I took another little look at the behaviour here.
My basic assumption is that, for any Real32.real r,
Real32.== (PackReal32Big.fromBytes (PackReal32Big.toBytes r), r)
should hold. (and the same for Little obviously)
With the current repo code, it's possible to construct values for which this is not true
- if you apply fromBytes to something with the lowest-order bit set, and then take
Real32.nextAfter, you get a value that "should" have one more bit set than is
preserved through this transformation. The value 1.000060916 is an example:
val r : Real32.real = 1.000060916;
val r = 1.000060916: Real32.real
PackReal32Big.toBytes r;
val it = fromList[0wx1F, 0wxC0, 0wx0, 0wxFF]: Word8Vector.vector
PackReal32Big.fromBytes (PackReal32Big.toBytes r);
val it = 1.000060797: PackReal32Big.real
Real32.== (PackReal32Big.fromBytes (PackReal32Big.toBytes r), r);
val it = false: bool
Note the result has been rounded down by 2^-23, which makes sense since the
IEEE 754 fraction part is 23 bits.
I experimentally went into PackReal32Tagged, subtracted 1 from all the shift
constants (the 56, 48, 40, 32), and rebuilt. With this change:
val r : Real32.real = 1.000060916;
val r = 1.000060916: Real32.real
PackReal32Big.toBytes r;
val it = fromList[0wx3F, 0wx80, 0wx1, 0wxFF]: Word8Vector.vector
Real32.== (PackReal32Big.fromBytes (PackReal32Big.toBytes r), r);
val it = true: bool
Also now
PackReal32Big.toBytes 1.0;
val it = fromList[0wx3F, 0wx80, 0wx0, 0wx0]: Word8Vector.vector
which is the expected result I mentioned in the previous email.
I'm imagining all this has something to do with the tag bit, but I don't really
know.
Chris
On Sun, 7 Feb 2021, at 18:06, Chris Cannam wrote:
Oh, thank you!
I had thought that the difference between x87 and SSE, and the
different internal precisions, mattered only for intermediate register
values during calculation - and that when a 32-bit float was "at rest",
i.e. being stored in 32 bits, it would always have IEEE 754
representation (as described e.g. at
https://en.wikipedia.org/wiki/Single-precision_floating-point_format#IEEE_754_single-precision_binary_floating-point_format:_binary32)
Is this not right? Do I have the wrong mental model here?
The current behaviour does indeed seem a bit off (Poly/ML rev
62a56474f0, 64-bit Linux).
If I take, say, 1.0 and convert it to bytes big-endian, I think I expect to see
sign bit: 0
exponent (8 bits): 127 (exponent is 0, stored unsigned with an offset of 127)
fraction (23 bits): 0 (as the 1 in 1.0 x 2^0 is implicit)
so 0111 1111 1000 0000 0000 0000 0000 0000 or 3F 80 00 00
and that's what PackReal32Big.toBytes 1.0 returns in MLton. In Poly/ML
I'm getting this
PackReal32Big.toBytes 1.0;
val it = fromList[0wx1F, 0wxC0, 0wx0, 0wx0]: Word8Vector.vector
1F C0 00 00 is the same bit pattern as 3F 80 00 00, but shifted right
by one bit, and no longer a normal IEEE 754 number I think. Is it
possible there's an off-by-one error in the bit lookup, or is this all
a symptom of my having the wrong idea about what's going on?
Thanks,
Chris
On Sat, 6 Feb 2021, at 16:24, David Matthews wrote:
I've added this to master. It seemed like a good idea although it was a
bit more complicated than PackReal because Real32.real values are
"boxed" in 32-bit Poly/ML but tagged in 64-bit.
I'm not exactly clear how useful PackRealN operations are for general
data interchange. Currently they just store and load the bytes that
make up the number but how those are interpreted will depend on the
platform. For example it seems that the X87 format used on X86/32 is
different from the SSE format used on X86/64.
David
On 02/02/2021 09:25, Chris Cannam wrote:
Hello! I find I could do with the PackReal32{Big,Little} structures, 32-bit
floats being often more amenable to serialisation and used in some storage
formats.
Would there be any appetite for adding these?
Thanks,
Chris
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