Following my earlier article on timing various square-root functions on the x86 Clomid For Sale, , commenter LeeN suggested that it would be useful to also test their impact on a more realistic scenario than square-rooting long arrays of independent numbers. In real gameplay code the most common use for sqrts is in finding the length of a vector or normalizing it, like when you need to perform a distance check between two characters to determine whether they can see/shoot/etc each other. So, I wrote up a group of normalize functions, each using a different sqrt technique, Cheap Clomid no rx, and timed them.
The testbed was, as last time, an array of 2048 single-precision floating point numbers, this time interpreted as a packed list of 682 three-dimensional vectors. This number was chosen so that both it and the output array were sure to fit in the L1 cache; however, because three floats add up to twelve bytes, is Clomid addictive, this means that three out of four vectors were not aligned to a 16-byte boundary, which is significant for the SIMD test case as I had to use the movups unaligned load op. Each timing case consisted of looping over this array of vectors 2048 times, normalizing each and writing the result to memory, Clomid For Sale.
Each normalize function computed the length of the vector 1/√(x2 + y2 + z2), multiplied each component by the reciprocal, and then wrote it back through an output pointer. Get Clomid, The main difference was in how the reciprocal square root was computed:
- via the x87 FPU, by simply compiling
1.0f/sqrt( x*x + y*y + z*z ) - via the SSE scalar unit, by compiling
1.0f/sqrt( x*x + y*y + z*z )with the /arch:SSE2 option set; this causes the compiler to issue asqrtssfollowed by anfdiv— ie, it computes the square root and then divides one by it
- via the SSE scalar unit, by using the estimated reciprocal square root intrinsic and then performing one step of Newton-Raphson iteration
- via the SSE SIMD unit, working on the whole vector at once
In all cases the results were accurate to 22 bits of precision. The results for 1, doses Clomid work,396,736 vector normalizations were:
| Method | Total time | Time per vector |
|---|---|---|
Compiler 1.0/sqrt(x) x87 FPU FSQRT | 52.469ms | 37.6ns |
Compiler 1.0/sqrt(x) SSE scalar sqrtss | 27.233ms | 19.5ns |
SSE scalar opsrsqrtss with one NR step | 21.631ms | 15.5ns |
SSE SIMD ops rsqrtss with one NR step | 20.034ms | 14.3ns |
Two things jump out here. First, even when the square root op is surrounded by lots of other math — multiplies, adds, Clomid use, loads, stores — optimizations such as this can make a huge difference. Clomid For Sale, It's not just the cost of the sqrt itself, but also that it's unpipelined, which means it ties up an execution unit and prevents any other work from being done until it's entirely completed.
Second, in this case, SIMD is only a very modest benefit. That's because the input vectors are unaligned, and the two key steps of this operation, online buying Clomid, the dot product and the square root, are scalar in nature. (This is what's meant by "horizontal" SIMD computation — operations between the components of one vector, rather than between the corresponding words of two vectors. Given a vector V ∋ <x, Comprar en línea Clomid, comprar Clomid baratos, y,z>, the sum x + y + z is horizontal, but with two vectors V1 and V2, V3 = <x1+x2, y1+y2, z1+z2> is vertical.) So it really doesn't play to SIMD's strengths at all, Clomid price.
On the other hand, if I were to normalize four vectors at a time, so that four dot products and four rsqrts could be performed in parallel in the four words of a vector register, then the speed advantage of SIMD would be much greater, Clomid For Sale. But, again, my goal wasn't to test performance in tight loops over packed data — it was to figure out the best way to do something like an angle check in the middle of a character's AI, where you usually deal with one vector at a time.
Source code for my testing functions below the jump. Order Clomid from United States pharmacy, Note that each function writes the normalized vector through an out pointer, but also returns the original vector's length. The hand-written intrinsic versions probably aren't totally optimal, but they ought to be good enough to make the point.
