No problem, glad to be helpful - especially since I'm the one who asked for the feature!
I also have the habit of viewing floating point as black magic, especially because of historical issues such as x87 intermediate precision and weird things like denormal numbers. So it's quite satisfying to go through a few test cases, figure out what the proper representation should be, and see that in this situation it's not in fact all that complicated. Thank you for implementing this and putting it to rights. Chris On Mon, 22 Feb 2021, at 07:31, David Matthews wrote: > Thank you for looking at this. You're quite right that the shifts were > wrong. I've pushed a fix for this that seems to have corrected it. I'm > not that familiar with the intricacies of floating point numbers so I'm > always glad when someone points out problems. > > David > > On 21/02/2021 13:50, Chris Cannam wrote: > > 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 > >>>> _______________________________________________ > >>>> polyml mailing list > >>>> [email protected] > >>>> http://lists.inf.ed.ac.uk/mailman/listinfo/polyml > >>>> > >>> > _______________________________________________ polyml mailing list [email protected] http://lists.inf.ed.ac.uk/mailman/listinfo/polyml
