mirror of
https://github.com/python/cpython
synced 2024-11-02 09:15:30 +00:00
2567 lines
70 KiB
C
2567 lines
70 KiB
C
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/* Float object implementation */
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/* XXX There should be overflow checks here, but it's hard to check
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for any kind of float exception without losing portability. */
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#include "Python.h"
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#include <ctype.h>
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#include <float.h>
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/* Special free list
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free_list is a singly-linked list of available PyFloatObjects, linked
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via abuse of their ob_type members.
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*/
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#ifndef PyFloat_MAXFREELIST
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#define PyFloat_MAXFREELIST 100
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#endif
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static int numfree = 0;
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static PyFloatObject *free_list = NULL;
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double
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PyFloat_GetMax(void)
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{
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return DBL_MAX;
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}
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double
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PyFloat_GetMin(void)
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{
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return DBL_MIN;
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}
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static PyTypeObject FloatInfoType;
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PyDoc_STRVAR(floatinfo__doc__,
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"sys.float_info\n\
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\n\
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A structseq holding information about the float type. It contains low level\n\
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information about the precision and internal representation. Please study\n\
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your system's :file:`float.h` for more information.");
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static PyStructSequence_Field floatinfo_fields[] = {
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{"max", "DBL_MAX -- maximum representable finite float"},
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{"max_exp", "DBL_MAX_EXP -- maximum int e such that radix**(e-1) "
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"is representable"},
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{"max_10_exp", "DBL_MAX_10_EXP -- maximum int e such that 10**e "
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"is representable"},
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{"min", "DBL_MIN -- Minimum positive normalizer float"},
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{"min_exp", "DBL_MIN_EXP -- minimum int e such that radix**(e-1) "
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"is a normalized float"},
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{"min_10_exp", "DBL_MIN_10_EXP -- minimum int e such that 10**e is "
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"a normalized"},
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{"dig", "DBL_DIG -- digits"},
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{"mant_dig", "DBL_MANT_DIG -- mantissa digits"},
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{"epsilon", "DBL_EPSILON -- Difference between 1 and the next "
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"representable float"},
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{"radix", "FLT_RADIX -- radix of exponent"},
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{"rounds", "FLT_ROUNDS -- addition rounds"},
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{0}
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};
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static PyStructSequence_Desc floatinfo_desc = {
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"sys.float_info", /* name */
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floatinfo__doc__, /* doc */
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floatinfo_fields, /* fields */
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11
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};
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PyObject *
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PyFloat_GetInfo(void)
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{
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PyObject* floatinfo;
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int pos = 0;
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floatinfo = PyStructSequence_New(&FloatInfoType);
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if (floatinfo == NULL) {
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return NULL;
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}
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#define SetIntFlag(flag) \
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PyStructSequence_SET_ITEM(floatinfo, pos++, PyLong_FromLong(flag))
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#define SetDblFlag(flag) \
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PyStructSequence_SET_ITEM(floatinfo, pos++, PyFloat_FromDouble(flag))
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SetDblFlag(DBL_MAX);
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SetIntFlag(DBL_MAX_EXP);
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SetIntFlag(DBL_MAX_10_EXP);
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SetDblFlag(DBL_MIN);
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SetIntFlag(DBL_MIN_EXP);
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SetIntFlag(DBL_MIN_10_EXP);
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SetIntFlag(DBL_DIG);
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SetIntFlag(DBL_MANT_DIG);
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SetDblFlag(DBL_EPSILON);
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SetIntFlag(FLT_RADIX);
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SetIntFlag(FLT_ROUNDS);
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#undef SetIntFlag
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#undef SetDblFlag
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if (PyErr_Occurred()) {
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Py_CLEAR(floatinfo);
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return NULL;
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}
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return floatinfo;
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}
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PyObject *
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PyFloat_FromDouble(double fval)
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{
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PyFloatObject *op = free_list;
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if (op != NULL) {
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free_list = (PyFloatObject *) Py_TYPE(op);
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numfree--;
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} else {
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op = (PyFloatObject*) PyObject_MALLOC(sizeof(PyFloatObject));
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if (!op)
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return PyErr_NoMemory();
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}
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/* Inline PyObject_New */
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(void)PyObject_INIT(op, &PyFloat_Type);
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op->ob_fval = fval;
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return (PyObject *) op;
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}
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PyObject *
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PyFloat_FromString(PyObject *v)
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{
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const char *s, *last, *end;
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double x;
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PyObject *s_buffer = NULL;
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Py_ssize_t len;
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Py_buffer view = {NULL, NULL};
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PyObject *result = NULL;
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if (PyUnicode_Check(v)) {
