The Steam Hardware & Software Survey as of September 2013 shows that 68% of users’ CPU support SSE4.1, leaving 32% still using SSE3 or less. It also shows that 99.7% of users’ CPU support SSE3. So what this tells me is that SSE3 is where it’s at, if you want your game to run on most CPUs, you won’t be able to use SSE 4.1 intrinsic functions.
Problem is, SSE4.1 is awesome. It’s awesome for many reasons but let’s focus on one of them: _mm_round_ps(). You can use this intrinsic, which yield a single ‘roundps‘ instruction, for computing math Floor, Ceil and – as its name suggest – Round.
Well this is great and all but what can we do using non-SSE4.1 instructions? You can always use the standard C math.h floor(), ceil() and your own flavor of round() but if you want to do some intensive and fast vector math in your game, SSE is your savior. If you do a search on Google, something like ‘sse floor’, you’ll probably get a lot of wrong algorithms. Most of them won’t work for negative integer values, flooring -10 to -11 for instance. So I took some time to figure out an algorithm using only SSE3 instructions.
inline __m128 _mm_floor_ps2(const __m128& x){
__m128i v0 = _mm_setzero_si128();
__m128i v1 = _mm_cmpeq_epi32(v0,v0);
__m128i ji = _mm_srli_epi32( v1, 25);
__m128 j = *(__m128*)&_mm_slli_epi32( ji, 23); //create vector 1.0f
__m128i i = _mm_cvttps_epi32(x);
__m128 fi = _mm_cvtepi32_ps(i);
__m128 igx = _mm_cmpgt_ps(fi, x);
j = _mm_and_ps(igx, j);
return _mm_sub_ps(fi, j);
}
inline __m128 _mm_ceil_ps2(const __m128& x){
__m128i v0 = _mm_setzero_si128();
__m128i v1 = _mm_cmpeq_epi32(v0,v0);
__m128i ji = _mm_srli_epi32( v1, 25);
__m128 j = *(__m128*)&_mm_slli_epi32( ji, 23); //create vector 1.0f
__m128i i = _mm_cvttps_epi32(x);
__m128 fi = _mm_cvtepi32_ps(i);
__m128 igx = _mm_cmplt_ps(fi, x);
j = _mm_and_ps(igx, j);
return _mm_add_ps(fi, j);
}
inline __m128 _mm_round_ps2(const __m128& a){
__m128 v0 = _mm_setzero_ps(); //generate the highest value < 2
__m128 v1 = _mm_cmpeq_ps(v0,v0);
__m128 vNearest2 = *(__m128*)&_mm_srli_epi32( *(__m128i*)&v1, 2);
__m128i i = _mm_cvttps_epi32(a);
__m128 aTrunc = _mm_cvtepi32_ps(i); // truncate a
__m128 rmd = _mm_sub_ps(a, aTrunc); // get remainder
__m128 rmd2 = _mm_mul_ps( rmd, vNearest2); // mul remainder by near 2 will yield the needed offset
__m128i rmd2i = _mm_cvttps_epi32(rmd2); // after being truncated of course
__m128 rmd2Trunc = _mm_cvtepi32_ps(rmd2i);
__m128 r =_mm_add_ps(aTrunc, rmd2Trunc);
return r;
}
Edit: Special thanks to obyzouth, he worked out better SSE code for floor and ceil functions. 🙂 It does not handle the NaNs and Infinite but those don’t have to be handled, they have to be eradicated. A good NaN is a non-existent NaN. You should use functions that handle them in your debug build though.
As you can see I use a conversion to int and back to float to round the value. This will not work for values that cannot be represented by an int. If you need these function to handle these kind of values you might have to reconsider using float to begin with as it loses quite a lot of precision in these ranges. But for the sake of absolute safety, here’s what you can do:
template< __m128 (FuncT)(const __m128&) >
inline __m128 _mm_safeInt_ps(const __m128& a){
__m128 v8388608 = *(__m128*)&_mm_set1_epi32(0x4b000000); //vector with value 8388608
__m128 aAbs = _mm_and_ps(a, *(__m128*)&_mm_set1_epi32(0x7fffffff)); //Abs(a)
__m128 aMask = _mm_cmpgt_ps(aAbs, v8388608); //if Abs(a) > 8388608
// select a if greater then 8388608.0f, otherwise select the result of FuncT
__m128 r = _mm_xor_ps( _mm_and_ps(aMask, a), _mm_andnot_ps(aMask, FuncT(a)) );
return r;
}
...
//then call your functions like so:
_mm_safeInt_ps<_mm_floor_ps2>( ... );
_mm_safeInt_ps<_mm_ceil_ps2 >( ... );
_mm_safeInt_ps<_mm_round_ps2>( ... );
8388608 is the lowest float value that cannot have decimals because of imprecision increasing with the value. So floor()/ceil()/round() will return the same value it receives for number greater or equal to that.
Bonus! Vector equivalent of fmod() :
inline __m128 _mm_mod_ps2(const __m128& a, const __m128& aDiv){
__m128 c = _mm_div_ps(a,aDiv);
__m128i i = _mm_cvttps_epi32(c);
__m128 cTrunc = _mm_cvtepi32_ps(i);
__m128 base = _mm_mul_ps(cTrunc, aDiv);
__m128 r = _mm_sub_ps(a, base);
return r;
}
Have you looked at the implementations in DirectXMath? The 3.06 version that ships in the Windows 8.1 SDK / VS 2013 had some improvements to XMVectorRound, XMVectorFloor, and XMVectorCeil that work on SSE/SSE2 systems.
Yes I looked at XMVectorFloor but the code doesn’t handle big floats correctly :/
For instance it will floor 88607.0f to 88606.0f.
You understand you want to renovate your house, but the truth is don’t know where to start, suited? Well, you’re not alone. Many householders dive into the renovation technique with no clue of what exactly is available. It’s only after they go through renovation mishaps that they rue not having a plan. Without prepare, the home renovation process could be full of disappointments because not like building a new house, gonna catch starting with a blank state. There can be unforeseen expenses together with issues that make the process complex. So before you go down the actual twists and turns of the renovation path, here are five things you must know before you start redecorating.
1. Invest in a Key Lockbox.
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5. Interview Numerous Contractors.
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6. Renovate Your special Kitchen First.
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7. Maybe be Specific About Design Concepts.
You’ll want to narrow down your format preferences before you meet with an inside designer. Get inspiration by means of browsing home decorating magazines, home decor websites, and design displays. Getting a handle on a style direction will help you avoid keeping yourself talked into a designer’s personalized ideas, which might be different from your own personal vision for the renovation. At the same time, keep your designer strictly with your budget. Don’t allow them to obtain expensive materials and set you back for it later. If you make an attempt to stay within a specific timeframe, your costs will stay little, too.
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