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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">that’s clearer now. after taking some time to refresh on IEEE I was confusing how you would think of a floating point with how it is actually encoded. that
link shows how it is stored in 64 bits and clearly it is not two int types, however the essence is that two integral numbers are used to determine the float value.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> delphi-bounces@listserver.123.net.nz [mailto:delphi-bounces@listserver.123.net.nz]
<b>On Behalf Of </b>Jolyon Smith<br>
<b>Sent:</b> Monday, 18 August 2014 11:26 a.m.<br>
<b>To:</b> NZ Borland Developers Group - Delphi List<br>
<b>Subject:</b> Re: [DUG] Int64 or floating point faster?<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal">That would be odd since the IEEE single and double types were introduced in TP 5.0 and use of these was always dependent on having a math co-pro.<br>
<br>
Perhaps it was the "real" type ? I'm not sure how that was implemented 'under the hood' back in the day (although these days it's just a synonym for Double) although with a range of 1E-32 to 1E+38, an int32.int32 pair wouldn't have worked (and iirc it was
a 48-bit type anyway, hence it lives [lived?] on as Real48 for people who really need/want it).<br>
<br>
I am interested to find out more about this elusive type as I'd be curious to see how it was implemented (I find this sort of thing fascinating). :)<o:p></o:p></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><o:p> </o:p></p>
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<p class="MsoNormal">On 18 August 2014 10:50, Pieter De Wit <<a href="mailto:pieter@insync.za.net" target="_blank">pieter@insync.za.net</a>> wrote:<o:p></o:p></p>
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<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Hey Jolyon,<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> <o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">I was also under the impression it was a double int. I am damn sure it was documented like this for Pascal 5.5. Even if I can find it now, it doesn't matter since I think we have proved that
Delphi uses the IEEE std :)<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> <o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Cheers,<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif";color:#888888"> <o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif";color:#888888">Pieter<o:p></o:p></span></p>
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<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> <o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">On 18/08/2014 08:47, Jolyon Smith wrote:<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">@Cameron, you appear to be confused.<br>
<br>
Yes, Delphi uses a standard implementation of single and double types - the IEEE standards. But I don't know where you got the idea that this standard involves a naive pairing of two ints (of any size). Floating point types are
<strong><span style="font-family:"Verdana","sans-serif"">far</span></strong> more complex than that. e.g. the internal representation of the value "1" in Double is not (0x00000001).(0x00000000) but (0x3fff0000).(0x00000000)<br>
<br>
How would I describe it otherwise ? Why, the same way that IEEE 754 describes it of course. ;)<br>
<br>
<a href="http://en.wikipedia.org/wiki/Double-precision_floating-point_format" target="_blank">http://en.wikipedia.org/wiki/Double-precision_floating-point_format</a><br>
<br>
Single is similarly not a naive pairing of two int16's. In fact, the closest I can even think that Delphi has to such a limited implementation for decimal values is the Curreny type, but even that isn't a "pair of integers", rather a straightforward "fixed
point" with a scalar of 10,000, yielding 4 fixed decimal places.<br>
<br>
<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">Back to the OP...<br>
<br>
If you are using Delphi 7 and were thinking of using Single precision, then I strongly recommend that you do some tests with some representative sample data to establish the most efficient approach, but as a rule of thumb I would expect to find that Single
precision would be more efficient than Double (and in the older.Win32 compilers I wouldn't be surprised if these had an even greater performance advantage over Int64). The question then is whether Single precision is adequate for your needs or if you need
the additional capacity of Double.<br>
<br>
If you are inclined toward Int64 for some reason, be aware that there was a bug in the Delphi Int64 arithmetic in older Delphi versions. The 32-bit compiler doesn't use hardware op-codes for Int64 operations but emulates these in software, which is why Int64
performs less well than Double:<br>
<br>
I'm fairly sure this is the case even today (hence the comparative performance of Double and Int64 even in the XE4 32-bit compiler), but absolutely certain that it is the case with the older Delphi compilers.<br>
<br>
The details of the bug escape my memory right now, other than that it was a basic arithmetic error in the compiler emitted code (and something of an edge case), rather than a bug in an RTL function. i.e. not something that can be easily avoided.<br>
<br>
