//========= Copyright Valve Corporation, All rights reserved. ============// // // Purpose: SSE Math primitives. // //=====================================================================================// #include #include // Needed for FLT_EPSILON #include "basetypes.h" #include #include "tier0/dbg.h" #include "mathlib/mathlib.h" #include "mathlib/vector.h" #include "sse.h" // memdbgon must be the last include file in a .cpp file!!! #include "tier0/memdbgon.h" #ifndef COMPILER_MSVC64 // Implement for 64-bit Windows if needed. static const uint32 _sincos_masks[] = { (uint32)0x0, (uint32)~0x0 }; static const uint32 _sincos_inv_masks[] = { (uint32)~0x0, (uint32)0x0 }; //----------------------------------------------------------------------------- // Macros and constants required by some of the SSE assembly: //----------------------------------------------------------------------------- #ifdef _WIN32 #define _PS_EXTERN_CONST(Name, Val) \ const __declspec(align(16)) float _ps_##Name[4] = { Val, Val, Val, Val } #define _PS_EXTERN_CONST_TYPE(Name, Type, Val) \ const __declspec(align(16)) Type _ps_##Name[4] = { Val, Val, Val, Val }; \ #define _EPI32_CONST(Name, Val) \ static const __declspec(align(16)) __int32 _epi32_##Name[4] = { Val, Val, Val, Val } #define _PS_CONST(Name, Val) \ static const __declspec(align(16)) float _ps_##Name[4] = { Val, Val, Val, Val } #elif POSIX #define _PS_EXTERN_CONST(Name, Val) \ const float _ps_##Name[4] __attribute__((aligned(16))) = { Val, Val, Val, Val } #define _PS_EXTERN_CONST_TYPE(Name, Type, Val) \ const Type _ps_##Name[4] __attribute__((aligned(16))) = { Val, Val, Val, Val }; \ #define _EPI32_CONST(Name, Val) \ static const int32 _epi32_##Name[4] __attribute__((aligned(16))) = { Val, Val, Val, Val } #define _PS_CONST(Name, Val) \ static const float _ps_##Name[4] __attribute__((aligned(16))) = { Val, Val, Val, Val } #endif _PS_EXTERN_CONST(am_0, 0.0f); _PS_EXTERN_CONST(am_1, 1.0f); _PS_EXTERN_CONST(am_m1, -1.0f); _PS_EXTERN_CONST(am_0p5, 0.5f); _PS_EXTERN_CONST(am_1p5, 1.5f); _PS_EXTERN_CONST(am_pi, (float)M_PI); _PS_EXTERN_CONST(am_pi_o_2, (float)(M_PI / 2.0)); _PS_EXTERN_CONST(am_2_o_pi, (float)(2.0 / M_PI)); _PS_EXTERN_CONST(am_pi_o_4, (float)(M_PI / 4.0)); _PS_EXTERN_CONST(am_4_o_pi, (float)(4.0 / M_PI)); _PS_EXTERN_CONST_TYPE(am_sign_mask, uint32, 0x80000000); _PS_EXTERN_CONST_TYPE(am_inv_sign_mask, uint32, ~0x80000000); _PS_EXTERN_CONST_TYPE(am_min_norm_pos,uint32, 0x00800000); _PS_EXTERN_CONST_TYPE(am_mant_mask, uint32, 0x7f800000); _PS_EXTERN_CONST_TYPE(am_inv_mant_mask, int32, ~0x7f800000); _EPI32_CONST(1, 1); _EPI32_CONST(2, 2); _PS_CONST(sincos_p0, 0.15707963267948963959e1f); _PS_CONST(sincos_p1, -0.64596409750621907082e0f); _PS_CONST(sincos_p2, 0.7969262624561800806e-1f); _PS_CONST(sincos_p3, -0.468175413106023168e-2f); #ifdef PFN_VECTORMA void __cdecl _SSE_VectorMA( const float *start, float scale, const float *direction, float *dest ); #endif //----------------------------------------------------------------------------- // SSE implementations of optimized routines: //----------------------------------------------------------------------------- float _SSE_Sqrt(float x) { Assert( s_bMathlibInitialized ); float root = 0.f; #ifdef _WIN32 _asm { sqrtss xmm0, x movss root, xmm0 } #elif POSIX _mm_store_ss( &root, _mm_sqrt_ss( _mm_load_ss( &x ) ) ); #endif return root; } // Single iteration NewtonRaphson reciprocal square root: // 0.5 * rsqrtps * (3 - x * rsqrtps(x) * rsqrtps(x)) // Very low error, and fine to use in place of 1.f / sqrtf(x). #if 0 float _SSE_RSqrtAccurate(float x) { Assert( s_bMathlibInitialized ); float rroot; _asm { rsqrtss xmm0, x movss rroot, xmm0 } return (0.5f * rroot) * (3.f - (x * rroot) * rroot); } #else #ifdef POSIX const __m128 f3 = _mm_set_ss(3.0f); // 3 as SSE value const __m128 f05 = _mm_set_ss(0.5f); // 0.5 as SSE value #endif // Intel / Kipps SSE RSqrt. Significantly faster than above. float _SSE_RSqrtAccurate(float a) { #ifdef _WIN32 float x; float half = 0.5f; float three = 3.f; __asm { movss xmm3, a; movss xmm1, half; movss xmm2, three; rsqrtss xmm0, xmm3; mulss xmm3, xmm0; mulss xmm1, xmm0; mulss xmm3, xmm0; subss xmm2, xmm3; mulss xmm1, xmm2; movss x, xmm1; } return x; #elif POSIX __m128 xx = _mm_load_ss( &a ); __m128 xr = _mm_rsqrt_ss( xx ); __m128 xt; xt = _mm_mul_ss( xr, xr ); xt = _mm_mul_ss( xt, xx ); xt = _mm_sub_ss( f3, xt ); xt = _mm_mul_ss( xt, f05 ); xr = _mm_mul_ss( xr, xt ); _mm_store_ss( &a, xr ); return a; #else #error "Not Implemented" #endif } #endif // Simple SSE rsqrt. Usually accurate to around 6 (relative) decimal places // or so, so ok for closed transforms. (ie, computing lighting normals) float _SSE_RSqrtFast(float x) { Assert( s_bMathlibInitialized ); float rroot; #ifdef _WIN32 _asm { rsqrtss xmm0, x movss rroot, xmm0 } #elif POSIX __asm__ __volatile__( "rsqrtss %0, %1" : "=x" (rroot) : "x" (x) ); #else #error #endif return rroot; } float FASTCALL _SSE_VectorNormalize (Vector& vec) { Assert( s_bMathlibInitialized ); // NOTE: This is necessary to prevent an memory overwrite... // sice vec only has 3 floats, we can't "movaps" directly into it. #ifdef _WIN32 __declspec(align(16)) float result[4]; #elif POSIX float result[4] __attribute__((aligned(16))); #endif float *v = &vec[0]; #ifdef _WIN32 float *r = &result[0]; #endif float radius = 0.f; // Blah, get rid of these comparisons ... in reality, if you have all 3 as zero, it shouldn't // be much of a performance win, considering you will very likely miss 3 branch predicts in a row. if ( v[0] || v[1] || v[2] ) { #ifdef _WIN32 _asm { mov eax, v mov edx, r #ifdef ALIGNED_VECTOR movaps xmm4, [eax] // r4 = vx, vy, vz, X movaps xmm1, xmm4 // r1 = r4 #else movups xmm4, [eax] // r4 = vx, vy, vz, X movaps xmm1, xmm4 // r1 = r4 #endif mulps xmm1, xmm4 // r1 = vx * vx, vy * vy, vz * vz, X movhlps xmm3, xmm1 // r3 = vz * vz, X, X, X movaps xmm2, xmm1 // r2 = r1 shufps xmm2, xmm2, 1 // r2 = vy * vy, X, X, X addss xmm1, xmm2 // r1 = (vx * vx) + (vy * vy), X, X, X addss xmm1, xmm3 // r1 = (vx * vx) + (vy * vy) + (vz * vz), X, X, X sqrtss xmm1, xmm1 // r1 = sqrt((vx * vx) + (vy * vy) + (vz * vz)), X, X, X movss radius, xmm1 // radius = sqrt((vx * vx) + (vy * vy) + (vz * vz)) rcpss xmm1, xmm1 // r1 = 1/radius, X, X, X shufps xmm1, xmm1, 0 // r1 = 1/radius, 1/radius, 1/radius, X mulps xmm4, xmm1 // r4 = vx * 1/radius, vy * 1/radius, vz * 1/radius, X movaps [edx], xmm4 // v = vx * 1/radius, vy * 1/radius, vz * 1/radius, X } #elif