[DDET Naive vector normalize, x87 FPU or SSE scalar]
Source
// Normalizes an assumed 3-element vector starting
// at pointer V, and returns the length of the original
// vector, Clomid used for.
inline float NaiveTestNormalize( float * RESTRICT vOut, const float * RESTRICT vIn )
{
const float l = vIn[0]*vIn[0] + vIn[1]*vIn[1] + vIn[2]*vIn[2];
const float rsqt = 1.0f / sqrt(l);
vOut[0] = vIn[0] * rsqt;
vOut[1] = vIn[1] * rsqt;
vOut[2] = vIn[2] * rsqt;
return rsqt * l;
}
Assembly (x87 FPU)
_TEXT SEGMENT
_vOut$ = 8 ; size = 4
_vIn$ = 12 ; size = 4
?TestNormalize@@YAMPIAMPIBM@Z PROC ; TestNormalize, COMDAT
; 396 : const float l = vIn[0]*vIn[0] + vIn[1]*vIn[1] + vIn[2]*vIn[2];
mov eax, DWORD PTR _vIn$[esp-4]
fld DWORD PTR [eax+8]
; 397 : const float rsqt = 1.0f / sqrt(l);
; 398 : vOut[0] = vIn[0] * rsqt;
mov ecx, DWORD PTR _vOut$[esp-4]
fld DWORD PTR [eax+4]
fld DWORD PTR [eax]
fmul ST(0), Order Clomid online overnight delivery no prescription, ST(0)
fld ST(1)
fmulp ST(2), ST(0)
faddp ST(1), ST(0)
fld ST(1)
fmulp ST(2), ST(0)
faddp ST(1), ST(0)
fld ST(0)
fsqrt
fld1
fdivrp ST(1), ST(0)
fld DWORD PTR [eax]
fmul ST(0), ST(1)
fstp DWORD PTR [ecx]
; 399 : vOut[1] = vIn[1] * rsqt;
fld ST(0)
fmul DWORD PTR [eax+4]
fstp DWORD PTR [ecx+4]
; 400 : vOut[2] = vIn[2] * rsqt;
fld ST(0)
fmul DWORD PTR [eax+8]
fstp DWORD PTR [ecx+8]
; 401 : return rsqt * l;
fmulp ST(1), Clomid mg, ST(0)
; 402 : }
ret 0
?TestNormalize@@YAMPIAMPIBM@Z ENDP ; TestNormalize
_TEXT ENDS
Assembly (compiler-issued SSE scalar)
_TEXT SEGMENT
_l$ = -4 ; size = 4
_vOut$ = 8 ; size = 4
_rsqt$ = 12 ; size = 4
_vIn$ = 12 ; size = 4
?TestNormalize@@YAMPIAMPIBM@Z PROC ; TestNormalize, COMDAT
; 392 : {
push ecx
; 393 : const float l = vIn[0]*vIn[0] + vIn[1]*vIn[1] + vIn[2]*vIn[2];
mov eax, DWORD PTR _vIn$[esp]
movss xmm1, DWORD PTR [eax+4]
movss xmm2, DWORD PTR [eax]
movss xmm0, Buying Clomid online over the counter, DWORD PTR [eax+8]
; 394 : const float rsqt = 1.0f / sqrt(l);
; 395 : vOut[0] = vIn[0] * rsqt;
mov eax, DWORD PTR _vOut$[esp]
movaps xmm3, xmm2
mulss xmm3, xmm2
movaps xmm4, xmm1
mulss xmm4, xmm1
addss xmm3, xmm4
movaps xmm4, low dose Clomid, xmm0
mulss xmm4, xmm0
addss xmm3, xmm4
movss DWORD PTR _l$[esp+4], xmm3
sqrtss xmm4, xmm3 ;; slow full-precision square root gets stored in xmm4
movss xmm3, Purchase Clomid online no prescription, DWORD PTR __real@3f800000 ;; store 1.0 in xmm3
divss xmm3, xmm4 ;; divide 1.0 / xmm4 to get the reciprocal square root !?.
