SF bug 705836: struct.pack of floats in non-native endian order

pack_float, pack_double, save_float:  All the routines for creating
IEEE-format packed representations of floats and doubles simply ignored
that rounding can (in rare cases) propagate out of a long string of
1 bits.  At worst, the end-off carry can (by mistake) interfere with
the exponent value, and then unpacking yields a result wrong by a factor
of 2.  In less severe cases, it can end up losing more low-order bits
than intended, or fail to catch overflow *caused* by rounding.

Bugfix candidate, but I already backported this to 2.2.

In 2.3, this code remains in severe need of refactoring.

Lib/test/test_struct.py

@@ -390,3 +390,49 @@ def test_p_code():
                              (code, input, got, expectedback))
 
 test_p_code()
+
+
+###########################################################################
+# 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.
+
+def test_705836():
+    import math
+
+    for base in range(1, 33):
+        # smaller <- largest representable float less than base.
+        delta = 0.5
+        while base - delta / 2.0 != base:
+            delta /= 2.0
+        smaller = base - delta
+        # Packing this rounds away a solid string of trailing 1 bits.
+        packed = struct.pack("<f", smaller)
+        unpacked = struct.unpack("<f", packed)[0]
+        # This failed at base = 2, 4, and 32, with unpacked = 1, 2, and
+        # 16, respectively.
+        verify(base == unpacked)
+        bigpacked = struct.pack(">f", smaller)
+        verify(bigpacked == string_reverse(packed),
+               ">f pack should be byte-reversal of <f pack")
+        unpacked = struct.unpack(">f", bigpacked)[0]
+        verify(base == unpacked)
+
+    # Largest finite IEEE single.
+    big = (1 << 24) - 1
+    big = math.ldexp(big, 127 - 23)
+    packed = struct.pack(">f", big)
+    unpacked = struct.unpack(">f", packed)[0]
+    verify(big == unpacked)
+
+    # The same, but tack on a 1 bit so it rounds up to infinity.
+    big = (1 << 25) - 1
+    big = math.ldexp(big, 127 - 24)
+    try:
+        packed = struct.pack(">f", big)
+    except OverflowError:
+        pass
+    else:
+        TestFailed("expected OverflowError")
+
+test_705836()