POSIX __asm__ __volatile__( #ifdef ALIGNED_VECTOR "movaps %2, %%xmm4 \n\t" "movaps %%xmm4, %%xmm1 \n\t" #else "movups %2, %%xmm4 \n\t" "movaps %%xmm4, %%xmm1 \n\t" #endif "mulps %%xmm4, %%xmm1 \n\t" "movhlps %%xmm1, %%xmm3 \n\t" "movaps %%xmm1, %%xmm2 \n\t" "shufps $1, %%xmm2, %%xmm2 \n\t" "addss %%xmm2, %%xmm1 \n\t" "addss %%xmm3, %%xmm1 \n\t" "sqrtss %%xmm1, %%xmm1 \n\t" "movss %%xmm1, %0 \n\t" "rcpss %%xmm1, %%xmm1 \n\t" "shufps $0, %%xmm1, %%xmm1 \n\t" "mulps %%xmm1, %%xmm4 \n\t" "movaps %%xmm4, %1 \n\t" : "=m" (radius), "=m" (result) : "m" (*v) : "xmm1", "xmm2", "xmm3", "xmm4" ); #else #error "Not Implemented" #endif vec.x = result[0]; vec.y = result[1]; vec.z = result[2]; } return radius; } void FASTCALL _SSE_VectorNormalizeFast (Vector& vec) { float ool = _SSE_RSqrtAccurate( FLT_EPSILON + vec.x * vec.x + vec.y * vec.y + vec.z * vec.z ); vec.x *= ool; vec.y *= ool; vec.z *= ool; } float _SSE_InvRSquared(const float* v) { float inv_r2 = 1.f; #ifdef _WIN32 _asm { // Intel SSE only routine mov eax, v movss xmm5, inv_r2 // x5 = 1.0, 0, 0, 0 #ifdef ALIGNED_VECTOR movaps xmm4, [eax] // x4 = vx, vy, vz, X #else movups xmm4, [eax] // x4 = vx, vy, vz, X #endif movaps xmm1, xmm4 // x1 = x4 mulps xmm1, xmm4 // x1 = vx * vx, vy * vy, vz * vz, X movhlps xmm3, xmm1 // x3 = vz * vz, X, X, X movaps xmm2, xmm1 // x2 = x1 shufps xmm2, xmm2, 1 // x2 = vy * vy, X, X, X addss xmm1, xmm2 // x1 = (vx * vx) + (vy * vy), X, X, X addss xmm1, xmm3 // x1 = (vx * vx) + (vy * vy) + (vz * vz), X, X, X maxss xmm1, xmm5 // x1 = max( 1.0, x1 ) rcpss xmm0, xmm1 // x0 = 1 / max( 1.0, x1 ) movss inv_r2, xmm0 // inv_r2 = x0 } #elif POSIX __asm__ __volatile__( "movss %0, %%xmm5 \n\t" #ifdef ALIGNED_VECTOR "movaps %1, %%xmm4 \n\t" #else "movups %1, %%xmm4 \n\t" #endif "movaps %%xmm4, %%xmm1 \n\t" "mulps %%xmm4, %%xmm1 \n\t" "movhlps %%xmm1, %%xmm3 \n\t" "movaps %%xmm1, %%xmm2 \n\t" "shufps $1, %%xmm2, %%xmm2 \n\t" "addss %%xmm2, %%xmm1 \n\t" "addss %%xmm3, %%xmm1 \n\t" "maxss %%xmm5, %%xmm1 \n\t" "rcpss %%xmm1, %%xmm0 \n\t" "movss %%xmm0, %0 \n\t" : "+m" (inv_r2) : "m" (*v) : "xmm0", "xmm1", "xmm2", "xmm3", "xmm4", "xmm5" ); #else #error "Not Implemented" #endif return inv_r2; } #ifdef POSIX // #define _PS_CONST(Name, Val) static const ALIGN16 float _ps_##Name[4] ALIGN16_POST = { Val, Val, Val, Val } #define _PS_CONST_TYPE(Name, Type, Val) static const ALIGN16 Type _ps_##Name[4] ALIGN16_POST = { Val, Val, Val, Val } _PS_CONST_TYPE(sign_mask, int, (int)0x80000000); _PS_CONST_TYPE(inv_sign_mask, int, ~0x80000000); #define _PI32_CONST(Name, Val) static const ALIGN16 int _pi32_##Name[4] ALIGN16_POST = { Val, Val, Val, Val } _PI32_CONST(1, 1); _PI32_CONST(inv1, ~1); _PI32_CONST(2, 2); _PI32_CONST(4, 4); _PI32_CONST(0x7f, 0x7f); _PS_CONST(1 , 1.0f); _PS_CONST(0p5, 0.5f); _PS_CONST(minus_cephes_DP1, -0.78515625); _PS_CONST(minus_cephes_DP2, -2.4187564849853515625e-4); _PS_CONST(minus_cephes_DP3, -3.77489497744594108e-8); _PS_CONST(sincof_p0, -1.9515295891E-4); _PS_CONST(sincof_p1, 8.3321608736E-3); _PS_CONST(sincof_p2, -1.6666654611E-1); _PS_CONST(coscof_p0, 2.443315711809948E-005); _PS_CONST(coscof_p1, -1.388731625493765E-003); _PS_CONST(coscof_p2, 4.166664568298827E-002); _PS_CONST(cephes_FOPI, 1.27323954473516); // 