movss DWORD PTR _rsqt$[esp], xmm3
; 396 : vOut[1] = vIn[1] * rsqt;
; 397 : vOut[2] = vIn[2] * rsqt;
; 398 : return rsqt * l;
fld DWORD PTR _rsqt$[esp]
mulss xmm2, xmm3
fmul DWORD PTR _l$[esp+4]
mulss xmm1, xmm3
mulss xmm0, xmm3
movss DWORD PTR [eax], where can i order Clomid without prescription, xmm2
movss DWORD PTR [eax+4], xmm1
movss DWORD PTR [eax+8], xmm0
; 399 : }
pop ecx
ret 0
?TestNormalize@@YAMPIAMPIBM@Z ENDP ; TestNormalize
_TEXT ENDS
[/DDET]
[DDET Vector normalize, hand-written SSE scalar by intrinsics]
Source
// SSE scalar reciprocal sqrt using rsqrt op, plus one Newton-Rhaphson iteration
inline __m128 SSERSqrtNR( const __m128 x )
{
__m128 recip = _mm_rsqrt_ss( x ); // "estimate" opcode
const static __m128 three = { 3, Generic Clomid, 3, 3, 3 }; // aligned consts for fast load
const static __m128 half = { 0.5,0.5,0.5,0.5 };
__m128 halfrecip = _mm_mul_ss( half, recip );
__m128 threeminus_xrr = _mm_sub_ss( three, Clomid samples, _mm_mul_ss( x, _mm_mul_ss ( recip, recip ) ) );
return _mm_mul_ss( halfrecip, threeminus_xrr );
}
inline __m128 SSE_ScalarTestNormalizeFast( float * RESTRICT vOut, float * RESTRICT vIn )
{
__m128 x = _mm_load_ss(&vIn[0]);
__m128 y = _mm_load_ss(&vIn[1]);
__m128 z = _mm_load_ss(&vIn[2]);
const __m128 l = // compute x*x + y*y + z*z
_mm_add_ss(
_mm_add_ss( _mm_mul_ss(x, Clomid online cod, x),
_mm_mul_ss(y,y)
),
_mm_mul_ss( z, z )
);
const __m128 rsqt = SSERSqrtNR( l );
_mm_store_ss( &vOut[0] , _mm_mul_ss( rsqt, x ) );
_mm_store_ss( &vOut[1], Clomid no rx, _mm_mul_ss( rsqt, y ) );
_mm_store_ss( &vOut[2] , _mm_mul_ss( rsqt, z ) );
return _mm_mul_ss( l , rsqt );
}
Assembly
_TEXT SEGMENT
_vOut$ = 8 ; size = 4
_vIn$ = 12 ; size = 4
?SSE_ScalarTestNormalizeFast@@YA?AT__m128@@PIAM0@Z PROC ; SSE_ScalarTestNormalizeFast, Clomid over the counter, COMDAT
push ebp
mov ebp, esp
and esp, -16 ; fffffff0H
mov eax, DWORD PTR _vIn$[ebp]
movss xmm0, DWORD PTR [eax]
movss xmm3, DWORD PTR [eax+4]
movaps xmm7, XMMWORD PTR ?three@?1??SSERSqrtNR@@YA?AT__m128@@T2@@Z@4T2@B
movaps xmm2, ordering Clomid online, xmm0
movss xmm0, DWORD PTR [eax+8]
mov eax, DWORD PTR _vOut$[ebp]
movaps xmm4, xmm0
movaps xmm0, xmm2
mulss xmm0, Australia, uk, us, usa, xmm2
movaps xmm1, xmm3
mulss xmm1, xmm3
addss xmm0, xmm1
movaps xmm1, xmm4
mulss xmm1, xmm4
addss xmm0, xmm1
movaps xmm1, Clomid dosage, xmm0
rsqrtss xmm1, xmm1
movaps xmm5, xmm1
mulss xmm1, xmm5
movaps xmm6, xmm0
mulss xmm6, Buy Clomid from mexico, xmm1
movaps xmm1, XMMWORD PTR ?half@?1??SSERSqrtNR@@YA?AT__m128@@T2@@Z@4T2@B
mulss xmm1, xmm5
subss xmm7, xmm6
mulss xmm1, xmm7
movaps xmm5, xmm1
mulss xmm5, xmm2
movss XMMWORD PTR [eax], Clomid cost, xmm5
movaps xmm2, xmm1
mulss xmm2, xmm3
movss XMMWORD PTR [eax+4], xmm2
movaps xmm2, xmm1
mulss xmm2, Clomid forum, xmm4
movss XMMWORD PTR [eax+8], xmm2
mulss xmm0, xmm1
mov esp, ebp
pop ebp
ret 0
