// Vectorise using Intel's or AMD's SSE // Use the type __m128 directly, without introducing a wrapper class // Use macros instead of inline functions #include #include #include #ifdef __SSE4_1__ // Intel's SSE 4.1 # include #endif #ifdef __SSE4A__ // AMD's SSE 4a # include #endif #ifdef __FMA4__ # include #endif #ifdef __SSE4_1__ # define vec4_architecture_SSE4_1 "+SSE4.1" #else # define vec4_architecture_SSE4_1 "" #endif #ifdef __SSE4A__ # define vec4_architecture_SSE4a "+SSE4A" #else # define vec4_architecture_SSE4a "" #endif #ifdef __FMA4__ # define vec4_architecture_FMA4 "+FMA4" #else # define vec4_architecture_FMA4 "" #endif #define vec4_architecture "SSE" vec4_architecture_SSE4_1 vec4_architecture_SSE4a vec4_architecture_FMA4 " (32-bit precision)" // Vector type corresponding to CCTK_REAL #define CCTK_REAL4_VEC __m128 // Number of vector elements in a CCTK_REAL_VEC #define CCTK_REAL4_VEC_SIZE 4 // Integer and boolean types corresponding to this real type #define CCTK_INTEGER4 CCTK_REAL4 #define CCTK_BOOLEAN4 CCTK_REAL4 #define CCTK_INTEGER4_VEC CCTK_REAL4_VEC #define CCTK_BOOLEAN4_VEC CCTK_REAL4_VEC union k4const_t { unsigned i[4]; float f[4]; __m128i vi; __m128 vf; }; #define K4_ZERO 0x00000000UL #define K4_IMIN 0x80000000UL #define K4_IMAX 0x7fffffffUL // Create vectors, extract vector elements #define vec4_set1(a) (_mm_set1_ps(a)) #define vec4_set(a,b,c,d) (_mm_set_ps(d,c,b,a)) // note reversed arguments // original order is 0123 #define vec4_swap1032(x_) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const x=x__; \ _mm_shuffle_ps(x,x, _MM_SHUFFLE(2,3,0,1)); \ }) #define vec4_swap2301(x_) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const x=x__; \ _mm_shuffle_ps(x,x, _MM_SHUFFLE(1,0,3,2)); \ }) #define vec4_swap3210(x_) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const x=x__; \ _mm_shuffle_ps(x,x, _MM_SHUFFLE(0,1,2,3)); \ }) #if defined(__PGI) // _mm_cvtss_f32 does not exist on PGI compilers # define vec4_elt0(x) \ ({ \ CCTK_REAL4 a; \ asm ("" : "=x" (a) : "0" (x)); \ a; \ }) #else # define vec4_elt0(x) (_mm_cvtss_f32(x)) // this is a no-op #endif #define vec4_elt1(x) vec4_elt0(vec4_swap1032(x)) #define vec4_elt2(x) vec4_elt0(vec4_swap2301(x)) #define vec4_elt3(x) vec4_elt0(vec4_swap3210(x)) #if defined(__PGI) # define vec4_elt(x_,d) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const x=x__; \ CCTK_REAL4 a; \ if (d==0) a=vec4_elt0(x); \ else if (d==1) a=vec4_elt1(x); \ else if (d==2) a=vec4_elt2(x); \ else if (d==3) a=vec4_elt3(x); \ a; \ }) #else # define vec4_elt(x_,d) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const x=x__; \ CCTK_REAL4 a; \ switch (d) { \ case 0: a=vec4_elt0(x); break; \ case 1: a=vec4_elt1(x); break; \ case 2: a=vec4_elt2(x); break; \ case 3: a=vec4_elt3(x); break; \ } \ a; \ }) #endif // Load and store vectors // Load a vector from memory (aligned and unaligned); this loads from // a reference to a scalar #define vec4_load(p) (_mm_load_ps(&(p))) #define vec4_loadu(p) (_mm_loadu_ps(&(p))) #if ! VECTORISE_ALWAYS_USE_ALIGNED_LOADS # define vec4_load_off1(p) vec_loadu(p) # define vec4_load_off2(p) vec_loadu(p) # define vec4_load_off3(p) vec_loadu(p) #else # define vec4_load_off1(p_) \ ({ \ CCTK_REAL4 const& p__=(p_); \ CCTK_REAL4 const& p=p__; \ CCTK_REAL4_VEC const lo=vec4_load((&p)[-1]); \ CCTK_REAL4_VEC const hi=vec4_load((&p)[+3]); \ assert(0); \ CCTK_REAL4_VEC const hi2=_mm_shuffle_ps(lo,hi, _MM_SHUFFLE(0,1,2,3)); \ _mm_shuffle_ps(lo,hi2, _MM_SHUFFLE(2,1,3,0)); \ }) # define vec4_load_off2(p_) \ ({ \ CCTK_REAL4 const& p__=(p_); \ CCTK_REAL4 const& p=p__; \ CCTK_REAL4_VEC const lo=vec4_load((&p)[-2]); \ CCTK_REAL4_VEC const hi=vec4_load((&p)[+2]); \ _mm_shuffle_ps(lo,hi, _MM_SHUFFLE(1,0,3,2)); \ }) # define vec4_load_off3(p_) \ ({ \ CCTK_REAL4 const& p__=(p_); \ CCTK_REAL4 const& p=p__; \ CCTK_REAL4_VEC const lo=vec4_load((&p)[-1]); \ CCTK_REAL4_VEC const hi=vec4_load((&p)[+3]); \ assert(0); \ CCTK_REAL4_VEC const lo2=_mm_shuffle_ps(lo,hi, _MM_SHUFFLE(0,1,2,3)); \ _mm_shuffle_ps(lo2,hi, _MM_SHUFFLE(3,0,2,1)); \ }) #endif // Load a vector from memory that may or may not be aligned, as // decided by the offset off and the vector size #if VECTORISE_ALWAYS_USE_UNALIGNED_LOADS // Implementation: Always use unaligned load # define vec4_loadu_maybe(off,p) vec4_loadu(p) # define vec4_loadu_maybe3(off1,off2,off3,p) vec4_loadu(p) #else # define vec4_loadu_maybe(off,p_) \ ({ \ CCTK_REAL4 const& p__=(p_); \ CCTK_REAL4 const& p=p__; \ (off) % CCTK_REAL4_VEC_SIZE == 0 ? \ vec4_load(p) : \ vec4_loadu(p); \ }) # if VECTORISE_ALIGNED_ARRAYS // Assume all array x sizes are multiples of the vector size # define vec4_loadu_maybe3(off1,off2,off3,p) \ vec4_loadu_maybe(off1,p) # else # define vec4_loadu_maybe3(off1,off2,off3,p) \ vec4_loadu_maybe((off1)|(off2)|(off3),p) # endif #endif // Store a vector to memory (aligned and non-temporal); this stores to // a reference to a scalar #define vec4_store(p,x) (_mm_store_ps(&(p),x)) #define vec4_storeu(p,x) (_mm_storeu_ps(&(p),x)) #if ! VECTORISE_STREAMING_STORES # define vec4_store_nta(p,x) vec4_store(p,x) #else # define vec4_store_nta(p,x) (_mm_stream_ps(&(p),x)) #endif // Store a partial vector (aligned and non-temporal) #define vec4_store_partial_prepare(i,imin,imax) \ int v4stp_lo_skip = (imin)-(i); \ int v4stp_hi_skip = (i)+CCTK_REAL_VEC_SIZE-(imax); \ if (CCTK_BUILTIN_EXPECT(v4stp_lo_skip < 0, true)) v4stp_lo_skip = 0; \ if (CCTK_BUILTIN_EXPECT(v4stp_hi_skip < 0, true)) v4stp_hi_skip = 0; // Ignoring VECTORISE_STREAMING_STORES for partial stores #define vec4_store_nta_partial(p_,x_) \ ({ \ CCTK_REAL4& p__=(p_); \ CCTK_REAL4& p=p__; \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const x=x__; \ if (CCTK_BUILTIN_EXPECT(v4stp_lo_skip==0 and v4stp_hi_skip==0, true)) { \ vec4_store_nta(p,x); \ } else { \ /* these cases fall through */ \ switch (v4stp_lo_skip) { \ case 0: \ (&p)[0] = vec4_elt0(x); \ case 1: \ if (v4stp_hi_skip>=3) break; \ (&p)[1] = vec4_elt1(x); \ case 2: \ if (v4stp_hi_skip>=2) break; \ (&p)[2] = vec4_elt2(x); \ case 3: \ if (v4stp_hi_skip>=1) break; \ (&p)[3] = vec4_elt3(x); \ } \ } \ }) // Ignoring VECTORISE_STREAMING_STORES for partial stores #define vec4_store_nta_partial_lo(p_,x_,n) \ ({ \ CCTK_REAL4 & p__=(p_); \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4 & p=p__; \ CCTK_REAL4_VEC const x=x__; \ /* these cases fall through */ \ switch (n) { \ case 3: (&p)[2] = vec4_elt2(x); \ case 2: (&p)[1] = vec4_elt1(x); \ case 1: (&p)[0] = vec4_elt0(x); \ } \ }) #define vec4_store_nta_partial_hi(p_,x_,n) \ ({ \ CCTK_REAL4 & p__=(p_); \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4 & p=p__; \ CCTK_REAL4_VEC const x=x__; \ /* these cases fall through */ \ switch (n) { \ case 3: (&p)[1]=vec4_elt1(x); \ case 2: (&p)[2]=vec4_elt2(x); \ case 1: (&p)[3]=vec4_elt3(x); \ } \ }) #define vec4_store_nta_partial_mid(p_,x_,nlo,nhi) \ ({ \ CCTK_REAL4 & p__=(p_); \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4 & p=p__; \ CCTK_REAL4_VEC const x=x__; \ /* these cases fall through */ \ switch (nhi) { \ case 3: if (nlo<2) break; (&p)[1] = vec4_elt1(x); \ case 2: if (nlo<3) break; (&p)[2] = vec4_elt2(x); \ } \ }) // Functions and operators static const k4const_t k4sign_mask = {{ K4_IMIN, K4_IMIN, K4_IMIN, K4_IMIN, }}; // Operators #define k4neg(x) (_mm_xor_ps(k4sign_mask.vf,x)) // #define k4inv(x) // TODO: provide k4inv via rcp and Newton-Raphson // This is described in AMD's publication 47414. // This should apply for AVX as well. #define k4add(x,y) (_mm_add_ps(x,y)) #define k4sub(x,y) (_mm_sub_ps(x,y)) #define k4mul(x,y) (_mm_mul_ps(x,y)) // TODO: use k4inv and k4mul instead #define k4div(x,y) (_mm_div_ps(x,y)) // Fused multiply-add, defined as [+-]x*y[+-]z #ifdef __FMA4__ # define k4madd(x,y,z) (_mm_macc_ps(x,y,z)) # define k4msub(x,y,z) (_mm_msub_ps(x,y,z)) # define k4nmadd(x,y,z) (_mm_nmsub_ps(x,y,z)) # define k4nmsub(x,y,z) (_mm_nmacc_ps(x,y,z)) #else # define k4madd(x,y,z) (k4add(k4mul(x,y),z)) # define k4msub(x,y,z) (k4sub(k4mul(x,y),z)) # define k4nmadd(x,y,z) (k4sub(k4neg(z),k4mul(x,y))) # define k4nmsub(x,y,z) (k4sub(z,k4mul(x,y))) #endif // Cheap functions #define k4copysign(x,y) \ (_mm_or_ps(_mm_andnot_ps(k4sign_mask.vf,x), \ _mm_and_ps(k4sign_mask.vf,y))) #define k4fabs(x) (_mm_andnot_ps(k4sign_mask.vf,x)) #define k4fmax(x,y) (_mm_max_ps(x,y)) #define k4fmin(x,y) (_mm_min_ps(x,y)) #define k4fnabs(x) (_mm_or_ps(k4sign_mask.vf,x)) #define k4sgn(x_) \ ({ \ CCTK_REAL_VEC const x__=(x_); \ CCTK_REAL_VEC const x=x__; \ CCTK_REAL_VEC const iszero = _mm_cmpeq_ps(vec4_set1(0.0f), x); \ CCTK_REAL_VEC const sign = _mm_and_ps(k4sign_mask.vf, x); \ CCTK_REAL_VEC const signedone = _mm_or_ps(vec4_set1(1.0f), sign); \ k4ifthen(iszero, vec4_set1(0.0f), signedone); \ }) // TODO: maybe use rsqrt and Newton-Raphson #define k4sqrt(x) (_mm_sqrt_ps(x)) // Expensive functions #define K4REPL(f,x_) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const x=x__; \ vec4_set(f(vec4_elt0(x)), \ f(vec4_elt1(x)), \ f(vec4_elt2(x)), \ f(vec4_elt3(x))); \ }) #define K4REPL2S(f,x_,a_) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4 const a__=(a_); \ CCTK_REAL4_VEC const x=x__; \ CCTK_REAL4 const a=a__; \ vec4_set(f(vec4_elt0(x),a), \ f(vec4_elt1(x),a), \ f(vec4_elt2(x),a), \ f(vec4_elt3(x),a)); \ }) #define K4REPL2(f,x_,y_) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const y__=(y_); \ CCTK_REAL4_VEC const x=x__; \ CCTK_REAL4_VEC const y=y__; \ vec4_set(f(vec4_elt0(x),vec4_elt0(y)), \ f(vec4_elt1(x),vec4_elt1(y)), \ f(vec4_elt2(x),vec4_elt2(y)), \ f(vec4_elt3(x),vec4_elt3(y))); \ }) #define k4acos(x) K4REPL(acosf,x) #define k4acosh(x) K4REPL(acoshf,x) #define k4asin(x) K4REPL(asinf,x) #define k4asinh(x) K4REPL(asinhf,x) #define k4atan(x) K4REPL(atanf,x) #define k4atan2(x,y) K4REPL2(atan2f,x,y) #define k4atanh(x) K4REPL(atanhf,x) #define k4cos(x) K4REPL(cosf,x) #define k4cosh(x) K4REPL(coshf,x) #define k4exp(x) K4REPL(expf,x) #define k4log(x) K4REPL(logf,x) #define k4pow(x,a) K4REPL2S(powf,x,a) #define k4sin(x) K4REPL(sinf,x) #define k4sinh(x) K4REPL(sinhf,x) #define k4tan(x) K4REPL(tanf,x) #define k4tanh(x) K4REPL(tanhf,x) static const k4const_t k4lfalse_ = {{ 0U, 0U, 0U, 0U, }}; static const k4const_t k4ltrue_ = {{ ~0U, ~0U, ~0U, ~0U, }}; #define k4lfalse (k4lfalse_.vf) #define k4ltrue (k4ltrue_.vf) #define k4lnot(x) (_mm_xor_ps(k4ltrue,x)) #define k4land(x,y) (_mm_and_ps(x,y)) #define k4lor(x,y) (_mm_or_ps(x,y)) #define k4lxor(x,y) (_mm_xor_ps(x,y)) #ifdef __SSE4_1__ # define k4ifthen(x,y,z) (_mm_blendv_ps(z,y,x)) #elif 0 # ifdef __cplusplus # define k4signbit(x) ({ using namespace std; signbit(x); }) # else # define k4signbit(x) (signbitf(x)) # endif # define k4ifthen(x,y,z) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const y__=(y_); \ CCTK_REAL4_VEC const z__=(z_); \ CCTK_REAL4_VEC const x=x__; \ CCTK_REAL4_VEC const y=y__; \ CCTK_REAL4_VEC const z=z__; \ vec4_set(k4signbit(vec4_elt0(x)) ? vec4_elt0(y) : vec4_elt0(z), \ k4signbit(vec4_elt1(x)) ? vec4_elt1(y) : vec4_elt1(z), \ k4signbit(vec4_elt2(x)) ? vec4_elt2(y) : vec4_elt2(z), \ k4signbit(vec4_elt3(x)) ? vec4_elt3(y) : vec4_elt3(z)); \ }) #elif 0 // We don't need to shift -- the condition (mask) will be either all // zeros or all ones # define k4ifthen(x_,y_,z_) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const y__=(y_); \ CCTK_REAL4_VEC const z__=(z_); \ CCTK_REAL4_VEC const x=x__; \ CCTK_REAL4_VEC const y=y__; \ CCTK_REAL4_VEC const z=z__; \ CCTK_REAL4_VEC const mask = \ (__m128)_mm_srai_epi32((__m128i)x, 31); \ /* (z & ~mask) | (y & mask) */ \ _mm_or_ps(_mm_andnot_ps(mask, z), _mm_and_ps(mask, y)); \ }) #else # define k4ifthen(x_,y_,z_) \ ({ \ CCTK_REAL4_VEC const x__=(x_); \ CCTK_REAL4_VEC const y__=(y_); \ CCTK_REAL4_VEC const z__=(z_); \ CCTK_REAL4_VEC const x=x__; \ CCTK_REAL4_VEC const y=y__; \ CCTK_REAL4_VEC const z=z__; \ /* (z & ~mask) | (y & mask) where imask = ~mask */ \ _mm_or_ps(_mm_and_ps(x, y), _mm_andnot_ps(x, z)); \ }) #endif #define k4cmpeq(x,y) (_mm_cmpeq_ps(x,y)) #define k4cmpne(x,y) (_mm_cmpneq_ps(x,y)) #define k4cmpgt(x,y) (_mm_cmpgt_ps(x,y)) #define k4cmpge(x,y) (_mm_cmpge_ps(x,y)) #define k4cmplt(x,y) (_mm_cmplt_ps(x,y)) #define k4cmple(x,y) (_mm_cmple_ps(x,y))