But I am sure your tests will show that Single or Double are more efficient anyway.<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif"">On 17 August 2014 20:09, Cameron Hart <<a href="mailto:Cameron.Hart@flowsoftware.co.nz" target="_blank">Cameron.Hart@flowsoftware.co.nz</a>> wrote:<o:p></o:p></span></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">I'm confused now as I'm pretty sure Delphi uses a standard format to represent float (the same format
used anywhere else for that matter). In which case a float is essentially two int32 (or other int's depending on the scale of the float). Ie a single used two int16.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">One int represented the mantissa the other the exponent (in essence the decimal portion). Together
they resulted in the floating point value.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">How would you describe this otherwise?</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"> </span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><strong><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></strong><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">
<a href="mailto:delphi-bounces@listserver.123.net.nz" target="_blank">delphi-bounces@listserver.123.net.nz</a> [mailto:<a href="mailto:delphi-bounces@listserver.123.net.nz" target="_blank">delphi-bounces@listserver.123.net.nz</a>]
<strong><span style="font-family:"Tahoma","sans-serif"">On Behalf Of </span></strong>Jolyon Smith<br>
<strong><span style="font-family:"Tahoma","sans-serif"">Sent:</span></strong> Sunday, 17 August 2014 12:54 p.m.</span><o:p></o:p></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""><br>
<strong><span style="font-family:"Verdana","sans-serif"">To:</span></strong> NZ Borland Developers Group - Delphi List<br>
<strong><span style="font-family:"Verdana","sans-serif"">Subject:</span></strong> Re: [DUG] Int64 or floating point faster?<o:p></o:p></span></p>
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<p><span style="font-size:10.0pt;font-family:"Verdana","sans-serif""> <o:p></o:p></span></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">That's curious. Who are "they" ? It doesn't sound like any floating point implementation I ever came across in Delphi (or anywhere else, for that matter). O.o<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">On 17 August 2014 12:28, Pieter De Wit <<a href="mailto:pieter@insync.za.net" target="_blank">pieter@insync.za.net</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">Hi Jolyon,<br>
<br>
>From memory, they used 2 int32's to make a float - this could have been int16's - memory is very vague on this :) The one was used to represent the whole numbers and the other was to show the decimal numbers<br>
<br>
Cheers,<br>
<br>
Pieter<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><br>
<br>
On 17/08/2014 12:05, Jolyon Smith wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">@Pieter - I don't understand what you mean when you say that "float was int32.int32". For starters, "float" is an imprecise term. If you mean "single" then the entire value was
always 32 bit in it's entirety. If you mean double then it was always 64 bit. What is this "in32.int32" type of which you speak ? O.o<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">On 17 August 2014 11:52, Jolyon Smith <<a href="mailto:jsmith@deltics.co.nz" target="_blank">jsmith@deltics.co.nz</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">I think there are too many variables involved to give an answer to this question without some of those variables being reduced to known values.<br>
<br>
e.g. what hardware ? what version of Delphi ? x64 target or x86 ? what precision of floating point ?<br>
<br>
Having said that, in a quick test knocked up in my Smoketest framework I found that Double comfortably outperforms Int64 when compiling for Win32 but that both Double and Int64 demonstrated improved performance when compiling for Win64 and that whilst Double
still showed some advantage it was not as significant (and in some test runs the difference was negligible).<br>
<br>
If you are targeting FireMonkey you will have to bear in mind that the back-end compiler is different to the x86/x64 backend, so results obtained using the WinXX compilers will not necessarily be indicative of performance on the ARM or LLVM platforms.
<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><br>
<br>
Conditions: <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><br>
- Delphi XE4<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> - Running in a 64-bit Win 7 VM<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> - No testing was done for correctness of the results.<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;margin-bottom:12.0pt"> <o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto">On 16 August 2014 15:30, Ross Levis <<a href="mailto:ross@stationplaylist.com" target="_blank">ross@stationplaylist.com</a>> wrote:<o:p></o:p></p>
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<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D">Would I be correct that int64 multiplications would be faster than floating point in Delphi? My app needs to do several million.</span><o:p></o:p></p>
<p class="MsoNormal" style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto"><span style="color:#1F497D"> </span><o:p></o:p></p>
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