?SSE_ScalarTestNormalizeFast@@YA?AT__m128@@PIAM0@Z ENDP ; SSE_ScalarTestNormalizeFast
_TEXT ENDS
[/DDET]
[DDET Vector normalize, hand-written SSE SIMD by intrinsics]
Source
inline __m128 SSE_SIMDTestNormalizeFast( float * RESTRICT vOut, float * RESTRICT vIn )
{
// load as a SIMD vector
const __m128 vec = _mm_loadu_ps(vIn);
// compute a dot product by computing the square, and
// then rotating the vector and adding, Clomid street price, so that the
// dot ends up in the low term (used by the scalar ops)
__m128 dot = _mm_mul_ps( vec, vec );
// rotate x under y and add together
__m128 rotated = _mm_shuffle_ps( dot, dot, _MM_SHUFFLE( 0,3, Clomid overnight, 2,1 ) ); // YZWX ( shuffle macro is high to low word )
dot = _mm_add_ss( dot, rotated ); // x^2 + y^2 in the low word
rotated = _mm_shuffle_ps( rotated, rotated, _MM_SHUFFLE( 0,3,2, purchase Clomid,1 ) ); // ZWXY
dot = _mm_add_ss( dot, rotated ); // x^2 + y^2 + z^2 in the low word
__m128 recipsqrt = SSERSqrtNR( dot ); // contains reciprocal square root in low term
recipsqrt = _mm_shuffle_ps( recipsqrt, recipsqrt, _MM_SHUFFLE( 0, 0, Clomid wiki, 0, 0 ) ); // broadcast low term to all words
// multiply 1/sqrt(dotproduct) against all vector components, and write back
const __m128 normalized = _mm_mul_ps( vec, recipsqrt );
_mm_storeu_ps(vOut, normalized);
return _mm_mul_ss( dot , recipsqrt );
}
Assembly
_TEXT SEGMENT
_vOut$ = 8 ; size = 4
_vIn$ = 12 ; size = 4
?SSE_SIMDTestNormalizeFast@@YA?AT__m128@@PIAM0@Z PROC ; SSE_SIMDTestNormalizeFast, COMDAT
push ebp
mov ebp, order Clomid from mexican pharmacy, esp
and esp, -16 ; fffffff0H
mov eax, DWORD PTR _vIn$[ebp]
movups xmm2, XMMWORD PTR [eax] ;; load the input vector
movaps xmm5, XMMWORD PTR ?three@?1??SSERSqrtNR@@YA?AT__m128@@T2@@Z@4T2@B ;; load the constant "3"
mov ecx, Clomid pharmacy, DWORD PTR _vOut$[ebp]
movaps xmm0, xmm2
mulps xmm0, xmm2
movaps xmm1, xmm0
shufps xmm1, xmm0, 57 ; shuffle to YZWX
addss xmm0, xmm1 ; add Y to low word of xmm0
shufps xmm1, buy Clomid online cod, xmm1, 57 ; shuffle to ZWXY
addss xmm0, xmm1 ; add Z to low word of xmm0
movaps xmm1, xmm0
rsqrtss xmm1, xmm1 ; reciprocal square root estimate
movaps xmm3, Real brand Clomid online, xmm1
mulss xmm1, xmm3
movaps xmm4, xmm0
mulss xmm4, xmm1
movaps xmm1, XMMWORD PTR ?half@?1??SSERSqrtNR@@YA?AT__m128@@T2@@Z@4T2@B
mulss xmm1, xmm3
subss xmm5, xmm4
mulss xmm1, xmm5 ; Newton-Raphson finishes here; 1/sqrt(dot) is in xmm1's low word
shufps xmm1, xmm1, 0 ; broadcast so that xmm1 has 1/sqrt(dot) in all words
movaps xmm3, xmm1
mulps xmm3, xmm2 ; multiply all words of original vector by 1/sqrt(dot)
movups XMMWORD PTR [ecx], xmm3 ; unaligned save to memory
; return dot * 1 / sqrt(dot) == sqrt(dot) == length of vector
mulss xmm0, xmm1
mov esp, ebp
pop ebp
ret 0
?SSE_SIMDTestNormalizeFast@@YA?AT__m128@@PIAM0@Z ENDP ; SSE_SIMDTestNormalizeFast
_TEXT ENDS
[/DDET].
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