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Issue #11734: Add support for IEEE 754 half-precision floats to the struct module. Original patch by Eli Stevens.
This commit is contained in:
Mark Dickinson
parent
2500c98278
commit
7c4e409d07
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@ -216,6 +216,8 @@ platform-dependent.
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+--------+--------------------------+--------------------+----------------+------------+
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| ``N`` | :c:type:`size_t` | integer | | \(4) |
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+--------+--------------------------+--------------------+----------------+------------+
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| ``e`` | \(7) | float | 2 | \(5) |
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+--------+--------------------------+--------------------+----------------+------------+
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| ``f`` | :c:type:`float` | float | 4 | \(5) |
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+--------+--------------------------+--------------------+----------------+------------+
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| ``d`` | :c:type:`double` | float | 8 | \(5) |
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@ -257,9 +259,10 @@ Notes:
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fits your application.
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(5)
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For the ``'f'`` and ``'d'`` conversion codes, the packed representation uses
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the IEEE 754 binary32 (for ``'f'``) or binary64 (for ``'d'``) format,
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regardless of the floating-point format used by the platform.
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For the ``'f'``, ``'d'`` and ``'e'`` conversion codes, the packed
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representation uses the IEEE 754 binary32, binary64 or binary16 format (for
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``'f'``, ``'d'`` or ``'e'`` respectively), regardless of the floating-point
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format used by the platform.
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(6)
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The ``'P'`` format character is only available for the native byte ordering
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@ -268,6 +271,16 @@ Notes:
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on the host system. The struct module does not interpret this as native
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ordering, so the ``'P'`` format is not available.
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(7)
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The IEEE 754 binary16 "half precision" type was introduced in the 2008
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revision of the `IEEE 754 standard <ieee 754 standard_>`_. It has a sign
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bit, a 5-bit exponent and 11-bit precision (with 10 bits explicitly stored),
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and can represent numbers between approximately ``6.1e-05`` and ``6.5e+04``
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at full precision. This type is not widely supported by C compilers: on a
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typical machine, an unsigned short can be used for storage, but not for math
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operations. See the Wikipedia page on the `half-precision floating-point
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format <half precision format_>`_ for more information.
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A format character may be preceded by an integral repeat count. For example,
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the format string ``'4h'`` means exactly the same as ``'hhhh'``.
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@ -430,3 +443,7 @@ The :mod:`struct` module also defines the following type:
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The calculated size of the struct (and hence of the bytes object produced
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by the :meth:`pack` method) corresponding to :attr:`format`.
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.. _half precision format: https://en.wikipedia.org/wiki/Half-precision_floating-point_format
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.. _ieee 754 standard: https://en.wikipedia.org/wiki/IEEE_floating_point#IEEE_754-2008
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@ -74,9 +74,9 @@ PyAPI_FUNC(double) PyFloat_AsDouble(PyObject *);
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* happens in such cases is partly accidental (alas).
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*/
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/* The pack routines write 4 or 8 bytes, starting at p. le is a bool
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/* The pack routines write 2, 4 or 8 bytes, starting at p. le is a bool
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* argument, true if you want the string in little-endian format (exponent
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* last, at p+3 or p+7), false if you want big-endian format (exponent
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* last, at p+1, p+3 or p+7), false if you want big-endian format (exponent
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* first, at p).
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* Return value: 0 if all is OK, -1 if error (and an exception is
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* set, most likely OverflowError).
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@ -84,6 +84,7 @@ PyAPI_FUNC(double) PyFloat_AsDouble(PyObject *);
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* 1): What this does is undefined if x is a NaN or infinity.
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* 2): -0.0 and +0.0 produce the same string.
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*/
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PyAPI_FUNC(int) _PyFloat_Pack2(double x, unsigned char *p, int le);
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PyAPI_FUNC(int) _PyFloat_Pack4(double x, unsigned char *p, int le);
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PyAPI_FUNC(int) _PyFloat_Pack8(double x, unsigned char *p, int le);
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@ -96,14 +97,15 @@ PyAPI_FUNC(int) _PyFloat_Repr(double x, char *p, size_t len);
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PyAPI_FUNC(int) _PyFloat_Digits(char *buf, double v, int *signum);
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PyAPI_FUNC(void) _PyFloat_DigitsInit(void);
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/* The unpack routines read 4 or 8 bytes, starting at p. le is a bool
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/* The unpack routines read 2, 4 or 8 bytes, starting at p. le is a bool
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* argument, true if the string is in little-endian format (exponent
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* last, at p+3 or p+7), false if big-endian (exponent first, at p).
