import math
from math import isinf, isnan, copysign, ldexp
import operator
-import random, fractions
+import random
+import fractions
+import sys
INF = float("inf")
NAN = float("nan")
self.assertEqual(v, eval(repr(v)))
floats_file.close()
+@unittest.skipUnless(float.__getformat__("double").startswith("IEEE"),
+ "test requires IEEE 754 doubles")
+class RoundTestCase(unittest.TestCase):
+ def test_second_argument_type(self):
+ # any type with an __index__ method should be permitted as
+ # a second argument
+ self.assertAlmostEqual(round(12.34, True), 12.3)
+
+ class MyIndex(object):
+ def __index__(self): return 4
+ self.assertAlmostEqual(round(-0.123456, MyIndex()), -0.1235)
+ # but floats should be illegal
+ self.assertRaises(TypeError, round, 3.14159, 2.0)
+
+ def test_inf_nan(self):
+ # rounding an infinity or nan returns the same number;
+ # (in py3k, rounding an infinity or nan raises an error,
+ # since the result can't be represented as a long).
+ self.assertEqual(round(INF), INF)
+ self.assertEqual(round(-INF), -INF)
+ self.assertTrue(math.isnan(round(NAN)))
+ for n in range(-5, 5):
+ self.assertEqual(round(INF, n), INF)
+ self.assertEqual(round(-INF, n), -INF)
+ self.assertTrue(math.isnan(round(NAN, n)))
+
+ def test_large_n(self):
+ for n in [324, 325, 400, 2**31-1, 2**31, 2**32, 2**100]:
+ self.assertEqual(round(123.456, n), 123.456)
+ self.assertEqual(round(-123.456, n), -123.456)
+ self.assertEqual(round(1e300, n), 1e300)
+ self.assertEqual(round(1e-320, n), 1e-320)
+ self.assertEqual(round(1e150, 300), 1e150)
+ self.assertEqual(round(1e300, 307), 1e300)
+ self.assertEqual(round(-3.1415, 308), -3.1415)
+ self.assertEqual(round(1e150, 309), 1e150)
+ self.assertEqual(round(1.4e-315, 315), 1e-315)
+
+ def test_small_n(self):
+ for n in [-308, -309, -400, 1-2**31, -2**31, -2**31-1, -2**100]:
+ self.assertEqual(round(123.456, n), 0.0)
+ self.assertEqual(round(-123.456, n), -0.0)
+ self.assertEqual(round(1e300, n), 0.0)
+ self.assertEqual(round(1e-320, n), 0.0)
+
+ def test_overflow(self):
+ self.assertRaises(OverflowError, round, 1.6e308, -308)
+ self.assertRaises(OverflowError, round, -1.7e308, -308)
+
+ @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
+ "test applies only when using short float repr style")
+ def test_previous_round_bugs(self):
+ # particular cases that have occurred in bug reports
+ self.assertEqual(round(562949953421312.5, 1),
+ 562949953421312.5)
+ self.assertEqual(round(56294995342131.5, 3),
+ 56294995342131.5)
+
+ @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
+ "test applies only when using short float repr style")
+ def test_halfway_cases(self):
+ # Halfway cases need special attention, since the current
+ # implementation has to deal with them specially. Note that
+ # 2.x rounds halfway values up (i.e., away from zero) while
+ # 3.x does round-half-to-even.
+ self.assertAlmostEqual(round(0.125, 2), 0.13)
+ self.assertAlmostEqual(round(0.375, 2), 0.38)
+ self.assertAlmostEqual(round(0.625, 2), 0.63)
+ self.assertAlmostEqual(round(0.875, 2), 0.88)
+ self.assertAlmostEqual(round(-0.125, 2), -0.13)
+ self.assertAlmostEqual(round(-0.375, 2), -0.38)
+ self.assertAlmostEqual(round(-0.625, 2), -0.63)
+ self.assertAlmostEqual(round(-0.875, 2), -0.88)
+
+ self.assertAlmostEqual(round(0.25, 1), 0.3)
+ self.assertAlmostEqual(round(0.75, 1), 0.8)
+ self.assertAlmostEqual(round(-0.25, 1), -0.3)
+ self.assertAlmostEqual(round(-0.75, 1), -0.8)
+
+ self.assertEqual(round(-6.5, 0), -7.0)
+ self.assertEqual(round(-5.5, 0), -6.0)
+ self.assertEqual(round(-1.5, 0), -2.0)
+ self.assertEqual(round(-0.5, 0), -1.0)
+ self.assertEqual(round(0.5, 0), 1.0)
+ self.assertEqual(round(1.5, 0), 2.0)
+ self.assertEqual(round(2.5, 0), 3.0)
+ self.assertEqual(round(3.5, 0), 4.0)
+ self.assertEqual(round(4.5, 0), 5.0)
+ self.assertEqual(round(5.5, 0), 6.0)
+ self.assertEqual(round(6.5, 0), 7.0)
+
+ # same but without an explicit second argument; in 3.x these
+ # will give integers