4 / M_PI typedef union xmm_mm_union { __m128 xmm; __m64 mm[2]; } xmm_mm_union; #define COPY_MM_TO_XMM(mm0_, mm1_, xmm_) { xmm_mm_union u; u.mm[0]=mm0_; u.mm[1]=mm1_; xmm_ = u.xmm; } typedef __m128 v4sf; // vector of 4 float (sse1) typedef __m64 v2si; // vector of 2 int (mmx) #endif void _SSE_SinCos(float x, float* s, float* c) { #ifdef _WIN32 float t4, t8, t12; __asm { movss xmm0, x movss t12, xmm0 movss xmm1, _ps_am_inv_sign_mask mov eax, t12 mulss xmm0, _ps_am_2_o_pi andps xmm0, xmm1 and eax, 0x80000000 cvttss2si edx, xmm0 mov ecx, edx mov t12, esi mov esi, edx add edx, 0x1 shl ecx, (31 - 1) shl edx, (31 - 1) movss xmm4, _ps_am_1 cvtsi2ss xmm3, esi mov t8, eax and esi, 0x1 subss xmm0, xmm3 movss xmm3, _sincos_inv_masks[esi * 4] minss xmm0, xmm4 subss xmm4, xmm0 movss xmm6, xmm4 andps xmm4, xmm3 and ecx, 0x80000000 movss xmm2, xmm3 andnps xmm3, xmm0 and edx, 0x80000000 movss xmm7, t8 andps xmm0, xmm2 mov t8, ecx mov t4, edx orps xmm4, xmm3 mov eax, s //mov eax, [esp + 4 + 16] mov edx, c //mov edx, [esp + 4 + 16 + 4] andnps xmm2, xmm6 orps xmm0, xmm2 movss xmm2, t8 movss xmm1, xmm0 movss xmm5, xmm4 xorps xmm7, xmm2 movss xmm3, _ps_sincos_p3 mulss xmm0, xmm0 mulss xmm4, xmm4 movss xmm2, xmm0 movss xmm6, xmm4 orps xmm1, xmm7 movss xmm7, _ps_sincos_p2 mulss xmm0, xmm3 mulss xmm4, xmm3 movss xmm3, _ps_sincos_p1 addss xmm0, xmm7 addss xmm4, xmm7 movss xmm7, _ps_sincos_p0 mulss xmm0, xmm2 mulss xmm4, xmm6 addss xmm0, xmm3 addss xmm4, xmm3 movss xmm3, t4 mulss xmm0, xmm2 mulss xmm4, xmm6 orps xmm5, xmm3 mov esi, t12 addss xmm0, xmm7 addss xmm4, xmm7 mulss xmm0, xmm1 mulss xmm4, xmm5 // use full stores since caller might reload with full loads movss [eax], xmm0 movss [edx], xmm4 } #elif POSIX Assert( "Needs testing, verify impl!\n" ); v4sf xx = _mm_load_ss( &x ); v4sf xmm1, xmm2, xmm3 = _mm_setzero_ps(), sign_bit_sin, y; v2si mm0, mm1, mm2, mm3, mm4, mm5; sign_bit_sin = xx; /* take the absolute value */ xx = _mm_and_ps(xx, *(v4sf*)_ps_inv_sign_mask); /* extract the sign bit (upper one) */ sign_bit_sin = _mm_and_ps(sign_bit_sin, *(v4sf*)_ps_sign_mask); /* scale by 4/Pi */ y = _mm_mul_ps(xx, *(v4sf*)_ps_cephes_FOPI); /* store the integer part of y in mm2:mm3 */ xmm3 = _mm_movehl_ps(xmm3, y); mm2 = _mm_cvttps_pi32(y); mm3 = _mm_cvttps_pi32(xmm3); /* j=(j+1) & (~1) (see the cephes sources) */ mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1); mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1); mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1); mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1); y = _mm_cvtpi32x2_ps(mm2, mm3); mm4 = mm2; mm5 = mm3; /* get the swap sign flag for the sine */ mm0 = _mm_and_si64(mm2, *(v2si*)_pi32_4); mm1 = _mm_and_si64(mm3, *(v2si*)_pi32_4); mm0 = _mm_slli_pi32(mm0, 29); mm1 = _mm_slli_pi32(mm1, 29); v4sf swap_sign_bit_sin; COPY_MM_TO_XMM(mm0, mm1, swap_sign_bit_sin); /* get the polynom selection mask for the sine */ mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2); mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2); mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64()); mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64()); v4sf poly_mask; COPY_MM_TO_XMM(mm2, mm3, poly_mask); /* The magic pass: "Extended