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
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 polyml at inf.ed.ac.uk http://lists.inf.ed.ac.uk/mailman/listinfo/polyml
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_75...)
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 polyml at inf.ed.ac.uk http://lists.inf.ed.ac.uk/mailman/listinfo/polyml
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_75...)
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 polyml at inf.ed.ac.uk http://lists.inf.ed.ac.uk/mailman/listinfo/polyml
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_75...)
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 polyml at inf.ed.ac.uk http://lists.inf.ed.ac.uk/mailman/listinfo/polyml
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_75...)
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 polyml at inf.ed.ac.uk http://lists.inf.ed.ac.uk/mailman/listinfo/polyml
Harking back to this, I've belatedly noticed that the tagged versions of subVec, subArr, and update all take the supplied index and use it directly in the Word8 array, when they should be multiplying it by bytesPerElem. The double-precision and boxed versions have this right, but as it stands the tagged version is only capable of retrieving or updating the first value in the array correctly.
Multiplying i by bytesPerElem in each case fixes this, i.e. doing something like this in all six of the tagged functions:
fun update(v, i, r) = let val w: word = r32AsWord r + val i = i * bytesPerElem open Word8Array
... but I notice the double/boxed version has some more logic to check the int is within range, so perhaps there is a more appropriate fix.
Chris
Hi Chris, Thanks for pointing this out. I've committed a fix that looks like it works. It would be really helpful to have some tests for structures such as these that could be included in the test suite. Actually, generally more tests would be welcome; most of those that are there are regression tests after bug fixes.
David
On 25/04/2021 11:37, Chris Cannam wrote:
Harking back to this, I've belatedly noticed that the tagged versions of subVec, subArr, and update all take the supplied index and use it directly in the Word8 array, when they should be multiplying it by bytesPerElem. The double-precision and boxed versions have this right, but as it stands the tagged version is only capable of retrieving or updating the first value in the array correctly.
Multiplying i by bytesPerElem in each case fixes this, i.e. doing something like this in all six of the tagged functions:
fun update(v, i, r) = let val w: word = r32AsWord r
val i = i * bytesPerElem open Word8Array... but I notice the double/boxed version has some more logic to check the int is within range, so perhaps there is a more appropriate fix.
Chris _______________________________________________ polyml mailing list polyml at inf.ed.ac.uk http://lists.inf.ed.ac.uk/mailman/listinfo/polyml
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