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s_buffer = _PyUnicode_TransformDecimalAndSpaceToASCII(v);
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if (s_buffer == NULL)
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return NULL;
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s = PyUnicode_AsUTF8AndSize(s_buffer, &len);
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if (s == NULL) {
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Py_DECREF(s_buffer);
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return NULL;
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}
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}
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else if (PyBytes_Check(v)) {
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s = PyBytes_AS_STRING(v);
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len = PyBytes_GET_SIZE(v);
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}
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else if (PyByteArray_Check(v)) {
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s = PyByteArray_AS_STRING(v);
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len = PyByteArray_GET_SIZE(v);
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}
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else if (PyObject_GetBuffer(v, &view, PyBUF_SIMPLE) == 0) {
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s = (const char *)view.buf;
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len = view.len;
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/* Copy to NUL-terminated buffer. */
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s_buffer = PyBytes_FromStringAndSize(s, len);
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if (s_buffer == NULL) {
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PyBuffer_Release(&view);
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return NULL;
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}
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s = PyBytes_AS_STRING(s_buffer);
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}
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else {
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PyErr_Format(PyExc_TypeError,
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"float() argument must be a string or a number, not '%.200s'",
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Py_TYPE(v)->tp_name);
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return NULL;
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}
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last = s + len;
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/* strip space */
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while (s < last && Py_ISSPACE(*s))
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s++;
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while (s < last - 1 && Py_ISSPACE(last[-1]))
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last--;
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/* We don't care about overflow or underflow. If the platform
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* supports them, infinities and signed zeroes (on underflow) are
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* fine. */
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x = PyOS_string_to_double(s, (char **)&end, NULL);
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if (end != last) {
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PyErr_Format(PyExc_ValueError,
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"could not convert string to float: "
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"%R", v);
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result = NULL;
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}
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else if (x == -1.0 && PyErr_Occurred())
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result = NULL;
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else
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result = PyFloat_FromDouble(x);
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PyBuffer_Release(&view);
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Py_XDECREF(s_buffer);
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return result;
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}
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static void
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float_dealloc(PyFloatObject *op)
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{
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if (PyFloat_CheckExact(op)) {
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if (numfree >= PyFloat_MAXFREELIST) {
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PyObject_FREE(op);
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return;
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}
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numfree++;
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Py_TYPE(op) = (struct _typeobject *)free_list;
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free_list = op;
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}
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else
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Py_TYPE(op)->tp_free((PyObject *)op);
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}
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double
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PyFloat_AsDouble(PyObject *op)
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{
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PyNumberMethods *nb;
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PyObject *res;
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double val;
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if (op == NULL) {
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PyErr_BadArgument();
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return -1;
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}
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if (PyFloat_Check(op)) {
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return PyFloat_AS_DOUBLE(op);
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}
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nb = Py_TYPE(op)->tp_as_number;
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if (nb == NULL || nb->nb_float == NULL) {
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PyErr_Format(PyExc_TypeError, "must be real number, not %.50s",
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op->ob_type->tp_name);
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return -1;
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}
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res = (*nb->nb_float) (op);
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if (res == NULL) {
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return -1;
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}
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if (!PyFloat_CheckExact(res)) {
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if (!PyFloat_Check(res)) {
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PyErr_Format(PyExc_TypeError,
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"%.50s.__float__ returned non-float (type %.50s)",
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op->ob_type->tp_name, res->ob_type->tp_name);
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Py_DECREF(res);
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return -1;
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}
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if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
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"%.50s.__float__ returned non-float (type %.50s). "
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"The ability to return an instance of a strict subclass of float "
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"is deprecated, and may be removed in a future version of Python.",
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op->ob_type->tp_name, res->ob_type->tp_name)) {
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Py_DECREF(res);
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return -1;
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}
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}
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val = PyFloat_AS_DOUBLE(res);
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Py_DECREF(res);
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return val;
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}
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/* Macro and helper that convert PyObject obj to a C double and store
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the value in dbl. If conversion to double raises an exception, obj is
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set to NULL, and the function invoking this macro returns NULL. If
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obj is not of float or int type, Py_NotImplemented is incref'ed,
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stored in obj, and returned from the function invoking this macro.
