Posts in category c++

A fast RGB to HSV floating point conversion

The operations typically performed to convert from RGB to HSV are the following:

  • find the largest RGB component
  • find the smallest RGB component
  • compute V and S
  • select the main circular sector for H
  • compute H

Here is, to my knowledge, the most commonly used RGB to HSV routine for floating point, with an extra minor optimisation (adding 1e-20f to divisors to avoid the need to care about divisions by zero):

static void RGB2HSV(float r, float g, float b,
                    float &h, float &s, float &v)
{
    float rgb_max = std::max(r, std::max(g, b));
    float rgb_min = std::min(r, std::min(g, b));
    float delta = rgb_max - rgb_min;
    s = delta / (rgb_max + 1e-20f);
    v = rgb_max;

    float hue;
    if (r == rgb_max)
        hue = (g - b) / (delta + 1e-20f);
    else if (g == rgb_max)
        hue = 2 + (b - r) / (delta + 1e-20f);
    else
        hue = 4 + (r - g) / (delta + 1e-20f);
    if (hue < 0)
        hue += 6.f;
    h = hue * (1.f / 6.f);
}

Several things seem worth noticing already:

  • Most of the complexity comes from the hue calculation.
  • Four min/max operations are performed to find rgb_max and rgb_min; however, sorting three values can be done with only 3 comparisons. This is not necessarily problematic because min/max could be wired in an efficient way depending on the CPU.
  • Two additional tests are performed to compare r and g to rgb_max; if rgb_max and rgb_min were computed using tests, this is a waste of time to compare them again.
  • Adding 6.f to the final hue value only has a 16.6% chance of happening.

The actual hue calculation depends on how r, g, and b are ordered:

$\operatorname{Hue_{0\dots 6}}(r,g,b)=\begin{cases}
    (g - b) / (r - b), & \text{if $r \ge g \ge b$}.\\
    6 + (g - b) / (r - g), & \text{if $r \ge b \ge g$}.\\
    2 + (b - r) / (g - r), & \text{if $g \ge b \ge r$}.\\
    2 + (b - r) / (g - b), & \text{if $g \ge r \ge b$}.\\
    4 + (r - g) / (b - g), & \text{if $b \ge r \ge g$}.\\
    4 + (r - g) / (b - r), & \text{if $b \ge g \ge r$}.\\
  \end{cases}$

But let’s rewrite this in terms of x, y and z, where x is the largest of (r,g,b), z is the smallest of the three, and y is inbetween:

$\operatorname{Hue_{0\dots 6}}(R,G,B)=\begin{cases}
    (y - z) / (x - z), & \text{if $r \ge g \ge b$}.\\
    6 + (z - y) / (x - z), & \text{if $r \ge b \ge g$}.\\
    2 + (y - z) / (x - z), & \text{if $g \ge b \ge r$}.\\
    2 + (z - y) / (x - z), & \text{if $g \ge r \ge b$}.\\
    4 + (y - z) / (x - z), & \text{if $b \ge r \ge g$}.\\
    4 + (z - y) / (x - z), & \text{if $b \ge b \ge r$}.\\
  \end{cases}$

There are a lot of similarities here. We can push it even further, using the fact that x ≥ z and y ≥ z by definition:

$\operatorname{Hue_{0\dots 6}}(R,G,B)=\left|K + \dfrac{y - z}{x - z}\right|,
 \text{with $K =\begin{cases}
    0, & \text{if $r \ge g \ge b$}.\\
    -6, & \text{if $r \ge b \ge g$}.\\
    2, & \text{if $g \ge b \ge r$}.\\
    -2, & \text{if $g \ge r \ge b$}.\\
    4, & \text{if $b \ge r \ge g$}.\\
    -4, & \text{if $b \ge b \ge r$}.\\
  \end{cases}$}$

That’s actually the same calculation! Only the hue offset K changes. The idea now is the following:

  • Sort the triplet (r,g,b) using comparisons
  • Build K while sorting the triplet
  • Perform the final calculation