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* last, at p+1, p+3 or p+7), false if big-endian (exponent first, at p).
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* Return value: The unpacked double. On error, this is -1.0 and
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* PyErr_Occurred() is true (and an exception is set, most likely
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* OverflowError). Note that on a non-IEEE platform this will refuse
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* to unpack a string that represents a NaN or infinity.
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*/
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PyAPI_FUNC(double) _PyFloat_Unpack2(const unsigned char *p, int le);
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PyAPI_FUNC(double) _PyFloat_Unpack4(const unsigned char *p, int le);
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PyAPI_FUNC(double) _PyFloat_Unpack8(const unsigned char *p, int le);
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@ -1,5 +1,6 @@
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from collections import abc
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import array
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import math
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import operator
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import unittest
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import struct
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@ -366,8 +367,6 @@ def test_705836(self):
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# SF bug 705836. "<f" and ">f" had a severe rounding bug, where a carry
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# from the low-order discarded bits could propagate into the exponent
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# field, causing the result to be wrong by a factor of 2.
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import math
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for base in range(1, 33):
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# smaller <- largest representable float less than base.
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delta = 0.5
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@ -659,6 +658,110 @@ def test_module_func(self):
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self.assertRaises(StopIteration, next, it)
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self.assertRaises(StopIteration, next, it)
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def test_half_float(self):
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# Little-endian examples from:
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# http://en.wikipedia.org/wiki/Half_precision_floating-point_format
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format_bits_float__cleanRoundtrip_list = [
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(b'\x00\x3c', 1.0),
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(b'\x00\xc0', -2.0),
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(b'\xff\x7b', 65504.0), # (max half precision)
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(b'\x00\x04', 2**-14), # ~= 6.10352 * 10**-5 (min pos normal)
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(b'\x01\x00', 2**-24), # ~= 5.96046 * 10**-8 (min pos subnormal)
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(b'\x00\x00', 0.0),
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(b'\x00\x80', -0.0),
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(b'\x00\x7c', float('+inf')),
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(b'\x00\xfc', float('-inf')),
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(b'\x55\x35', 0.333251953125), # ~= 1/3
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]
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for le_bits, f in format_bits_float__cleanRoundtrip_list:
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be_bits = le_bits[::-1]
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self.assertEqual(f, struct.unpack('<e', le_bits)[0])
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self.assertEqual(le_bits, struct.pack('<e', f))
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self.assertEqual(f, struct.unpack('>e', be_bits)[0])
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self.assertEqual(be_bits, struct.pack('>e', f))
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if sys.byteorder == 'little':
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self.assertEqual(f, struct.unpack('e', le_bits)[0])
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self.assertEqual(le_bits, struct.pack('e', f))
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else:
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self.assertEqual(f, struct.unpack('e', be_bits)[0])
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self.assertEqual(be_bits, struct.pack('e', f))
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# Check for NaN handling:
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format_bits__nan_list = [
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('<e', b'\x01\xfc'),
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('<e', b'\x00\xfe'),
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('<e', b'\xff\xff'),
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('<e', b'\x01\x7c'),
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('<e', b'\x00\x7e'),
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('<e', b'\xff\x7f'),
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]
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for formatcode, bits in format_bits__nan_list:
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self.assertTrue(math.isnan(struct.unpack('<e', bits)[0]))
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self.assertTrue(math.isnan(struct.unpack('>e', bits[::-1])[0]))
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# Check that packing produces a bit pattern representing a quiet NaN:
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# all exponent bits and the msb of the fraction should all be 1.
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packed = struct.pack('<e', math.nan)
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self.assertEqual(packed[1] & 0x7e, 0x7e)
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packed = struct.pack('<e', -math.nan)
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self.assertEqual(packed[1] & 0x7e, 0x7e)
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# Checks for round-to-even behavior
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format_bits_float__rounding_list = [
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('>e', b'\x00\x01', 2.0**-25 + 2.0**-35), # Rounds to minimum subnormal
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('>e', b'\x00\x00', 2.0**-25), # Underflows to zero (nearest even mode)
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('>e', b'\x00\x00', 2.0**-26), # Underflows to zero
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('>e', b'\x03\xff', 2.0**-14 - 2.0**-24), # Largest subnormal.
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('>e', b'\x03\xff', 2.0**-14 - 2.0**-25 - 2.0**-65),
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('>e', b'\x04\x00', 2.0**-14 - 2.0**-25),
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('>e', b'\x04\x00', 2.0**-14), # Smallest normal.