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*/
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#define CONVERT_TO_DOUBLE(obj, dbl) \
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if (PyFloat_Check(obj)) \
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dbl = PyFloat_AS_DOUBLE(obj); \
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else if (convert_to_double(&(obj), &(dbl)) < 0) \
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return obj;
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/* Methods */
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static int
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convert_to_double(PyObject **v, double *dbl)
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{
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PyObject *obj = *v;
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if (PyLong_Check(obj)) {
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*dbl = PyLong_AsDouble(obj);
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if (*dbl == -1.0 && PyErr_Occurred()) {
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*v = NULL;
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return -1;
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}
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}
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else {
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Py_INCREF(Py_NotImplemented);
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*v = Py_NotImplemented;
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return -1;
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}
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return 0;
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}
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static PyObject *
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float_repr(PyFloatObject *v)
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{
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PyObject *result;
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char *buf;
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buf = PyOS_double_to_string(PyFloat_AS_DOUBLE(v),
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'r', 0,
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Py_DTSF_ADD_DOT_0,
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NULL);
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if (!buf)
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return PyErr_NoMemory();
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result = _PyUnicode_FromASCII(buf, strlen(buf));
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PyMem_Free(buf);
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return result;
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}
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/* Comparison is pretty much a nightmare. When comparing float to float,
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* we do it as straightforwardly (and long-windedly) as conceivable, so
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* that, e.g., Python x == y delivers the same result as the platform
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* C x == y when x and/or y is a NaN.
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* When mixing float with an integer type, there's no good *uniform* approach.
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* Converting the double to an integer obviously doesn't work, since we
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* may lose info from fractional bits. Converting the integer to a double
|
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* also has two failure modes: (1) an int may trigger overflow (too
|
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* large to fit in the dynamic range of a C double); (2) even a C long may have
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* more bits than fit in a C double (e.g., on a 64-bit box long may have
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* 63 bits of precision, but a C double probably has only 53), and then
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* we can falsely claim equality when low-order integer bits are lost by
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* coercion to double. So this part is painful too.
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*/
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static PyObject*
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float_richcompare(PyObject *v, PyObject *w, int op)
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{
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double i, j;
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int r = 0;
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assert(PyFloat_Check(v));
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i = PyFloat_AS_DOUBLE(v);
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/* Switch on the type of w. Set i and j to doubles to be compared,
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* and op to the richcomp to use.
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*/
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if (PyFloat_Check(w))
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j = PyFloat_AS_DOUBLE(w);
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else if (!Py_IS_FINITE(i)) {
|
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if (PyLong_Check(w))
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/* If i is an infinity, its magnitude exceeds any
|
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* finite integer, so it doesn't matter which int we
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* compare i with. If i is a NaN, similarly.
|
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*/
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j = 0.0;
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else
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goto Unimplemented;
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}
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|
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else if (PyLong_Check(w)) {
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int vsign = i == 0.0 ? 0 : i < 0.0 ? -1 : 1;
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int wsign = _PyLong_Sign(w);
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size_t nbits;
|
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int exponent;
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|
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if (vsign != wsign) {
|
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/* Magnitudes are irrelevant -- the signs alone
|
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* determine the outcome.
