple_Pack(2, numerator, denominator);
+
+#undef INPLACE_UPDATE
+error:
+ Py_XDECREF(py_exponent);
+ Py_XDECREF(denominator);
+ Py_XDECREF(numerator);
+ return result_pair;
+}
+
+PyDoc_STRVAR(float_as_integer_ratio_doc,
+"float.as_integer_ratio() -> (int, int)\n"
+"\n"
+"Return a pair of integers, whose ratio is exactly equal to the original\n"
+"float and with a positive denominator.\n"
+"Raise 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 PyObject *
+float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds);
+
+static PyObject *
+float_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
+{
+ 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 (PyString_CheckExact(x))
+ return PyFloat_FromString(x, NULL);
+ 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 *args, PyObject *kwds)
+{
+ 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;
+}
+
+static PyObject *
+float_getnewargs(PyFloatObject *v)
+{
+ return Py_BuildValue("(d)", v->ob_fval);
+}
+
+/* this is for the benefit of the pack/unpack routines below */
+
+typedef enum {
+ unknown_format, ieee_big_endian_format, ieee_little_endian_format
+} float_format_type;
+
+static float_format_type double_format, float_format;
+static float_format_type detected_double_format, detected_float_format;
+
+static PyObject *
+float_getformat(PyTypeObject *v, PyObject* arg)
+{
+ char* s;
+ float_format_type r;
+
+ if (!PyString_Check(arg)) {
+ PyErr_Format(PyExc_TypeError,
+ "__getformat__() argument must be string, not %.500s",
+ Py_TYPE(arg)->tp_name);
+ return NULL;
+ }
+ s = PyString_AS_STRING(arg);
+ 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 PyString_FromString("unknown");
+ case ieee_little_endian_format:
+ return PyString_FromString("IEEE, little-endian");
+ case ieee_big_endian_format:
+ return PyString_FromString("IEEE, big-endian");
+ default:
+ Py_FatalError("insane float_format or double_format");
+ return NULL;
+ }
+}
+
+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 PyObject *
+float_setformat(PyTypeObject *v, PyObject* args)
+{
+ 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;
+}
+
+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"
+"Override the automatic determination of C-level floating point type.\n"
+"This affects how floats are converted to and from binary strings.");
+
+static PyObject *
+float_getzero(PyObject *v, void *closure)
+{
+ return PyFloat_FromDouble(0.0);
+}
+
+static PyObject *
+float__format__(PyObject *self, PyObject *args)
+{
+ PyObject *format_spec;
+
+ if (!PyArg_ParseTuple(args, "O:__format__", &format_spec))
+ return NULL;
+ if (PyBytes_Check(format_spec))
+ return _PyFloat_FormatAdvanced(self,
+ PyBytes_AS_STRING(format_spec),
+ PyBytes_GET_SIZE(format_spec));
+ if (PyUnicode_Check(format_spec)) {
+ /* Convert format_spec to a str */
+ PyObject *result;
+ PyObject *str_spec = PyObject_Str(format_spec);
+
+ if (str_spec == NULL)
+ return NULL;
+
+ result = _PyFloat_FormatAdvanced(self,
+ PyBytes_AS_STRING(str_spec),
+ PyBytes_GET_SIZE(str_spec));
+
+ Py_DECREF(str_spec);
+ return result;
+ }
+ PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode");
+ return NULL;
+}
+
+PyDoc_STRVAR(float__format__doc,
+"float.__format__(format_spec) -> string\n"
+"\n"
+"Formats the float according to format_spec.");
+
+
+static PyMethodDef float_methods[] = {
+ {"conjugate", (PyCFunction)float_float, METH_NOARGS,
+ "Return self, the complex conjugate of any float."},
+ {"__trunc__", (PyCFunction)float_trunc, METH_NOARGS,
+ "Return the Integral closest to x between 0 and x."},
+ {"as_integer_ratio", (PyCFunction)float_as_integer_ratio, METH_NOARGS,
+ float_as_integer_ratio_doc},
+ {"fromhex", (PyCFunction)float_fromhex,
+ METH_O|METH_CLASS, float_fromhex_doc},