precision modular arithmetic" x = ((x - y * DP1) - y * DP2) - y * DP3; */ xmm1 = *(v4sf*)_ps_minus_cephes_DP1; xmm2 = *(v4sf*)_ps_minus_cephes_DP2; xmm3 = *(v4sf*)_ps_minus_cephes_DP3; xmm1 = _mm_mul_ps(y, xmm1); xmm2 = _mm_mul_ps(y, xmm2); xmm3 = _mm_mul_ps(y, xmm3); xx = _mm_add_ps(xx, xmm1); xx = _mm_add_ps(xx, xmm2); xx = _mm_add_ps(xx, xmm3); /* get the sign flag for the cosine */ mm4 = _mm_sub_pi32(mm4, *(v2si*)_pi32_2); mm5 = _mm_sub_pi32(mm5, *(v2si*)_pi32_2); mm4 = _mm_andnot_si64(mm4, *(v2si*)_pi32_4); mm5 = _mm_andnot_si64(mm5, *(v2si*)_pi32_4); mm4 = _mm_slli_pi32(mm4, 29); mm5 = _mm_slli_pi32(mm5, 29); v4sf sign_bit_cos; COPY_MM_TO_XMM(mm4, mm5, sign_bit_cos); _mm_empty(); /* good-bye mmx */ sign_bit_sin = _mm_xor_ps(sign_bit_sin, swap_sign_bit_sin); /* Evaluate the first polynom (0 <= x <= Pi/4) */ v4sf z = _mm_mul_ps(xx,xx); y = *(v4sf*)_ps_coscof_p0; y = _mm_mul_ps(y, z); y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1); y = _mm_mul_ps(y, z); y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2); y = _mm_mul_ps(y, z); y = _mm_mul_ps(y, z); v4sf tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5); y = _mm_sub_ps(y, tmp); y = _mm_add_ps(y, *(v4sf*)_ps_1); /* Evaluate the second polynom (Pi/4 <= x <= 0) */ v4sf y2 = *(v4sf*)_ps_sincof_p0; y2 = _mm_mul_ps(y2, z); y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1); y2 = _mm_mul_ps(y2, z); y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2); y2 = _mm_mul_ps(y2, z); y2 = _mm_mul_ps(y2, xx); y2 = _mm_add_ps(y2, xx); /* select the correct result from the two polynoms */ xmm3 = poly_mask; v4sf ysin2 = _mm_and_ps(xmm3, y2); v4sf ysin1 = _mm_andnot_ps(xmm3, y); y2 = _mm_sub_ps(y2,ysin2); y = _mm_sub_ps(y, ysin1); xmm1 = _mm_add_ps(ysin1,ysin2); xmm2 = _mm_add_ps(y,y2); /* update the sign */ _mm_store_ss( s, _mm_xor_ps(xmm1, sign_bit_sin) ); _mm_store_ss( c, _mm_xor_ps(xmm2, sign_bit_cos) ); #else #error "Not Implemented" #endif } float _SSE_cos( float x ) { #ifdef _WIN32 float temp; __asm { movss xmm0, x movss xmm1, _ps_am_inv_sign_mask andps xmm0, xmm1 addss xmm0, _ps_am_pi_o_2 mulss xmm0, _ps_am_2_o_pi cvttss2si ecx, xmm0 movss xmm5, _ps_am_1 mov edx, ecx shl edx, (31 - 1) cvtsi2ss xmm1, ecx and edx, 0x80000000 and ecx, 0x1 subss xmm0, xmm1 movss xmm6, _sincos_masks[ecx * 4] minss xmm0, xmm5 movss xmm1, _ps_sincos_p3 subss xmm5, xmm0 andps xmm5, xmm6 movss xmm7, _ps_sincos_p2 andnps xmm6, xmm0 mov temp, edx orps xmm5, xmm6 movss xmm0, xmm5 mulss xmm5, xmm5 movss xmm4, _ps_sincos_p1 movss xmm2, xmm5 mulss xmm5, xmm1 movss xmm1, _ps_sincos_p0 addss xmm5, xmm7 mulss xmm5, xmm2 movss xmm3, temp addss xmm5, xmm4 mulss xmm5, xmm2 orps xmm0, xmm3 addss xmm5, xmm1 mulss xmm0, xmm5 movss x, xmm0 } #elif POSIX Assert( "Needs testing, verify impl!