|
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*/
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i = (double)vsign;
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j = (double)wsign;
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goto Compare;
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}
|
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/* The signs are the same. */
|
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/* Convert w to a double if it fits. In particular, 0 fits. */
|
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nbits = _PyLong_NumBits(w);
|
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if (nbits == (size_t)-1 && PyErr_Occurred()) {
|
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/* This long is so large that size_t isn't big enough
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* to hold the # of bits. Replace with little doubles
|
|
* that give the same outcome -- w is so large that
|
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* its magnitude must exceed the magnitude of any
|
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* finite float.
|
|
*/
|
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PyErr_Clear();
|
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i = (double)vsign;
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assert(wsign != 0);
|
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j = wsign * 2.0;
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goto Compare;
|
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}
|
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if (nbits <= 48) {
|
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j = PyLong_AsDouble(w);
|
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/* It's impossible that <= 48 bits overflowed. */
|
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assert(j != -1.0 || ! PyErr_Occurred());
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goto Compare;
|
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}
|
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assert(wsign != 0); /* else nbits was 0 */
|
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assert(vsign != 0); /* if vsign were 0, then since wsign is
|
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* not 0, we would have taken the
|
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* vsign != wsign branch at the start */
|
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/* We want to work with non-negative numbers. */
|
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if (vsign < 0) {
|
|
/* "Multiply both sides" by -1; this also swaps the
|
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* comparator.
|
|
*/
|
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i = -i;
|
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op = _Py_SwappedOp[op];
|
|
}
|
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assert(i > 0.0);
|
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(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
|
|
*/
|
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if (exponent < 0 || (size_t)exponent < nbits) {
|
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i = 1.0;
|
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j = 2.0;
|
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goto Compare;
|
|
}
|
|
if ((size_t)exponent > nbits) {
|
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i = 2.0;
|
|
j = 1.0;
|
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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 || o_ndigits == Py_None) {
|
|
/* single-argument round or with None ndigits:
|
|
* round to nearest integer */
|
|
rounded = round(x);
|
|
if (fabs(x-rounded) == 0.5)
|
|
/* halfway case: round to even */
|
|
rounded = 2.0*round(x/2.0);
|
|
return PyLong_FromDouble(rounded);
|
|
}
|
|
|
|
