[swift-dev] Why are BinaryFloatingPoint's RawSignificand and RawExponent different type?
Jens Persson
jens at bitcycle.com
Fri Aug 26 19:31:05 CDT 2016
Ok, I've learned a lot, thanks!
/Jens
On Sat, Aug 27, 2016 at 2:26 AM, Stephen Canon <scanon at apple.com> wrote:
> For any given concrete type, it’s pretty straightforward to map [0, .max]
> to [0,1) — note that this is a bit different from what you seem to have
> been doing originally, mapping e.g. [0, 2**52) to [0, 1):
>
> init(unitRange s: UInt64) {
> self = Self(s >> UInt64(63 - Self.significandBitCount)) * .
> ulpOfOne/2
> }
>
> Making this generic over integer types is painful without the SE-0104
> integer protocols, however.
>
> – Steve
>
>
> On Aug 26, 2016, at 8:13 PM, Jens Persson <jens at bitcycle.com> wrote:
>
> Ah, right! Thanks again.
> How would you make all integer type (UIntN, IntN) convertible/mappable
> from their respective [.min, .max] range to Double/Float unit range [0, 1)?
> /Jens
>
> On Sat, Aug 27, 2016 at 2:06 AM, Stephen Canon <scanon at apple.com> wrote:
>
>> Note that with the bug fixed, the result will still not be 1.nextDown,
>> because the size of an ulp changes at 1; the values you produce will be
>> space .ulpOfOne apart, but 1.nextDown is 1 - ulpOfOne/2.
>>
>> – Steve
>>
>> On Aug 26, 2016, at 8:00 PM, Jens Persson <jens at bitcycle.com> wrote:
>>
>> Thanks, but there seem to be something not working the same as in my
>> original code, here is a quick test of your code:
>>
>> protocol BinaryFloatingPointWithBitPattern: BinaryFloatingPoint {
>> init(bitPattern: RawSignificand)
>> var bitPattern: RawSignificand { get }
>> }
>>
>> extension Float: BinaryFloatingPointWithBitPattern { }
>> extension Double: BinaryFloatingPointWithBitPattern { }
>>
>> extension BinaryFloatingPointWithBitPattern {
>> init(unitRangeFromRawSignificand s: RawSignificand) {
>> self = Self(bitPattern: Self(1).bitPattern | s) - 1
>> }
>> }
>>
>> typealias T = Double
>> // typealias T = Float
>>
>> let allSignificantBitsSet = T.RawSignificand((1 << T.significandBitCount)
>> - 1)
>> print("bits set in signigicant:", String(allSignificantBitsSet, radix:
>> 2).characters.count) // 52
>> let a = T.init(bitPattern: 0)
>> let b = T.init(bitPattern: allSignificantBitsSet)
>> print(a) // 0.0, correct.
>> print(b) // 2.2250738585072e-308. Wrong, this should be (1.0).nextDown.
>>
>>
>> On Sat, Aug 27, 2016 at 1:57 AM, Stephen Canon <scanon at apple.com> wrote:
>>
>>> If BinaryFloatingPoint had init(_: RawSignificand), you could also just
>>> write:
>>>
>>> extension BinaryFloatingPoint {
>>> init(unitRangeFromRawSignificand s: RawSignificand) {
>>> self = Self(s) * .ulpOfOne
>>> }
>>> }
>>>
>>> (this is why I ask if RawSignificand is really the type you want; if you
>>> use some concrete integer type this will work). But once we have all the
>>> new integer protocol conformances, we’ll have a generic init from any
>>> integer type (this was already reviewed for FloatingPoint, but isn’t
>>> implementable without the Integer support), which will also make this
>>> possible.
>>>
>>> On Aug 26, 2016, at 7:47 PM, Stephen Canon via swift-dev <
>>> swift-dev at swift.org> wrote:
>>>
>>> Assuming RawSignificand really is the type you want, I think this does
>>> what you’re looking for?
>>>
>>> protocol BinaryFloatingPointWithBitPattern: BinaryFloatingPoint {
>>> init(bitPattern: RawSignificand)
>>> var bitPattern: RawSignificand { get }
>>> }
>>>
>>> extension Float: BinaryFloatingPointWithBitPattern { }
>>> extension Double: BinaryFloatingPointWithBitPattern { }
>>>
>>> extension BinaryFloatingPointWithBitPattern {
>>> init(unitRangeFromRawSignificand s: RawSignificand) {
>>> self = Self(bitPattern: Self(1).bitPattern | s) - 1
>>> }
>>> }
>>>
>>> On Aug 26, 2016, at 7:38 PM, Stephen Canon via swift-dev <
>>> swift-dev at swift.org> wrote:
>>>
>>> Where does your RawSignificand input come from? Is that really the type
>>> that you want?