+ {"hex", (PyCFunction)float_hex,
+ METH_NOARGS, float_hex_doc},
+ {"is_integer", (PyCFunction)float_is_integer, METH_NOARGS,
+ "Return True if the float is an integer."},
+#if 0
+ {"is_inf", (PyCFunction)float_is_inf, METH_NOARGS,
+ "Return True if the float is positive or negative infinite."},
+ {"is_finite", (PyCFunction)float_is_finite, METH_NOARGS,
+ "Return True if the float is finite, neither infinite nor NaN."},
+ {"is_nan", (PyCFunction)float_is_nan, METH_NOARGS,
+ "Return True if the float is not a number (NaN)."},
+#endif
+ {"__getnewargs__", (PyCFunction)float_getnewargs, METH_NOARGS},
+ {"__getformat__", (PyCFunction)float_getformat,
+ METH_O|METH_CLASS, float_getformat_doc},
+ {"__setformat__", (PyCFunction)float_setformat,
+ METH_VARARGS|METH_CLASS, float_setformat_doc},
+ {"__format__", (PyCFunction)float__format__,
+ METH_VARARGS, float__format__doc},
+ {NULL, NULL} /* sentinel */
+};
+
+static PyGetSetDef float_getset[] = {
+ {"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} /* Sentinel */
+};
+
+PyDoc_STRVAR(float_doc,
+"float(x) -> floating point number\n\
+\n\
+Convert a string or number to a floating point number, if possible.");
+
+
+static PyNumberMethods float_as_number = {
+ float_add, /*nb_add*/
+ float_sub, /*nb_subtract*/
+ float_mul, /*nb_multiply*/
+ float_classic_div, /*nb_divide*/
+ float_rem, /*nb_remainder*/
+ float_divmod, /*nb_divmod*/
+ float_pow, /*nb_power*/
+ (unaryfunc)float_neg, /*nb_negative*/
+ (unaryfunc)float_float, /*nb_positive*/
+ (unaryfunc)float_abs, /*nb_absolute*/
+ (inquiry)float_nonzero, /*nb_nonzero*/
+ 0, /*nb_invert*/
+ 0, /*nb_lshift*/
+ 0, /*nb_rshift*/
+ 0, /*nb_and*/
+ 0, /*nb_xor*/
+ 0, /*nb_or*/
+ float_coerce, /*nb_coerce*/
+ float_trunc, /*nb_int*/
+ float_long, /*nb_long*/
+ float_float, /*nb_float*/
+ 0, /* nb_oct */
+ 0, /* nb_hex */
+ 0, /* nb_inplace_add */
+ 0, /* nb_inplace_subtract */
+ 0, /* nb_inplace_multiply */
+ 0, /* nb_inplace_divide */
+ 0, /* nb_inplace_remainder */
+ 0, /* nb_inplace_power */
+ 0, /* nb_inplace_lshift */
+ 0, /* nb_inplace_rshift */
+ 0, /* nb_inplace_and */
+ 0, /* nb_inplace_xor */
+ 0, /* nb_inplace_or */
+ 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 */
+ (printfunc)float_print, /* tp_print */
+ 0, /* tp_getattr */
+ 0, /* tp_setattr */
+ 0, /* tp_compare */
+ (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 */
+ (reprfunc)float_str, /* tp_str */
+ PyObject_GenericGetAttr, /* tp_getattro */
+ 0, /* tp_setattro */
+ 0, /* tp_as_buffer */
+ Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
+ Py_TPFLAGS_BASETYPE, /* tp_flags */
+ float_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 */
+};
+
+void
+_PyFloat_Init(void)
+{
+ /* 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);
+}
+
+int
+PyFloat_ClearFreeList(void)
+{
+ PyFloatObject *p;
+ PyFloatBlock *list, *next;
+ int i;
+ int u; /* remaining unfreed ints 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;
+}
+
+void
+PyFloat_Fini(void)
+{
+ 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;
+ }
+ }
+}
+
+/*----------------------------------------------------------------------------
+ * _PyFloat_{Pack,Unpack}{4,8}. See floatobject.h.
+ */
+int
+_PyFloat_Pack4(double x, unsigned char *p, int le)
+{
+ 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;
+}
+
+int
+_PyFloat_Pack8(double x, unsigned char *p, int le)
+{
+ 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; Unneeded (for now) */
+
+ /* 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;
+ }
+}
+
+double
+_PyFloat_Unpack4(const unsigned char *p, int le)
+{
+ 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;
+ }
+}
+
+double
+_PyFloat_Unpack8(const unsigned char *p, int le)
+{
+ 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;
+ }
+}
|