Putting the idea into practice gives us the following code:

static void RGB2HSV(float r, float g, float b,
                    float &h, float &s, float &v)
{
    float K = 0.f;

    if (g < b)
    {
        float tmp = g; g = b; b = tmp;
        K = -1.f;
    }

    if (r < g)
    {
        float tmp = r; r = g; g = tmp;
        K = -2.f / 6.f - K;
    }

    if (g < b)
    {
        float tmp = g; g = b; b = tmp;
        K = -K;
    }

    float chroma = r - b;
    h = fabs(K + (g - b) / (6.f * chroma + 1e-20f));
    s = chroma / (r + 1e-20f);
    v = r;
}

You can check for yourself that the values for K explicited above are properly generated by that function. There were many other ways to sort (r,g,b) but this specific one lets us do one final optimisation.

We notice that the last swap effectively changes the sign of K and the sign of g - b. Since both are then added and passed to fabs(), the sign reversal can actually be omitted.

That additional trickery gives us this final code:

static void RGB2HSV(float r, float g, float b,
                    float &h, float &s, float &v)
{
    float K = 0.f;

    if (g < b)
    {
        std::swap(g, b);
        K = -1.f;
    }

    if (r < g)
    {
        std::swap(r, g);
        K = -2.f / 6.f - K;
    }

    float chroma = r - std::min(g, b);
    h = fabs(K + (g - b) / (6.f * chroma + 1e-20f));
    s = chroma / (r + 1e-20f);
    v = r;
}

That’s 2 tests and 1 std::min call instead of the previous 3 tests and 4 std::min/max calls. We really should see some kind of performance gain here.

And as expected, benchmarks indicate a performance increase of 25 to 40 % with a great variety of CPUs, compilers and compiler flags. The following graph (average nanoseconds per conversion) is on a Core i7-2600K CPU, using g++ 4.7.2 with -O3 -ffast-math:

  • Posted: 2013-01-13 06:19 (Updated: 2013-02-11 13:48)
  • Author: sam
  • Categories: optim c++
  • Comments (44)

Fuck you, Microsoft: the sorry state of Visual Studio syntax highlighting

TL;DR: you can’t even choose a different colour for “return” and “float” in Visual Studio.

I mostly use Vim as my everyday editor. This is not the place to go through the details of why, but basically it does exactly what I want. One thing Vim does well for me is syntax highlighting. Here is a bit of Lol Engine C++ using Vim’s default colour scheme:

The colour scheme is simple here:

  • yellow for control flow
  • green for types and qualifiers
  • magenta for constants
  • light grey for everything else

You may notice that the vec3 or quat types, which are not C++ base types but which behave exactly as if, are coloured just like float. This is simply done by adding the following line to my main config file or to a separate configuration file:

au Syntax cpp syn keyword cType vec2 vec3 vec4 quat

Okay now I would like you to read that again.

  • yellow for control flow
  • green for types (including custom types) and qualifiers
  • I get all that shit by adding one single configuration line

And I am going to show you the pain it is to do the same in Visual Studio.

First Visual Studio attempt: usertype.dat

Since at least Visual Studio 2003, the usertype.dat file can be used to add a list of user types. This is still true in Visual Studio 2010. So let’s add those new types to usertype.dat:

vec2
vec3
vec4
quat

Not quite there.

M_PI is not coloured, and if I add it to the list it becomes green instead of magenta, but let’s forget about it for now.

float and const are still yellow and there is no way to fix that! Of course I thought about adding them to the list of user types, but the scanner decides that they’re C++ keywords way before it checks for user types.

Second Visual Studio attempt: a Language Service add-in

Visual Studio add-ins are very powerful. Almost any part of the editor can be modified and augmented. There are hundreds of add-ins available and you can write your own.

This looks promising: you can write your own language handler, but you can certainly modify an existing one quite easily (or so I thought).