/* interpret second argument as a Py_ssize_t; clips on overflow */
|
|
ndigits = PyNumber_AsSsize_t(o_ndigits, NULL);
|
|
if (ndigits == -1 && PyErr_Occurred())
|
|
return NULL;
|
|
|
|
/* nans and infinities round to themselves */
|
|
if (!Py_IS_FINITE(x))
|
|
return PyFloat_FromDouble(x);
|
|
|
|
/* Deal with extreme values for ndigits. For ndigits > NDIGITS_MAX, x
|
|
always rounds to itself. For ndigits < NDIGITS_MIN, x always
|
|
rounds to +-0.0. Here 0.30103 is an upper bound for log10(2). */
|
|
#define NDIGITS_MAX ((int)((DBL_MANT_DIG-DBL_MIN_EXP) * 0.30103))
|
|
#define NDIGITS_MIN (-(int)((DBL_MAX_EXP + 1) * 0.30103))
|
|
if (ndigits > NDIGITS_MAX)
|
|
/* return x */
|
|
return PyFloat_FromDouble(x);
|
|
else if (ndigits < NDIGITS_MIN)
|
|
/* return 0.0, but with sign of x */
|
|
return PyFloat_FromDouble(0.0*x);
|
|
else
|
|
/* finite x, and ndigits is not unreasonably large */
|
|
return double_round(x, (int)ndigits);
|
|
#undef NDIGITS_MAX
|
|
#undef NDIGITS_MIN
|
|
}
|
|
|
|
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 Py_hexdigits[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_repr((PyFloatObject *)v);
|
|
|
|
if (x == 0.0) {
|
|
if (copysign(1.0, x) == -1.0)
|
|
return PyUnicode_FromString("-0x0.0p+0");
|
|
else
|
|
return PyUnicode_FromString("0x0.0p+0");
|
|
}
|
|
|
|
m = frexp(fabs(x), &e);
|
|
shift = 1 - Py_MAX(DBL_MIN_EXP - e, 0);
|
|
m = ldexp(m, shift);
|
|
e -= shift;
|
|
|
|
si = 0;
|
|
s[si] = char_from_hex((int)m);
|
|
si++;
|
|
m -= (int)m;
|
|
s[si] = '.';
|
|
si++;
|
|
for (i=0; i < (TOHEX_NBITS-1)/4; i++) {
|
|
m *= 16.0;
|
|
s[si] = char_from_hex((int)m);
|
|
si++;
|
|
m -= (int)m;
|
|
}
|
|
s[si] = '\0';
|
|
|
|
if (e < 0) {
|
|
esign = (int)'-';
|
|
e = -e;
|
|
}
|
|
else
|
|
esign = (int)'+';
|
|
|
|
if (x < 0.0)
|
|
return PyUnicode_FromFormat("-0x%sp%c%d", s, esign, e);
|
|
else
|
|
return PyUnicode_FromFormat("0x%sp%c%d", s, esign, e);
|
|
}
|
|
|
|
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'");
|
|
|
|
/* Convert a hexadecimal string to a float. */
|
|
|
|
static PyObject *
|
|
float_fromhex(PyObject *cls, PyObject *arg)
|
|
{
|
|
PyObject *result;
|
|
double x;
|
|
long exp, top_exp, lsb, key_digit;
|
|
char *s, *coeff_start, *s_store, *coeff_end, *exp_start, *s_end;
|
|
int half_eps, digit, round_up, negate=0;
|
|
Py_ssize_t length, ndigits, fdigits, i;
|
|
|
|
/*
|
|
* For the sake of simplicity and correctness, we impose an artificial
|
|
* limit on ndigits, the total number of hex digits in the coefficient
|
|
* The limit is chosen to ensure that, writing exp for the exponent,
|
|
*
|
|
* (1) if exp > LONG_MAX/2 then the value of the hex string is
|
|
* guaranteed to overflow (provided it's nonzero)
|
|
*
|
|
* (2) if exp < LONG_MIN/2 then the value of the hex string is
|
|
* guaranteed to underflow to 0.
|
|
*
|
|
* (3) if LONG_MIN/2 <= exp <= LONG_MAX/2 then there's no danger of
|
|
* overflow in the calculation of exp and top_exp below.
|
|
*
|
|
* More specifically, ndigits is assumed to satisfy the following
|
|
* inequalities:
|
|
*
|
|
* 4*ndigits <= DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2
|
|
* 4*ndigits <= LONG_MAX/2 + 1 - DBL_MAX_EXP
|
|
*
|
|
* If either of these inequalities is not satisfied, a ValueError is
|
|
* raised. Otherwise, write x for the value of the hex string, and
|
|
* assume x is nonzero. Then
|
|
*
|
|
* 2**(exp-4*ndigits) <= |x| < 2**(exp+4*ndigits).
|
|
*
|
|
* Now if exp > LONG_MAX/2 then:
|
|
*
|
|
* exp - 4*ndigits >= LONG_MAX/2 + 1 - (LONG_MAX/2 + 1 - DBL_MAX_EXP)
|
|
* = DBL_MAX_EXP
|
|
*
|
|
* so |x| >= 2**DBL_MAX_EXP, which is too large to be stored in C
|
|
* double, so overflows. If exp < LONG_MIN/2, then
|
|
*
|
|
* exp + 4*ndigits <= LONG_MIN/2 - 1 + (
|
|
* DBL_MIN_EXP - DBL_MANT_DIG - LONG_MIN/2)
|
|
* = DBL_MIN_EXP - DBL_MANT_DIG - 1
|
|
*
|
|
* and so |x| < 2**(DBL_MIN_EXP-DBL_MANT_DIG-1), hence underflows to 0
|
|
* when converted to a C double.