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('>e', b'\x3c\x01', 1.0+2.0**-11 + 2.0**-16), # rounds to 1.0+2**(-10)
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('>e', b'\x3c\x00', 1.0+2.0**-11), # rounds to 1.0 (nearest even mode)
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('>e', b'\x3c\x00', 1.0+2.0**-12), # rounds to 1.0
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('>e', b'\x7b\xff', 65504), # largest normal
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('>e', b'\x7b\xff', 65519), # rounds to 65504
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('>e', b'\x80\x01', -2.0**-25 - 2.0**-35), # Rounds to minimum subnormal
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('>e', b'\x80\x00', -2.0**-25), # Underflows to zero (nearest even mode)
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('>e', b'\x80\x00', -2.0**-26), # Underflows to zero
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('>e', b'\xbc\x01', -1.0-2.0**-11 - 2.0**-16), # rounds to 1.0+2**(-10)
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('>e', b'\xbc\x00', -1.0-2.0**-11), # rounds to 1.0 (nearest even mode)
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('>e', b'\xbc\x00', -1.0-2.0**-12), # rounds to 1.0
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('>e', b'\xfb\xff', -65519), # rounds to 65504
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]
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for formatcode, bits, f in format_bits_float__rounding_list:
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self.assertEqual(bits, struct.pack(formatcode, f))
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# This overflows, and so raises an error
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format_bits_float__roundingError_list = [
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# Values that round to infinity.
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('>e', 65520.0),
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('>e', 65536.0),
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('>e', 1e300),
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('>e', -65520.0),
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('>e', -65536.0),
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('>e', -1e300),
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('<e', 65520.0),
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('<e', 65536.0),
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('<e', 1e300),
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('<e', -65520.0),
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('<e', -65536.0),
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('<e', -1e300),
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]
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for formatcode, f in format_bits_float__roundingError_list:
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self.assertRaises(OverflowError, struct.pack, formatcode, f)
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# Double rounding
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format_bits_float__doubleRoundingError_list = [
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('>e', b'\x67\xff', 0x1ffdffffff * 2**-26), # should be 2047, if double-rounded 64>32>16, becomes 2048
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]
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for formatcode, bits, f in format_bits_float__doubleRoundingError_list:
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self.assertEqual(bits, struct.pack(formatcode, f))
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if __name__ == '__main__':
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unittest.main()
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@ -1435,6 +1435,7 @@ Greg Stein
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Marek Stepniowski
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Baruch Sterin
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Chris Stern
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Eli Stevens
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Alex Stewart
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Victor Stinner
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Richard Stoakley
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@ -69,6 +69,9 @@ Core and Builtins
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Library
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-------
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- Issue #11734: Add support for IEEE 754 half-precision floats to the
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struct module. Based on a patch by Eli Stevens.
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- Issue #27919: Deprecated ``extra_path`` distribution option in distutils
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packaging.
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@ -266,6 +266,33 @@ get_size_t(PyObject *v, size_t *p)
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/* Floating point helpers */
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static PyObject *
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unpack_halffloat(const char *p, /* start of 2-byte string */
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int le) /* true for little-endian, false for big-endian */
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{
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double x;
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x = _PyFloat_Unpack2((unsigned char *)p, le);
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if (x == -1.0 && PyErr_Occurred()) {
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return NULL;
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}
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return PyFloat_FromDouble(x);
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}
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static int
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pack_halffloat(char *p, /* start of 2-byte string */
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PyObject *v, /* value to pack */
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int le) /* true for little-endian, false for big-endian */
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{
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double x = PyFloat_AsDouble(v);
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if (x == -1.0 && PyErr_Occurred()) {
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PyErr_SetString(StructError,
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"required argument is not a float");
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return -1;
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}
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return _PyFloat_Pack2(x, (unsigned char *)p, le);
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}
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static PyObject *
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unpack_float(const char *p, /* start of 4-byte string */
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int le) /* true for little-endian, false for big-endian */
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@ -469,6 +496,16 @@ nu_bool(const char *p, const formatdef *f)
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}
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static PyObject *
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nu_halffloat(const char *p, const formatdef *f)
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{
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#if PY_LITTLE_ENDIAN
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return unpack_halffloat(p, 1);
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#else
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return unpack_halffloat(p, 0);
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#endif
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}
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static PyObject *