To handle a new language, you need to subclass the LanguageService class and you register that new class in Visual Studio. One of the methods you need to implement in the language service is GetScanner:

class MyLanguageService : LanguageService
{
    [...]

    public override IScanner GetScanner(IVsTextLines buffer)
    {
        return new MyScanner(buffer);
    }
}

And the IScanner interface has a ScanTokenAndProvideInfoAboutIt method that is responsible for choosing the colour of tokens:

class MyScanner : IScanner
{
    [...]

    bool IScanner.ScanTokenAndProvideInfoAboutIt(TokenInfo tokeninfo, ref int state)
    {
        [...]

        if (FoundKeyword)
        {
            tokeninfo.Color = TokenColor.Keyword;
            return true;
        }

        [...]
    }
}

This is brilliant. I mean, with such an architecture, you can implement your own sublanguage, add colour schemes, modify whatever you want. Honestly, this is perfect for my needs.

So here is the plan:

  1. find the LanguageService class responsible for parsing C++
  2. inherit from it and reimplement GetScanner() to use our own IScanner
  3. in our version of ScanTokenAndProvideInfoAboutIt, just call the C++ scanner’s version of ScanTokenAndProvideInfoAboutIt and inspect tokeninfo
  4. if the token info says this is a keyword, match that keyword with our list of types, and change its colour if necessary
  5. register our new language service with a higher priority

This sounds pretty simple and elegant. It’s some kind of two-level proxy pattern.

Except it has absolutely no chance to work. Because there is no language service class for C++.

That’s right. Visual Studio does not use its own advertised architecture to handle the C++ language. If you want to slightly change the behaviour of the C++ language service, you need to fully reimplement it. And by fully reimplement, that means fully, even the completion stuff for IntelliSense.

Third Visual Studio attempt: a Classifier add-in

A classifier add-in differs from a regular language add-in in that it only affects the text that is being displayed. It has no knowledge of the language syntax or structure or what the underlying parser has analysed, but it does know about what the underlying classifier did. For instance, it doesn't know whether a given chunk of text is a C-style or a C++-style comment, but it does know that it was classified as "comment".

This proved to be the correct thing to use! My Visual Studio colour scheme now looks a lot more like my Vim setup:

There are still limitations, but it's a good start. When another plugin comes in and has higher priority, it undoes everything my add-in did, which is arguably the fault of those other plugins, but I believe the lack of a properly pluggable architecture is definitely the issue.

Further thoughts

I know this is a rant, but I will nonetheless add my own constructive information here, as well as anything readers may wish to contribute.

There are other paths I have not explored yet:

  • disassemble the Visual Studio DLLs

I am pretty sure people will suggest that I use VAX (Visual Assist X). I am already using it. I am even a paying customer. In fact I asked for that feature more than three years ago and was more or less ignored (the only answer I got was about a minor point where the person thought I was wrong — I wasn’t). While most of the bugs I reported against VAX were fixed, I have a problem with their stance on accessibility, illustrated by their attitude on this bug. My general feeling is that VAX is a pathetic, slow and annoying piece of crap. The only reason I do not rant more about it is that I know how painful it is to write Visual Studio extensions.

I asked for advice on StackOverflow but since my problem is very specific and probably has no solution, it’s not surprising that I haven’t got any answers yet.

Someone wanted to extend the syntax colouring but was told that apparently “this can't be accomplished with an add-in”, “you may be looking at implementing a full language service to provide this feature” and “Todays language services are currently not architected to be extensible”. One suggestion was to replace a whole COM object using only its CLSID.

Another person wanted to leverage existing language services from within Visual Studio in order to use it for his own language, and was told it was not possible. The workaround mentioned in that thread involves creating a whole new virtual project that would mirror files, hide them, rename them to .c or .h, and analyse the result.

Conclusion

Honestly, the only reasons I still use Visual Studio are:

  • I use it at work
  • a lot of people use it and I need to provide them with a usable environment
  • there’s no other acceptable way to develop for the Xbox 360

But given how it sucks, and has sucked for years, and made my life miserable, and how some of the bugs I have reported back in 1997 are still present, I can only hope that this pathetic piece of crap either becomes opensource (wishful thinking) or just dies and we get something really extensible instead.

The stolen bytes: Visual Studio, virtual methods and data alignment

This article describes a design choice in the C++ ABI of the Visual Studio compiler that I believe should be considered a bug. I propose a trivial workaround at the end.