|
|
*
|
|
* It's easy to show that if LONG_MIN/2 <= exp <= LONG_MAX/2 then both
|
|
* exp+4*ndigits and exp-4*ndigits are within the range of a long.
|
|
*/
|
|
|
|
s = _PyUnicode_AsStringAndSize(arg, &length);
|
|
if (s == NULL)
|
|
return NULL;
|
|
s_end = s + length;
|
|
|
|
/********************
|
|
* Parse the string *
|
|
********************/
|
|
|
|
/* leading whitespace */
|
|
while (Py_ISSPACE(*s))
|
|
s++;
|
|
|
|
/* infinities and nans */
|
|
x = _Py_parse_inf_or_nan(s, &coeff_end);
|
|
if (coeff_end != s) {
|
|
s = coeff_end;
|
|
goto finished;
|
|
}
|
|
|
|
/* optional sign */
|
|
if (*s == '-') {
|
|
s++;
|
|
negate = 1;
|
|
}
|
|
else if (*s == '+')
|
|
s++;
|
|
|
|
/* [0x] */
|
|
s_store = s;
|
|
if (*s == '0') {
|
|
s++;
|
|
if (*s == 'x' || *s == 'X')
|
|
s++;
|
|
else
|
|
s = s_store;
|
|
}
|
|
|
|
/* coefficient: <integer> [. <fraction>] */
|
|
coeff_start = s;
|
|
while (hex_from_char(*s) >= 0)
|
|
s++;
|
|
s_store = s;
|
|
if (*s == '.') {
|
|
s++;
|
|
while (hex_from_char(*s) >= 0)
|
|
s++;
|
|
coeff_end = s-1;
|
|
}
|
|
else
|
|
coeff_end = s;
|
|
|
|
/* ndigits = total # of hex digits; fdigits = # after point */
|
|
ndigits = coeff_end - coeff_start;
|
|
fdigits = coeff_end - s_store;
|
|
if (ndigits == 0)
|
|
goto parse_error;
|
|
if (ndigits > Py_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 = Py_MAX(top_exp, (long)DBL_MIN_EXP) - DBL_MANT_DIG;
|
|
|
|
x = 0.0;
|
|
if (exp >= lsb) {
|
|
/* no rounding required */
|
|
for (i = ndigits-1; i >= 0; i--)
|
|
x = 16.0*x + HEX_DIGIT(i);
|
|
x = ldexp(x, (int)(exp));
|
|
goto finished;
|
|
}
|
|
/* rounding required. key_digit is the index of the hex digit
|
|
containing the first bit to be rounded away. */
|
|
half_eps = 1 << (int)((lsb - exp - 1) % 4);
|
|
key_digit = (lsb - exp - 1) / 4;
|
|
for (i = ndigits-1; i > key_digit; i--)
|
|
x = 16.0*x + HEX_DIGIT(i);
|
|
digit = HEX_DIGIT(key_digit);
|
|
x = 16.0*x + (double)(digit & (16-2*half_eps));
|
|
|
|
/* round-half-even: round up if bit lsb-1 is 1 and at least one of
|
|
bits lsb, lsb-2, lsb-3, lsb-4, ... is 1. */
|
|
if ((digit & half_eps) != 0) {
|
|
round_up = 0;
|
|
if ((digit & (3*half_eps-1)) != 0 ||
|
|
(half_eps == 8 && (HEX_DIGIT(key_digit+1) & 1) != 0))
|
|
round_up = 1;
|
|
else
|
|
for (i = key_digit-1; i >= 0; i--)
|
|
if (HEX_DIGIT(i) != 0) {
|
|
round_up = 1;
|
|
break;
|
|
}
|
|
if (round_up) {
|
|
x += 2*half_eps;
|
|
if (top_exp == DBL_MAX_EXP &&
|
|
x == ldexp((double)(2*half_eps), DBL_MANT_DIG))
|
|
/* overflow corner case: pre-rounded value <
|
|
2**DBL_MAX_EXP; rounded=2**DBL_MAX_EXP. */
|
|
goto overflow_error;
|
|
}
|
|
}
|
|
x = ldexp(x, (int)(exp+4*key_digit));
|
|
|
|
finished:
|
|
/* optional trailing whitespace leading to the end of the string */
|
|
while (Py_ISSPACE(*s))
|
|
s++;
|
|
if (s != s_end)
|
|
goto parse_error;
|
|
result = PyFloat_FromDouble(negate ? -x : x);
|
|
if (cls != (PyObject *)&PyFloat_Type && result != NULL) {
|
|
Py_SETREF(result, PyObject_CallFunctionObjArgs(cls, result, NULL));
|
|
}
|
|
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\
|
|
-5e-324");
|
|
|
|
