Issue #11734: Add support for IEEE 754 half-precision floats to the struct module. Original patch by Eli Stevens.

Lib/test/test_struct.py

@@ -1,5 +1,6 @@
 from collections import abc
 import array
+import math
 import operator
 import unittest
 import struct
@@ -366,8 +367,6 @@ class StructTest(unittest.TestCase):
         # SF bug 705836.  "<f" and ">f" had a severe rounding bug, where a carry
         # from the low-order discarded bits could propagate into the exponent
         # field, causing the result to be wrong by a factor of 2.
-        import math
-
         for base in range(1, 33):
             # smaller <- largest representable float less than base.
             delta = 0.5
@@ -659,6 +658,110 @@ class UnpackIteratorTest(unittest.TestCase):
         self.assertRaises(StopIteration, next, it)
         self.assertRaises(StopIteration, next, it)
 
+    def test_half_float(self):
+        # Little-endian examples from:
+        # http://en.wikipedia.org/wiki/Half_precision_floating-point_format
+        format_bits_float__cleanRoundtrip_list = [
+            (b'\x00\x3c', 1.0),
+            (b'\x00\xc0', -2.0),
+            (b'\xff\x7b', 65504.0), #  (max half precision)
+            (b'\x00\x04', 2**-14), # ~= 6.10352 * 10**-5 (min pos normal)
+            (b'\x01\x00', 2**-24), # ~= 5.96046 * 10**-8 (min pos subnormal)
+            (b'\x00\x00', 0.0),
+            (b'\x00\x80', -0.0),
+            (b'\x00\x7c', float('+inf')),
+            (b'\x00\xfc', float('-inf')),
+            (b'\x55\x35', 0.333251953125), # ~= 1/3
+        ]
+
+        for le_bits, f in format_bits_float__cleanRoundtrip_list:
+            be_bits = le_bits[::-1]
+            self.assertEqual(f, struct.unpack('<e', le_bits)[0])
+            self.assertEqual(le_bits, struct.pack('<e', f))
+            self.assertEqual(f, struct.unpack('>e', be_bits)[0])
+            self.assertEqual(be_bits, struct.pack('>e', f))
+            if sys.byteorder == 'little':
+                self.assertEqual(f, struct.unpack('e', le_bits)[0])
+                self.assertEqual(le_bits, struct.pack('e', f))
+            else:
+                self.assertEqual(f, struct.unpack('e', be_bits)[0])
+                self.assertEqual(be_bits, struct.pack('e', f))
+
+        # Check for NaN handling:
+        format_bits__nan_list = [
+            ('<e', b'\x01\xfc'),
+            ('<e', b'\x00\xfe'),
+            ('<e', b'\xff\xff'),
+            ('<e', b'\x01\x7c'),
+            ('<e', b'\x00\x7e'),
+            ('<e', b'\xff\x7f'),
+        ]
+
+        for formatcode, bits in format_bits__nan_list:
+            self.assertTrue(math.isnan(struct.unpack('<e', bits)[0]))
+            self.assertTrue(math.isnan(struct.unpack('>e', bits[::-1])[0]))
+
+        # Check that packing produces a bit pattern representing a quiet NaN:
+        # all exponent bits and the msb of the fraction should all be 1.
+        packed = struct.pack('<e', math.nan)
+        self.assertEqual(packed[1] & 0x7e, 0x7e)
+        packed = struct.pack('<e', -math.nan)
+        self.assertEqual(packed[1] & 0x7e, 0x7e)
+
+        # Checks for round-to-even behavior
+        format_bits_float__rounding_list = [
+            ('>e', b'\x00\x01', 2.0**-25 + 2.0**-35), # Rounds to minimum subnormal
+            ('>e', b'\x00\x00', 2.0**-25), # Underflows to zero (nearest even mode)
+            ('>e', b'\x00\x00', 2.0**-26), # Underflows to zero
+            ('>e', b'\x03\xff', 2.0**-14 - 2.0**-24), # Largest subnormal.
+            ('>e', b'\x03\xff', 2.0**-14 - 2.0**-25 - 2.0**-65),
+            ('>e', b'\x04\x00', 2.0**-14 - 2.0**-25),
+            ('>e', b'\x04\x00', 2.0**-14), # Smallest normal.
+            ('>e', b'\x3c\x01', 1.0+2.0**-11 + 2.0**-16), # rounds to 1.0+2**(-10)
+            ('>e', b'\x3c\x00', 1.0+2.0**-11), # rounds to 1.0 (nearest even mode)
+            ('>e', b'\x3c\x00', 1.0+2.0**-12), # rounds to 1.0
+            ('>e', b'\x7b\xff', 65504), # largest normal
+            ('>e', b'\x7b\xff', 65519), # rounds to 65504
+            ('>e', b'\x80\x01', -2.0**-25 - 2.0**-35), # Rounds to minimum subnormal
+            ('>e', b'\x80\x00', -2.0**-25), # Underflows to zero (nearest even mode)
+            ('>e', b'\x80\x00', -2.0**-26), # Underflows to zero
+            ('>e', b'\xbc\x01', -1.0-2.0**-11 - 2.0**-16), # rounds to 1.0+2**(-10)
+            ('>e', b'\xbc\x00', -1.0-2.0**-11), # rounds to 1.0 (nearest even mode)
+            ('>e', b'\xbc\x00', -1.0-2.0**-12), # rounds to 1.0
+            ('>e', b'\xfb\xff', -65519), # rounds to 65504
+        ]
+
+        for formatcode, bits, f in format_bits_float__rounding_list:
+            self.assertEqual(bits, struct.pack(formatcode, f))
+
+        # This overflows, and so raises an error
+        format_bits_float__roundingError_list = [
+            # Values that round to infinity.
+            ('>e', 65520.0),
+            ('>e', 65536.0),
+            ('>e', 1e300),
+            ('>e', -65520.0),
+            ('>e', -65536.0),
+            ('>e', -1e300),
+            ('<e', 65520.0),
+            ('<e', 65536.0),
+            ('<e', 1e300),
+            ('<e', -65520.0),
+            ('<e', -65536.0),
+            ('<e', -1e300),
+        ]
+
+        for formatcode, f in format_bits_float__roundingError_list:
+            self.assertRaises(OverflowError, struct.pack, formatcode, f)
+
+        # Double rounding
+        format_bits_float__doubleRoundingError_list = [
+            ('>e', b'\x67\xff', 0x1ffdffffff * 2**-26), # should be 2047, if double-rounded 64>32>16, becomes 2048
+        ]
+
+        for formatcode, bits, f in format_bits_float__doubleRoundingError_list:
+            self.assertEqual(bits, struct.pack(formatcode, f))
+
 
 if __name__ == '__main__':
     unittest.main()