TL;DR — if the topmost polymorphic class in a hierarchy has members with alignment requirement N where N > sizeof(void *), the Visual Studio compiler may add up to N bytes of useless padding to your objects.

Update: be sure to read the explanation by Jan Gray, who designed the relevant part of the MS C++ ABI some 22 years ago, in the comments section below.

My colleague Benlitz first hit the problem when trying to squeeze memory out of some of our game’s most often instantiated classes. I think it is best illustrated with the following minimal example:

class Foo
{
    virtual void Hello() {}

    float f;     /* 4 bytes */
};
class Bar
{
    virtual void Hello() {}

    float f;     /* 4 bytes */
    double d;    /* 8 bytes */
};

This is the size of Foo and Bar on various 32-bit platforms:

Platform sizeof(Foo) sizeof(Bar) Madness?
Linux x86 (gcc) 8 16 no
Linux ARMv9 (gcc) 8 16 no
Win32 (gcc) 8 16 no
Win32 (Visual Studio 2010) 8 24 yes
Xbox 360 (Visual Studio 2010) 8 24 yes
PlayStation 3 (gcc) 8 16 no
PlayStation 3 (SNC) 8 16 no
Mac OS X x86 (gcc) 8 16 no

There is no trick. This is by design. The Visual Studio compiler is literally stealing 8 bytes from us!

What the fuck is happening?

This is the memory layout of Foo on all observed platforms:

\begin{tabular}{|r|llll|llll|}
\hline
byte & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hline
field & \multicolumn{4}{|c|}{\textit{vfptr}}
      & \multicolumn{4}{|c|}{\texttt{float f;}} \\
\hline
\end{tabular}

The vfptr field is a special pointer to the vtable. The vtable is probably the most widespread compiler-specific way to implement virtual methods. Since all the platforms studied here are 32-bit, this pointer requires 4 bytes. A float requires 4 bytes, too. The total size of the class is therefore 8 bytes.

This is the memory layout of Bar on eg. Linux using GCC:

\begin{tabular}{|r|llll|llll|llllllll|}
\hline
byte & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7
     & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
\hline
field & \multicolumn{4}{|c|}{\textit{vfptr}}
      & \multicolumn{4}{|c|}{\texttt{float f;}}
      & \multicolumn{8}{|c|}{\texttt{double d;}} \\
\hline
\end{tabular}

The double type has an alignment requirement of 8 bytes, which makes it fit perfectly at byte offset 8.

And finally, this is the memory layout of Bar on Win32 using Visual Studio 2010:

\begin{tabular}{|r|llll|llll|llll|llll|llllllll|}
\hline
byte & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7
     & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15
     & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 \\
\hline
field & \multicolumn{4}{|c|}{\textit{vfptr}}
      & \multicolumn{4}{|c|}{\textit{padding}}
      & \multicolumn{4}{|c|}{\texttt{float f;}}
      & \multicolumn{4}{|c|}{\textit{padding}}
      & \multicolumn{8}{|c|}{\texttt{double d;}} \\
\hline
\end{tabular}

This is madness! The requirement for the class to be 8-byte aligned causes the first element of the class to be 8-byte aligned, too! I demand a rational explanation for this design choice.

The problem is that the compiler decides to add the vtable pointer after it has aligned the class data, resulting in excessive realignment.

Compilers affected

The Visual Studio compilers for Win32, x64 and Xbox 360 all appear to create spurious padding in classes.

Though this article focuses on 32-bit platforms for the sake of simplicity, 64-bit Windows is affected, too.