\n" ); v4sf xmm1, xmm2 = _mm_setzero_ps(), xmm3, y; v2si mm0, mm1, mm2, mm3; /* take the absolute value */ v4sf xx = _mm_load_ss( &x ); xx = _mm_and_ps(xx, *(v4sf*)_ps_inv_sign_mask); /* scale by 4/Pi */ y = _mm_mul_ps(xx, *(v4sf*)_ps_cephes_FOPI); /* store the integer part of y in mm0:mm1 */ xmm2 = _mm_movehl_ps(xmm2, y); mm2 = _mm_cvttps_pi32(y); mm3 = _mm_cvttps_pi32(xmm2); /* j=(j+1) & (~1) (see the cephes sources) */ mm2 = _mm_add_pi32(mm2, *(v2si*)_pi32_1); mm3 = _mm_add_pi32(mm3, *(v2si*)_pi32_1); mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_inv1); mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_inv1); y = _mm_cvtpi32x2_ps(mm2, mm3); mm2 = _mm_sub_pi32(mm2, *(v2si*)_pi32_2); mm3 = _mm_sub_pi32(mm3, *(v2si*)_pi32_2); /* get the swap sign flag in mm0:mm1 and the polynom selection mask in mm2:mm3 */ mm0 = _mm_andnot_si64(mm2, *(v2si*)_pi32_4); mm1 = _mm_andnot_si64(mm3, *(v2si*)_pi32_4); mm0 = _mm_slli_pi32(mm0, 29); mm1 = _mm_slli_pi32(mm1, 29); mm2 = _mm_and_si64(mm2, *(v2si*)_pi32_2); mm3 = _mm_and_si64(mm3, *(v2si*)_pi32_2); mm2 = _mm_cmpeq_pi32(mm2, _mm_setzero_si64()); mm3 = _mm_cmpeq_pi32(mm3, _mm_setzero_si64()); v4sf sign_bit, poly_mask; COPY_MM_TO_XMM(mm0, mm1, sign_bit); COPY_MM_TO_XMM(mm2, mm3, poly_mask); _mm_empty(); /* good-bye mmx */ /* The magic pass: "Extended precision modular arithmetic" x = ((x - y * DP1) - y * DP2) - y * DP3; */ xmm1 = *(v4sf*)_ps_minus_cephes_DP1; xmm2 = *(v4sf*)_ps_minus_cephes_DP2; xmm3 = *(v4sf*)_ps_minus_cephes_DP3; xmm1 = _mm_mul_ps(y, xmm1); xmm2 = _mm_mul_ps(y, xmm2); xmm3 = _mm_mul_ps(y, xmm3); xx = _mm_add_ps(xx, xmm1); xx = _mm_add_ps(xx, xmm2); xx = _mm_add_ps(xx, xmm3); /* Evaluate the first polynom (0 <= x <= Pi/4) */ y = *(v4sf*)_ps_coscof_p0; v4sf z = _mm_mul_ps(xx,xx); y = _mm_mul_ps(y, z); y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p1); y = _mm_mul_ps(y, z); y = _mm_add_ps(y, *(v4sf*)_ps_coscof_p2); y = _mm_mul_ps(y, z); y = _mm_mul_ps(y, z); v4sf tmp = _mm_mul_ps(z, *(v4sf*)_ps_0p5); y = _mm_sub_ps(y, tmp); y = _mm_add_ps(y, *(v4sf*)_ps_1); /* Evaluate the second polynom (Pi/4 <= x <= 0) */ v4sf y2 = *(v4sf*)_ps_sincof_p0; y2 = _mm_mul_ps(y2, z); y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p1); y2 = _mm_mul_ps(y2, z); y2 = _mm_add_ps(y2, *(v4sf*)_ps_sincof_p2); y2 = _mm_mul_ps(y2, z); y2 = _mm_mul_ps(y2, xx); y2 = _mm_add_ps(y2, xx); /* select the correct result from the two polynoms */ xmm3 = poly_mask; y2 = _mm_and_ps(xmm3, y2); //, xmm3); y = _mm_andnot_ps(xmm3, y); y = _mm_add_ps(y,y2); /* update the sign */ _mm_store_ss( &x, _mm_xor_ps(y, sign_bit) ); #else #error "Not Implemented" #endif return x; } //----------------------------------------------------------------------------- // SSE2 implementations of optimized routines: //----------------------------------------------------------------------------- #ifdef PLATFORM_WINDOWS_PC32 void _SSE2_SinCos(float x, float* s, float* c) // any x { #ifdef _WIN32 __asm { movss xmm0, x movaps xmm7, xmm0 movss xmm1, _ps_am_inv_sign_mask movss xmm2, _ps_am_sign_mask movss xmm3, _ps_am_2_o_pi andps xmm0, xmm1 andps xmm7, xmm2 mulss xmm0, xmm3 pxor xmm3, xmm3 movd xmm5, _epi32_1 movss xmm4, _ps_am_1 cvttps2dq xmm2, xmm0 pand xmm5, xmm2 movd xmm1, _epi32_2 pcmpeqd xmm5, xmm3 movd xmm3, _epi32_1 cvtdq2ps xmm6, xmm2 paddd xmm3, xmm2 pand xmm2, xmm1 pand xmm3, xmm1 subss xmm0, xmm6 pslld xmm2, (31 - 1) minss xmm0, xmm4 mov eax, s // mov eax, [esp + 4 + 16] mov edx, c // mov edx, [esp + 4 + 16 + 4] subss xmm4, xmm0 pslld xmm3, (31 - 1) movaps xmm6, xmm4 xorps xmm2, xmm7 movaps xmm7, xmm5 andps xmm6, xmm7 andnps xmm7, xmm0 andps xmm0, xmm5 andnps xmm5, xmm4 movss xmm4, _ps_sincos_p3 orps xmm6, xmm7 orps xmm0, xmm5 