|
|
static PyObject *
|
|
float_as_integer_ratio(PyObject *v, PyObject *unused)
|
|
{
|
|
double self;
|
|
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(v, self);
|
|
|
|
if (Py_IS_INFINITY(self)) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"cannot convert Infinity to integer ratio");
|
|
return NULL;
|
|
}
|
|
if (Py_IS_NAN(self)) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"cannot convert NaN to integer ratio");
|
|
return NULL;
|
|
}
|
|
|
|
PyFPE_START_PROTECT("as_integer_ratio", goto error);
|
|
float_part = frexp(self, &exponent); /* self == float_part * 2**exponent exactly */
|
|
PyFPE_END_PROTECT(float_part);
|
|
|
|
for (i=0; i<300 && float_part != floor(float_part) ; i++) {
|
|
float_part *= 2.0;
|
|
exponent--;
|
|
}
|
|
/* self == float_part * 2**exponent exactly and float_part is integral.
|
|
If FLT_RADIX != 2, the 300 steps may leave a tiny fractional part
|
|
to be truncated by PyLong_FromDouble(). */
|
|
|
|
numerator = PyLong_FromDouble(float_part);
|
|
if (numerator == NULL)
|
|
goto error;
|
|
denominator = PyLong_FromLong(1);
|
|
if (denominator == NULL)
|
|
goto error;
|
|
py_exponent = PyLong_FromLong(Py_ABS(exponent));
|
|
if (py_exponent == NULL)
|
|
goto error;
|
|
|
|
/* fold in 2**exponent */
|
|
if (exponent > 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;
|
|
}
|
|
|
|
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 (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 *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_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_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 (!PyUnicode_Check(arg)) {
|
|
PyErr_Format(PyExc_TypeError,
|
|
"__getformat__() argument must be string, not %.500s",
|
|
Py_TYPE(arg)->tp_name);
|
|
return NULL;
|
|
}
|
|
s = _PyUnicode_AsString(arg);
|
|
if (s == NULL)
|
|
return NULL;
|
|
if (strcmp(s, "double") == 0) {
|
|
r = double_format;
|
|
}
|
|
else if (strcmp(s, "float") == 0) {
|
|
r = float_format;
|
|
}
|
|
else {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"__getformat__() argument 1 must be "
|
|
"'double' or 'float'");
|
|
return NULL;
|
|
}
|
|
|
|
switch (r) {
|
|
case unknown_format:
|
|
return PyUnicode_FromString("unknown");
|
|
case ieee_little_endian_format:
|
|
return PyUnicode_FromString("IEEE, little-endian");
|
|
case ieee_big_endian_format:
|
|
return PyUnicode_FromString("IEEE, big-endian");
|
|
default:
|
|
Py_FatalError("insane float_format or double_format");
|
|
return NULL;
|
|
}
|
|
}
|
|
|
|
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;
|
|
_PyUnicodeWriter writer;
|
|
int ret;
|
|
|
|
if (!PyArg_ParseTuple(args, "U:__format__", &format_spec))
|
|
return NULL;
|
|
|
|
_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);
|
|
}
|
|
|
|
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."},
|
|
{"__round__", (PyCFunction)float_round, METH_VARARGS,
|
|
"Return the Integral closest to x, rounding half toward even.\n"
|
|
"When an argument is passed, work like built-in round(x, ndigits)."},
|
|