The problem becomes even worse with larger alignment requirements, for instance with SSE3 or AltiVec types that require 16-byte storage alignment such as _FP128:

class Quux
{
    virtual void Hello() {}

    float f;     /* 4 bytes */
    _FP128 dd;   /* 16 bytes */
};

This is the GCC memory layout on both 32-bit and 64-bit platforms:

\begin{tabular}{|r|c|c|c|c|c|c|c|c|}
\hline
byte & 0--3 & 4--7 & 8--11 & 12--15
     & 16--19 & 20--23 & 24--27 & 28--31 \\
\hline
\hline
field (32-bit) & \textit{vfptr}
                & \texttt{float f;}
                & \multicolumn{2}{|c|}{\textit{padding}}
                & \multicolumn{4}{|c|}{\texttt{\_FP128 dd;}} \\
\hline
field (64-bit) & \multicolumn{2}{|c|}{\textit{vfptr}}
               & \texttt{float f;}
               & \textit{padding}
               & \multicolumn{4}{|c|}{\texttt{\_FP128 dd;}} \\
\hline
\end{tabular}

The padding there is perfectly normal and expected, because of the alignment requirements for dd.

But this is how Visual Studio decides to lay it out:

\begin{tabular}{|r|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
byte & 0--3 & 4--7 & 8--11 & 12--15
     & 16--19 & 20--23 & 24--27 & 28--31
     & 32--35 & 36--39 & 40--43 & 44--47 \\
\hline
\hline
field (32-bit) & \textit{vfptr}
               & \multicolumn{3}{|c|}{\textit{padding}}
               & \texttt{float f;}
               & \multicolumn{3}{|c|}{\textit{padding}}
               & \multicolumn{4}{|c|}{\texttt{\_FP128 dd;}} \\
\hline
field (64-bit) & \multicolumn{2}{|c|}{\textit{vfptr}}
               & \multicolumn{2}{|c|}{\textit{padding}}
               & \texttt{float f;}
               & \multicolumn{3}{|c|}{\textit{padding}}
               & \multicolumn{4}{|c|}{\texttt{\_FP128 dd;}} \\
\hline
\end{tabular}

That is 16 lost bytes, both on 32-bit and 64-bit versions of Windows.

Workaround

There is fortunately a workaround if you want to get rid of the useless padding. It is so trivial that it actually makes me angry that the problem exists in the first place.

This will get you your bytes back:

class EmptyBase
{
protected:
    virtual ~EmptyBase() {}
};

class Bar : public EmptyBase
{
    virtual void Hello() {}

    float f;     /* 4 bytes */
    double d;    /* 8 bytes */
};

And this is the size of Bar on the same 32-bit platforms:

Platform sizeof(Bar)
Linux x86 (gcc) 16
Linux ARMv9 (gcc) 16
Win32 (gcc) 16
Win32 (Visual Studio 2010) 16
Xbox 360 (Visual Studio 2010) 16
PlayStation 3 (gcc) 16
PlayStation 3 (SNC) 16
Mac OS X x86 (gcc) 16

Phew. Sanity restored.

\begin{tabular}{|r|cccc|cccc|cccccccc|}
\hline
byte & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7
     & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 \\
\hline
\texttt{EmptyBase} fields & \multicolumn{4}{|c|}{\textit{vfptr}}
                          & \multicolumn{12}{|c|}{} \\
\hline
\texttt{Bar} fields & \multicolumn{4}{c}{\texttt{EmptyBase}}
                    & \multicolumn{4}{|c|}{\texttt{float f;}}
                    & \multicolumn{8}{|c|}{\texttt{double d;}} \\
\hline
\end{tabular}

The compiler is a lot less confused now: it no longer has to create space for a vfptr in Bar since it is technically already part of EmptyBase.

Conclusion

Lessons learned:

  • The pointer to the vtable isn’t just like any other pointer.
  • Various C++ ABIs have different stances on padding and alignment.
  • Inheriting from an empty abstract class can make your objects smaller on Windows and Xbox 360!
  • Design decisions can haunt you for decades!

The workaround is so simple that it sounds like a good idea to always use it, preemptively.

Beyond De Bruijn: fast binary logarithm of a 10-bit number

Recently I needed a method for retrieving the binary logarithm of a 10-bit number (for the curious, it was for the purpose of converting between 32-bit and 16-bit floating point numbers).

Computing the binary logarithm is equivalent to knowing the position of the highest order set bit. For instance, log2(0x1) is 0 and log2(0x100) is 8.