movss xmm5, _ps_sincos_p2 movaps xmm1, xmm0 movaps xmm7, xmm6 mulss xmm0, xmm0 mulss xmm6, xmm6 orps xmm1, xmm2 orps xmm7, xmm3 movaps xmm2, xmm0 movaps xmm3, xmm6 mulss xmm0, xmm4 mulss xmm6, xmm4 movss xmm4, _ps_sincos_p1 addss xmm0, xmm5 addss xmm6, xmm5 movss xmm5, _ps_sincos_p0 mulss xmm0, xmm2 mulss xmm6, xmm3 addss xmm0, xmm4 addss xmm6, xmm4 mulss xmm0, xmm2 mulss xmm6, xmm3 addss xmm0, xmm5 addss xmm6, xmm5 mulss xmm0, xmm1 mulss xmm6, xmm7 // use full stores since caller might reload with full loads movss [eax], xmm0 movss [edx], xmm6 } #elif POSIX #warning "_SSE2_SinCos NOT implemented!" Assert( 0 ); #else #error "Not Implemented" #endif } #endif // PLATFORM_WINDOWS_PC32 #ifdef PLATFORM_WINDOWS_PC32 float _SSE2_cos(float x) { #ifdef _WIN32 __asm { movss xmm0, x movss xmm1, _ps_am_inv_sign_mask movss xmm2, _ps_am_pi_o_2 movss xmm3, _ps_am_2_o_pi andps xmm0, xmm1 addss xmm0, xmm2 mulss xmm0, xmm3 pxor xmm3, xmm3 movd xmm5, _epi32_1 movss xmm4, _ps_am_1 cvttps2dq xmm2, xmm0 pand xmm5, xmm2 movd xmm1, _epi32_2 pcmpeqd xmm5, xmm3 cvtdq2ps xmm6, xmm2 pand xmm2, xmm1 pslld xmm2, (31 - 1) subss xmm0, xmm6 movss xmm3, _ps_sincos_p3 minss xmm0, xmm4 subss xmm4, xmm0 andps xmm0, xmm5 andnps xmm5, xmm4 orps xmm0, xmm5 movaps xmm1, xmm0 movss xmm4, _ps_sincos_p2 mulss xmm0, xmm0 movss xmm5, _ps_sincos_p1 orps xmm1, xmm2 movaps xmm7, xmm0 mulss xmm0, xmm3 movss xmm6, _ps_sincos_p0 addss xmm0, xmm4 mulss xmm0, xmm7 addss xmm0, xmm5 mulss xmm0, xmm7 addss xmm0, xmm6 mulss xmm0, xmm1 movss x, xmm0 } #elif POSIX #warning "_SSE2_cos NOT implemented!" Assert( 0 ); #else #error "Not Implemented" #endif return x; } #endif // PLATFORM_WINDOWS_PC32 #if 0 // SSE Version of VectorTransform void VectorTransformSSE(const float *in1, const matrix3x4_t& in2, float *out1) { Assert( s_bMathlibInitialized ); Assert( in1 != out1 ); #ifdef _WIN32 __asm { mov eax, in1; mov ecx, in2; mov edx, out1; movss xmm0, [eax]; mulss xmm0, [ecx]; movss xmm1, [eax+4]; mulss xmm1, [ecx+4]; movss xmm2, [eax+8]; mulss xmm2, [ecx+8]; addss xmm0, xmm1; addss xmm0, xmm2; addss xmm0, [ecx+12] movss [edx], xmm0; add ecx, 16; movss xmm0, [eax]; mulss xmm0, [ecx]; movss xmm1, [eax+4]; mulss xmm1, [ecx+4]; movss xmm2, [eax+8]; mulss xmm2, [ecx+8]; addss xmm0, xmm1; addss xmm0, xmm2; addss xmm0, [ecx+12] movss [edx+4], xmm0; add ecx, 16; movss xmm0, [eax]; mulss xmm0, [ecx]; movss xmm1, [eax+4]; mulss xmm1, [ecx+4]; movss xmm2, [eax+8]; mulss xmm2, [ecx+8]; addss xmm0, xmm1; addss xmm0, xmm2; addss xmm0, [ecx+12] movss [edx+8], xmm0; } #elif POSIX #warning "VectorTransformSSE C implementation only" out1[0] = DotProduct(in1, in2[0]) + in2[0][3]; out1[1] = DotProduct(in1, in2[1]) + in2[1][3]; out1[2] = DotProduct(in1, in2[2]) + in2[2][3]; #else #error "Not Implemented" #endif } #endif #if 0 void VectorRotateSSE( const float *in1, const matrix3x4_t& in2, float *out1 ) { Assert( s_bMathlibInitialized ); Assert( in1 != out1 ); #ifdef _WIN32 __asm { mov eax, in1; mov ecx, in2; mov edx, out1; movss xmm0, [eax]; mulss xmm0, [ecx]; movss xmm1, [eax+4]; mulss xmm1, [ecx+4]; movss xmm2, [eax+8]; mulss xmm2, [ecx+8]; addss xmm0, xmm1; addss xmm0, xmm2; movss [edx], xmm0; add ecx, 16; movss xmm0, [eax]; mulss xmm0, [ecx]; movss xmm1, [eax+4]; mulss