[swift-dev] Why are BinaryFloatingPoint's RawSignificand and RawExponent different type?
Jens Persson
jens at bitcycle.com
Fri Aug 26 19:13:45 CDT 2016
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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