One well known method for fast binary logarithm is presented at Bit Twiddling Hacks. It is a two-step method where first all lower bits are set to 1 and then a De Bruijn-like sequence is used to perform a table lookup:

int fastlog2(uint32_t v)
{
    static const int MultiplyDeBruijnBitPosition[32] = 
    {
        0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30,
        8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31
    };

    v |= v >> 1;
    v |= v >> 2;
    v |= v >> 4;
    v |= v >> 8;
    v |= v >> 16;

    return MultiplyDeBruijnBitPosition[(uint32_t)(v * 0x07C4ACDDU) >> 27];
}

That is 12 integer operations and a table lookup.

Optimising

It should be obvious what the sequence of operations on v does: fill the integer with ones starting from the highest order bit. Here are a few examples of what happens to v at each step:

v v |= v >> 1 v |= v >> 2 v |= v >> 4 v |= v >> 8 v |= v >> 16
0x0001 0x0001 0x0001 0x0001 0x0001 0x0001
0x0002 0x0003 0x0003 0x0003 0x0003 0x0003
0x0003 0x0003 0x0003 0x0003 0x0003 0x0003
0x0004 0x0006 0x0007 0x0007 0x0007 0x0007
0x0100 0x0180 0x01e0 0x01fe 0x01ff 0x01ff
0x80000000 0xc0000000 0xf0000000 0xff000000 0xffff0000 0xffffffff

There is one obvious optimisation available: since the input is only 10-bit, the last shift operation v |= v >> 16 can be omitted because the final value was already reached.

int fastlog2(uint32_t v)
{
    static const int MultiplyDeBruijnBitPosition[32] = 
    {
        0, 9, 1, 10, 13, 21, 2, 29, 11, 14, 16, 18, 22, 25, 3, 30,
        8, 12, 20, 28, 15, 17, 24, 7, 19, 27, 23, 6, 26, 5, 4, 31
    };

    v |= v >> 1;
    v |= v >> 2;
    v |= v >> 4;
    v |= v >> 8;

    return MultiplyDeBruijnBitPosition[(uint32_t)(v * 0x07C4ACDDU) >> 27];
}

10 instructions instead of 12. Not really amazing, but worth mentioning.

Optimising more?

Could we do better? Now the last line is v |= v >> 8; and it is only useful to propagate the 9th and 10th bits to positions 1 and 2. What happens if we omit that line? Let’s see:

  • For most values of v, the expected value is obtained.
  • For values of v with a highest order bit at 9th position, 0x1fe could be obtained instead of 0x1ff.
  • For values of v with a highest order bit at 10th position, one of 0x3fc, 0x3fd or 0x3fe could be obtained instead of 0x3ff.

The list of possible output values would therefore be 0x1, 0x3, 0x7, 0xf, 0x1f, 0x3f, 0x7f, 0xff, 0x1fe, 0x1ff, 0x3fc, 0x3fd, 0x3fe, 0x3ff. What happens to these values when multiplying them with the De Bruijn sequence? Let's see:

v v * 0x07C4ACDDU) >> 27
0x1 0
0x3 2
0x7 6
0xf 14
0x1f 30
0x3f 29
0x7f 27
0xff 23
0x1fe 15
0x1ff 16
0x3fc 30
0x3fd 31
0x3fe 0
0x3ff 1

Damn! Two values are colliding. It looks like we cannot omit the last line after all.

Beyond De Bruijn

Let’s give another try at the problem. Usually De Bruijn sequences are built using either nontrivial algorithms, or brute force. Maybe we could find another sequence that has no collision? Or a sequence that is not a De Bruijn sequence but that works for our problem?

Well, let’s just brute force!

(2 seconds later)

int fastlog2(uint32_t v)
{
    static const int MagicTable[16] = 
    {
        0, 1, 2, 8, -1, 3, 5, 9, 9, 7, 4, -1, 6, -1, -1, -1
    };

    v |= v >> 1;
    v |= v >> 2;
    v |= v >> 4;

    return MagicTable[(uint32_t)(v * 0x5a1a1a2u) >> 28];
}

Down to 8 instructions instead of 12. And the lookup table is now half the size!