xmm1, [ecx+4]; movss xmm2, [eax+8]; mulss xmm2, [ecx+8]; addss xmm0, xmm1; addss xmm0, xmm2; movss [edx+4], xmm0; add ecx, 16; movss xmm0, [eax]; mulss xmm0, [ecx]; movss xmm1, [eax+4]; mulss xmm1, [ecx+4]; movss xmm2, [eax+8]; mulss xmm2, [ecx+8]; addss xmm0, xmm1; addss xmm0, xmm2; movss [edx+8], xmm0; } #elif POSIX #warning "VectorRotateSSE C implementation only" out1[0] = DotProduct( in1, in2[0] ); out1[1] = DotProduct( in1, in2[1] ); out1[2] = DotProduct( in1, in2[2] ); #else #error "Not Implemented" #endif } #endif #ifdef _WIN32 void _declspec(naked) _SSE_VectorMA( const float *start, float scale, const float *direction, float *dest ) { // FIXME: This don't work!! It will overwrite memory in the write to dest Assert(0); Assert( s_bMathlibInitialized ); _asm { // Intel SSE only routine mov eax, DWORD PTR [esp+0x04] ; *start, s0..s2 mov ecx, DWORD PTR [esp+0x0c] ; *direction, d0..d2 mov edx, DWORD PTR [esp+0x10] ; *dest movss xmm2, [esp+0x08] ; x2 = scale, 0, 0, 0 #ifdef ALIGNED_VECTOR movaps xmm3, [ecx] ; x3 = dir0,dir1,dir2,X pshufd xmm2, xmm2, 0 ; x2 = scale, scale, scale, scale movaps xmm1, [eax] ; x1 = start1, start2, start3, X mulps xmm3, xmm2 ; x3 *= x2 addps xmm3, xmm1 ; x3 += x1 movaps [edx], xmm3 ; *dest = x3 #else movups xmm3, [ecx] ; x3 = dir0,dir1,dir2,X pshufd xmm2, xmm2, 0 ; x2 = scale, scale, scale, scale movups xmm1, [eax] ; x1 = start1, start2, start3, X mulps xmm3, xmm2 ; x3 *= x2 addps xmm3, xmm1 ; x3 += x1 movups [edx], xmm3 ; *dest = x3 #endif } } #endif #ifdef _WIN32 #ifdef PFN_VECTORMA void _declspec(naked) __cdecl _SSE_VectorMA( const Vector &start, float scale, const Vector &direction, Vector &dest ) { // FIXME: This don't work!! It will overwrite memory in the write to dest Assert(0); Assert( s_bMathlibInitialized ); _asm { // Intel SSE only routine mov eax, DWORD PTR [esp+0x04] ; *start, s0..s2 mov ecx, DWORD PTR [esp+0x0c] ; *direction, d0..d2 mov edx, DWORD PTR [esp+0x10] ; *dest movss xmm2, [esp+0x08] ; x2 = scale, 0, 0, 0 #ifdef ALIGNED_VECTOR movaps xmm3, [ecx] ; x3 = dir0,dir1,dir2,X pshufd xmm2, xmm2, 0 ; x2 = scale, scale, scale, scale movaps xmm1, [eax] ; x1 = start1, start2, start3, X mulps xmm3, xmm2 ; x3 *= x2 addps xmm3, xmm1 ; x3 += x1 movaps [edx], xmm3 ; *dest = x3 #else movups xmm3, [ecx] ; x3 = dir0,dir1,dir2,X pshufd xmm2, xmm2, 0 ; x2 = scale, scale, scale, scale movups xmm1, [eax] ; x1 = start1, start2, start3, X mulps xmm3, xmm2 ; x3 *= x2 addps xmm3, xmm1 ; x3 += x1 movups [edx], xmm3 ; *dest = x3 #endif } } float (__cdecl *pfVectorMA)(Vector& v) = _VectorMA; #endif #endif // SSE DotProduct -- it's a smidgen faster than the asm DotProduct... // Should be validated too! :) // NJS: (Nov 1 2002) -NOT- faster. may time a couple cycles faster in a single function like // this, but when inlined, and instruction scheduled, the C version is faster. // Verified this via VTune /* vec_t DotProduct (const vec_t *a, const vec_t *c) { vec_t temp; __asm { mov eax, a; mov ecx, c; mov edx, DWORD PTR [temp] movss xmm0, [eax]; mulss xmm0, [ecx]; movss xmm1, [eax+4]; mulss xmm1, [ecx+4]; movss xmm2, [eax+8]; mulss xmm2, [ecx+8]; addss xmm0, xmm1; addss xmm0, xmm2; movss [edx], xmm0; fld DWORD PTR [edx]; ret } } */ #endif // COMPILER_MSVC64