{"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_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_bool, /*nb_bool*/
|
|
0, /*nb_invert*/
|
|
0, /*nb_lshift*/
|
|
0, /*nb_rshift*/
|
|
0, /*nb_and*/
|
|
0, /*nb_xor*/
|
|
0, /*nb_or*/
|
|
float_trunc, /*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_print */
|
|
0, /* tp_getattr */
|
|
0, /* tp_setattr */
|
|
0, /* tp_reserved */
|
|
(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_repr, /* tp_str */
|
|
PyObject_GenericGetAttr, /* tp_getattro */
|
|
0, /* tp_setattro */
|
|
0, /* tp_as_buffer */
|
|
Py_TPFLAGS_DEFAULT | 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 */
|
|
};
|
|
|
|
int
|
|
_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 == NULL) {
|
|
if (PyStructSequence_InitType2(&FloatInfoType, &floatinfo_desc) < 0)
|
|
return 0;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
int
|
|
PyFloat_ClearFreeList(void)
|
|
{
|
|
PyFloatObject *f = free_list, *next;
|
|
int i = numfree;
|
|
while (f) {
|
|
next = (PyFloatObject*) Py_TYPE(f);
|
|
PyObject_FREE(f);
|
|
f = next;
|
|
}
|
|
free_list = NULL;
|
|
numfree = 0;
|
|
return i;
|
|
}
|
|
|
|
void
|
|
PyFloat_Fini(void)
|
|
{
|
|
(void)PyFloat_ClearFreeList();
|
|
}
|
|
|
|
/* Print summary info about the state of the optimized allocator */
|
|
void
|
|
_PyFloat_DebugMallocStats(FILE *out)
|
|
{
|
|
_PyDebugAllocatorStats(out,
|
|
"free PyFloatObject",
|
|
numfree, sizeof(PyFloatObject));
|
|
}
|
|
|
|
|
|
/*----------------------------------------------------------------------------
|
|
* _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, unsigned char *p, int le)
|
|
{
|
|
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 << 10) | (sign << 15);
|
|
|
|
/* Write out result. */
|
|
if (le) {
|
|
p += 1;
|
|
incr = -1;
|
|
}
|
|
|
|
/* First byte */
|
|
*p = (unsigned char)((bits >> 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, 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 unsigned char *s = (unsigned 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; */
|
|
|
|
/* 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 unsigned char *p, int le)
|
|
{
|
|
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) << 8;
|
|
p += incr;
|
|
|
|
/* Second byte */
|
|
f |= *p;
|
|
|
|
if (e == 0x1f) {
|
|
#ifdef PY_NO_SHORT_FLOAT_REPR
|
|
if (f == 0) {
|
|
/* Infinity */
|
|
return sign ? -Py_HUGE_VAL : Py_HUGE_VAL;
|
|
}
|
|
else {
|
|
/* NaN */
|
|
#ifdef Py_NAN
|
|
return sign ? -Py_NAN : Py_NAN;
|
|
#else
|
|
PyErr_SetString(
|
|
PyExc_ValueError,
|
|
"can't unpack IEEE 754 NaN "
|
|
"on platform that does not support NaNs");
|
|
return -1;
|
|
#endif /* #ifdef Py_NAN */
|
|
}
|
|
#else
|
|
if (f == 0) {
|
|
/* Infinity */
|
|
return _Py_dg_infinity(sign);
|
|
}
|
|
else {
|
|
/* NaN */
|
|
return _Py_dg_stdnan(sign);
|
|
}
|
|
#endif /* #ifdef PY_NO_SHORT_FLOAT_REPR */
|
|
}
|
|
|
|
x = (double)f / 1024.0;
|
|
|
|
if (e == 0) {
|
|
e = -14;
|
|
}
|
|
else {
|
|
x += 1.0;
|
|
e -= 15;
|
|
}
|
|
x = ldexp(x, e);
|
|
|
|
if (sign)
|
|
x = -x;
|
|
|
|
return x;
|
|
}
|
|
|
|
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;
|
|
}
|
|
}
|