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nu_float(const char *p, const formatdef *f)
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{
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@ -680,6 +717,16 @@ np_bool(char *p, PyObject *v, const formatdef *f)
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return 0;
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}
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static int
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np_halffloat(char *p, PyObject *v, const formatdef *f)
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{
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#if PY_LITTLE_ENDIAN
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return pack_halffloat(p, v, 1);
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#else
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return pack_halffloat(p, v, 0);
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#endif
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}
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static int
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np_float(char *p, PyObject *v, const formatdef *f)
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{
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@ -743,6 +790,7 @@ static const formatdef native_table[] = {
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{'Q', sizeof(PY_LONG_LONG), LONG_LONG_ALIGN, nu_ulonglong,np_ulonglong},
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#endif
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{'?', sizeof(BOOL_TYPE), BOOL_ALIGN, nu_bool, np_bool},
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{'e', sizeof(short), SHORT_ALIGN, nu_halffloat, np_halffloat},
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{'f', sizeof(float), FLOAT_ALIGN, nu_float, np_float},
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{'d', sizeof(double), DOUBLE_ALIGN, nu_double, np_double},
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{'P', sizeof(void *), VOID_P_ALIGN, nu_void_p, np_void_p},
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@ -825,6 +873,12 @@ bu_ulonglong(const char *p, const formatdef *f)
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#endif
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}
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static PyObject *
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bu_halffloat(const char *p, const formatdef *f)
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{
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return unpack_halffloat(p, 0);
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}
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static PyObject *
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bu_float(const char *p, const formatdef *f)
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{
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@ -921,6 +975,12 @@ bp_ulonglong(char *p, PyObject *v, const formatdef *f)
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return res;
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}
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static int
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bp_halffloat(char *p, PyObject *v, const formatdef *f)
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{
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return pack_halffloat(p, v, 0);
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}
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static int
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bp_float(char *p, PyObject *v, const formatdef *f)
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{
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@ -972,6 +1032,7 @@ static formatdef bigendian_table[] = {
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{'q', 8, 0, bu_longlong, bp_longlong},
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{'Q', 8, 0, bu_ulonglong, bp_ulonglong},
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{'?', 1, 0, bu_bool, bp_bool},
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{'e', 2, 0, bu_halffloat, bp_halffloat},
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{'f', 4, 0, bu_float, bp_float},
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{'d', 8, 0, bu_double, bp_double},
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{0}
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@ -1053,6 +1114,12 @@ lu_ulonglong(const char *p, const formatdef *f)
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#endif
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}
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static PyObject *
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lu_halffloat(const char *p, const formatdef *f)
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{
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return unpack_halffloat(p, 1);
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}
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static PyObject *
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lu_float(const char *p, const formatdef *f)
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{
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@ -1141,6 +1208,12 @@ lp_ulonglong(char *p, PyObject *v, const formatdef *f)
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return res;
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}
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static int
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lp_halffloat(char *p, PyObject *v, const formatdef *f)
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{
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return pack_halffloat(p, v, 1);
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}
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static int
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lp_float(char *p, PyObject *v, const formatdef *f)
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{
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@ -1182,6 +1255,7 @@ static formatdef lilendian_table[] = {
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{'Q', 8, 0, lu_ulonglong, lp_ulonglong},
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{'?', 1, 0, bu_bool, bp_bool}, /* Std rep not endian dep,
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but potentially different from native rep -- reuse bx_bool funcs. */
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{'e', 2, 0, lu_halffloat, lp_halffloat},
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{'f', 4, 0, lu_float, lp_float},
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{'d', 8, 0, lu_double, lp_double},
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{0}
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@ -2239,7 +2313,7 @@ these can be preceded by a decimal repeat count:\n\
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x: pad byte (no data); c:char; b:signed byte; B:unsigned byte;\n\
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?: _Bool (requires C99; if not available, char is used instead)\n\
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h:short; H:unsigned short; i:int; I:unsigned int;\n\
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l:long; L:unsigned long; f:float; d:double.\n\
|
||||
l:long; L:unsigned long; f:float; d:double; e:half-float.\n\
|
||||
Special cases (preceding decimal count indicates length):\n\
|
||||
s:string (array of char); p: pascal string (with count byte).\n\
|
||||
Special cases (only available in native format):\n\
|
||||
|
|
|
|||
|
|
@ -1975,8 +1975,120 @@ _PyFloat_DebugMallocStats(FILE *out)
|
|||
|
||||
|
||||
/*----------------------------------------------------------------------------
|
||||
* _PyFloat_{Pack,Unpack}{4,8}. See floatobject.h.
|
||||
* _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)
|
||||
{
|
||||
|
|
@ -2211,6 +2323,76 @@ _PyFloat_Pack8(double x, unsigned char *p, int le)
|
|||
}
|
||||
}
|
||||
|
||||
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)
|
||||
{
|
||||
|
|
|
|||
Loading…
Reference in a new issue