So as a concrete example, consider a signal that changes from the value
(3/5.) to the value (1000/3.).
The "exact" double-precision floating-point values formatted as decimals
with 17 digits of precision are:
5.99999999999999978e-01 # 3/5 = .600...
3.33333333333333314e+02 # 1000/3 = 333.3...
The "exact" single-precision floating-point values formatted as decimals
with 7 digits of precision are:
6.0000002e-01
3.3333334e+02
And the values that could arise from a read which gets a half-modified
value are:
6.00000063578287723e-01
3.33333300781249989e+02
Here, I arrange them next to the single-precision values for eyeball
comparison:
6.00000063578287723e-01
6.0000002e-01
3.33333300781249989e+02
3.3333334e+02
.. only the digit that corresponds to the least significant digit in
single-precision floating point differs.
And that's why doing nothing is probably best, even if it's got
theoretical problems.
Jeff
PS Here's Python code for word-swapping a pair of doubles, and for
forcing a Python floating-point value to 'float' precision:
import struct
def mix(v1, v2):
s = struct.pack("2d", v1, v2)
v1h, v1l, v2h, v2l = struct.unpack("4I", s)
t = struct.pack("4I", v1h, v2l, v2h, v1l)
return struct.unpack("2d", t)
def force_float(v):
return struct.unpack("f", struct.pack("f", v))[0]
PPS It occurred to me to wonder what becomes of special values like inf and
nan, even though we never intend to store them on hal pins:
>>> mix(inf, nan)
(nan, inf)
>>> mix(inf, 3.14)
(3.1399993896484375, nan)
>>> mix(nan, 3.14)
(3.1399993896484375, nan)
so it's interesting to note that an inf can get turned into a nan when this
problem bites.
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