+ self.assertEqual(round(-6.5), -7.0)
+ self.assertEqual(round(-5.5), -6.0)
+ self.assertEqual(round(-1.5), -2.0)
+ self.assertEqual(round(-0.5), -1.0)
+ self.assertEqual(round(0.5), 1.0)
+ self.assertEqual(round(1.5), 2.0)
+ self.assertEqual(round(2.5), 3.0)
+ self.assertEqual(round(3.5), 4.0)
+ self.assertEqual(round(4.5), 5.0)
+ self.assertEqual(round(5.5), 6.0)
+ self.assertEqual(round(6.5), 7.0)
+
+ self.assertEqual(round(-25.0, -1), -30.0)
+ self.assertEqual(round(-15.0, -1), -20.0)
+ self.assertEqual(round(-5.0, -1), -10.0)
+ self.assertEqual(round(5.0, -1), 10.0)
+ self.assertEqual(round(15.0, -1), 20.0)
+ self.assertEqual(round(25.0, -1), 30.0)
+ self.assertEqual(round(35.0, -1), 40.0)
+ self.assertEqual(round(45.0, -1), 50.0)
+ self.assertEqual(round(55.0, -1), 60.0)
+ self.assertEqual(round(65.0, -1), 70.0)
+ self.assertEqual(round(75.0, -1), 80.0)
+ self.assertEqual(round(85.0, -1), 90.0)
+ self.assertEqual(round(95.0, -1), 100.0)
+ self.assertEqual(round(12325.0, -1), 12330.0)
+
+ self.assertEqual(round(350.0, -2), 400.0)
+ self.assertEqual(round(450.0, -2), 500.0)
+
+ self.assertAlmostEqual(round(0.5e21, -21), 1e21)
+ self.assertAlmostEqual(round(1.5e21, -21), 2e21)
+ self.assertAlmostEqual(round(2.5e21, -21), 3e21)
+ self.assertAlmostEqual(round(5.5e21, -21), 6e21)
+ self.assertAlmostEqual(round(8.5e21, -21), 9e21)
+
+ self.assertAlmostEqual(round(-1.5e22, -22), -2e22)
+ self.assertAlmostEqual(round(-0.5e22, -22), -1e22)
+ self.assertAlmostEqual(round(0.5e22, -22), 1e22)
+ self.assertAlmostEqual(round(1.5e22, -22), 2e22)
+
+
# Beginning with Python 2.6 float has cross platform compatible
# ways to create and represent inf and nan
class InfNanTest(unittest.TestCase):
UnknownFormatTestCase,
IEEEFormatTestCase,
ReprTestCase,
+ RoundTestCase,
InfNanTest,
HexFloatTestCase,
)
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;
+
+ /* 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 */
+ buf = _Py_dg_dtoa(x, 3, ndigits+halfway_case, &decpt, &sign, &buf_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;
+ rounded = _Py_dg_strtod(mybuf, NULL);
+ if (errno == ERANGE && fabs(rounded) >= 1.)
+ PyErr_SetString(PyExc_OverflowError,
+ "rounded value too large to represent");
+ else
+ result = PyFloat_FromDouble(rounded);
+
+ /* done computing value; now clean up */
+ if (mybuf != shortbuf)
+ PyMem_Free(mybuf);
+ exit:
+ _Py_dg_freedtoa(buf);
+ return result;
+}
+
+#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)
{
#include "eval.h"
#include <ctype.h>
+#include <float.h> /* for DBL_MANT_DIG and friends */
#ifdef RISCOS
#include "unixstuff.h"
static PyObject *
builtin_round(PyObject *self, PyObject *args, PyObject *kwds)
{
- double number;
- double f;
- int ndigits = 0;
- int i;
+ double x;
+ PyObject *o_ndigits = NULL;
+ Py_ssize_t ndigits;
static char *kwlist[] = {"number", "ndigits", 0};
- if (!PyArg_ParseTupleAndKeywords(args, kwds, "d|i:round",
- kwlist, &number, &ndigits))
+ if (!PyArg_ParseTupleAndKeywords(args, kwds, "d|O:round",
+ kwlist, &x, &o_ndigits))
return NULL;
- f = 1.0;
- i = abs(ndigits);
- while (--i >= 0)
- f = f*10.0;
- if (ndigits < 0)
- number /= f;
- else
- number *= f;
- number = round(number);
- if (ndigits < 0)
- number *= f;
+
+ /* nans, infinities and zeros round to themselves */
+ if (!Py_IS_FINITE(x) || x == 0.0)
+ return PyFloat_FromDouble(x);
+
+ if (o_ndigits == NULL) {
+ /* second argument defaults to 0 */
+ ndigits = 0;
+ }
+ else {
+ /* interpret 2nd argument as a Py_ssize_t; clip on overflow */
+ ndigits = PyNumber_AsSsize_t(o_ndigits, NULL);
+ if (ndigits == -1 && PyErr_Occurred())
+ return NULL;
+ }
+
+ /* 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
- number /= f;
- return PyFloat_FromDouble(number);
+ /* finite x, and ndigits is not unreasonably large */
+ /* _Py_double_round is defined in floatobject.c */
+ return _Py_double_round(x, (int)ndigits);
+#undef NDIGITS_MAX
+#undef NDIGITS_MIN
}
PyDoc_STRVAR(round_doc,
projects / python / commitdiff