struct.unpack(struct.pack(float)) has roundoff err

Question

When testing my library, Construct, I found out that tests fail when numbers are built then parsed back to a float. Should floats not be represented exactly as in-memory floats?

In [14]: d = struct.Struct("<f")

In [15]: d.unpack(d.pack(1.23))
Out[15]: (1.2300000190734863,)

Answer 1

Floating point is inherently imprecise, but you are packing a double-precision float (binary64) into a single-precision (binary32) space there. See Basic and interchange formats in the Wikipedia article on IEEE floating point formats; the Python float format uses double precision (see the standard types docs; Floating point numbers are usually implemented using double in C).

Use d to use double precision:

>>> import struct
>>> d = struct.Struct("<d")
>>> d.unpack(d.pack(1.23))
(1.23,)

From the Format characters section:

format: f, C Type: float, Python type: float, Standard size: 4, Footnote: (5)
format: d, C Type: double, Python type: float, Standard size: 8, Footnote: (5)

5. For the 'f' and 'd' conversion codes, the packed representation uses the IEEE 754 binary32 (for 'f') or binary64 (for 'd') format, regardless of the floating-point format used by the platform.