>>>
>>> I don’t think you really need very much boilerplate at all here.
>>>
>>> On Aug 26, 2016, at 7:30 PM, Jens Persson <jens at bitcycle.com> wrote:
>>>
>>> I understand.
>>> It's just very tempting to try and use the new static computed
>>> properties for eg 23 and 52 etc.
>>> I guess I'll just have to write a lot of boilerplate, or perhaps a
>>> protocol that is just implemented by Double and Float (that will be very
>>> similar to BinaryFloatingPoint in a lot of ways).
>>> /Jens
>>>
>>> On Sat, Aug 27, 2016 at 1:25 AM, Stephen Canon <scanon at apple.com> wrote:
>>> This doesn’t really scale up very well, though. BinaryFloatingPoint
>>> needs to also be able to model e.g. Float2048 or similar; we generally
>>> don't want to require that RawExponent to be the same type as
>>> RawSignificand (which I think is what you’re really suggesting), because in
>>> typical bignum usage significands are much larger than exponents.
>>>
>>> It sounds like maybe you actually want to be operating directly on
>>> bitPatterns, rather than the abstract fields of the types.
>>>
>>> – Steve
>>>
>>> On Aug 26, 2016, at 7:21 PM, Jens Persson <jens at bitcycle.com> wrote:
>>>
>>> Oh, to more directly answer your question: I don't like having to create
>>> a UInt (UInt64) value when all my bit manipulaton code happens in UInt32
>>> (for Float) for example.
>>>
>>> The most probable context for using these computed properties and types
>>> of BinaryFloatingPoint is one in which specific fixed width types really
>>> matters a lot (look at the name of the protocol and the properties and
>>> assocated types we are talking about).
>>>
>>> /Jens
>>>
>>>
>>> On Sat, Aug 27, 2016 at 1:15 AM, Jens Persson <jens at bitcycle.com> wrote:
>>> Reason for asking is that I have this:
>>>
>>> extension Double {
>>> init(unitRangeFromRawSignificand s: RawSignificand) {
>>> let bitPattern = s | (1023 << 52)
>>> self = unsafeBitCast(bitPattern, to: Double.self) - 1.0
>>> }
>>> }
>>> extension Float {
>>> init(unitRangeFromRawSignificand s: RawSignificand) {
>>> let bitPattern = s | (127 << 23)
>>> self = unsafeBitCast(bitPattern, to: Float.self) - 1.0
>>> }
>>> }
>>>
>>> But they would be better as:
>>> extension BinaryFloatingPoint {
>>> init(unitRangeFromRawSignificand s: RawSignificand) {
>>> ... problems here, have to try casting things into
>>> RawSignificand's type ...
>>> }
>>> }
>>>
>>> Please have a go at that and perhaps you see what I mean or you will
>>> come up with a nice solution that I have missed. (Speed is very important
>>> btw.)
>>>
>>> /Jens
>>>
>>>
>>> On Sat, Aug 27, 2016 at 1:02 AM, Stephen Canon <scanon at apple.com> wrote:
>>> > On Aug 26, 2016, at 6:06 PM, Jens Persson via swift-dev <
>>> swift-dev at swift.org> wrote:
>>> >
>>> > I can understand why
>>> > Double.RawSignificand is UInt64
>>> > and
>>> > Float.RawSignificand is UInt32
>>> >
>>> > But I can't understand why both
>>> > Double.RawExponent
>>> > and
>>> > Float.RawExponent
>>> > should be UInt.
>>> >
>>> > Why aren't they also just UInt64 and UInt32, resp.?
>>>
>>> Let me flip the question: why would they be UInt64 and UInt32? Absent a
>>> reason to prefer a specific fixed-with type, Swift integers should
>>> generally default to being [U]Int (and ideally Int, but RawExponent
>>> is Unsigned).
>>>
>>> – Steve
>>>
>>>
>>>
>>>
>>>
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>>>
>>
>>
>
>
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