Conclusion

It is possible for multiply-and-shift techniques similar to the De Bruijn sequence algorithm to exist for a larger set of problems. Brute forcing the search is a totally valid method for 32-bit multiplication.

The code used for this article is included in the attached file.

C++ trick: selectively restrict implicit conversions

TL;DR: given a class Foo with an implicit constructor from int, how to allow the implicit conversion in f(42); but not in g(42); where both f and g take a Foo const & argument?

Background

So I have this real class that performs numeric operations that I want use just like any other C++ numeric type. For instance, I can write the following:

float f = 15, g = 3.5;
int x = f / g;

If I decide that I need double precision, I can write:

double f = 15, g = 3.5;
int x = f / g;

And of course, using my real class for even higher precision:

real f = 15, g = 3.5;
int x = f / g;

I like that. I can just write code as usual, and when I need higher precision, I use real instead of double. It's transparent and convenient.

Implementation example

Here is a highly simplified example of a real class:

struct real
{
    inline real(double d) : m_value(d) {}
    inline operator int() const { return (int)m_value; }
    /* ... */
    long double m_value;
};

It is possible to write real f = 15 because of the implicit constructor. Actually, C++ constructors are always implicit unless specified otherwise.

It is possible to write int x = f / g because of the conversion operator.

So far, so good.

The problem with implicit promotion

Here is how fabs could be implemented:

real fabs(real const &r)
{
    return real(r.m_value < 0 ? -r.m_value : r.m_value);
}

But now we have a problem. A subtle problem. Consider the following code:

double x = fabs(-5.0);

What does this do? Well, it depends. It depends whether <cmath> was included or not. Because if <cmath> wasn’t included, then that code is going to automatically promote -5.0 to a real and call our custom function instead of the one provided by the math library! With no compile-time warning!

This is confusing. It should not happen. But it is a well known problem and there are several obvious workarounds:

  1. What most professional C++ programmers will tell you: use namespaces
  2. Mark the real(int) constructor explicit

The problem with 1. is that I am not a professional C++ programmer. I am a C programmer who uses C++. I use preprocessor macros and printf and memalign and goto. Try and stop me!

The problem with 2. is that I can no longer write real f = 15, I would need real f(15) or real f = real(15) instead. This is not acceptable, I want real to behave exactly like float and others, to the fullest extent of what the language allows.

Another solution

Fortunately, the C++ standard has a solution for us: “Implicit conversions will be performed [...] if the parameter type contains no template-parameters that participate in template argument deduction” (ISO/IEC 14882:1998, section 14.8.1.4). You cannot have implicit conversion and template argument deduction at the same time.

It means we just have to make fabs a template function! Which means making real a template class, too.

A quick way to fix real would be:

/* N is unused */
template<int N> struct real_base
{
    inline real_base(double d) : m_value(d) {}
    inline operator int() const { return (int)m_value; }
    /* ... */
    long double m_value;
};

typedef real_base<0> real;

The template argument is useless, unfortunately. It will just have to be here, forever. But who knows, you might find a use for it one day.

And to fix fabs:

/* A generic template declaration is needed */
template<int N> real_base<N> fabs(real_base<N> const &r);

/* Here we just add template<> to the previous version */
template<>
real fabs(real const &r)
{
    return real(r.m_value < 0 ? -r.m_value : r.m_value);
}

So, what happens with double x = fabs(-5.0); when we forget to include <cmath> now? Well, here is what GCC says:

In function ‘int main()’:
error: no matching function for call to ‘fabs(double)’
note: candidate is:
note: template<int N> real_base<N> fabs(const real_base<N>&)

It seems we’ve successfully managed to avoid the problematic implicit conversion, yet still allow it in places where it was useful!

So what is the rule? It’s simple: where implicit conversion should not be allowed, make the function a specialised template function.

  • Posted: 2012-02-08 22:14 (Updated: 2012-02-09 00:31)
  • Author: sam
  • Categories: code tip c++
  • Comments (48)