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sse.cpp
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//========= Copyright Valve Corporation, All rights reserved. ============//
//
// Purpose: SSE Math primitives.
//
//=====================================================================================//
#include <math.h>
#include <float.h> // Needed for FLT_EPSILON
#include "basetypes.h"
#include <memory.h>
#include "tier0/dbg.h"
#include "mathlib/mathlib.h"
#include "mathlib/vector.h"
#if defined(__arm__) || defined(__aarch64__)
#include "sse2neon.h"
#endif
#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;
#if defined(__arm__) || defined(__aarch64__)
rroot = _SSE_RSqrtAccurate(x);
#elif _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];
float *r = &result[0];
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] )
{
#if defined(__arm__) || defined(__aarch64__)
float rsqrt = _SSE_RSqrtAccurate( v[0] * v[0] + v[1] * v[1] + v[2] * v[2] );
r[0] = v[0] * rsqrt;
r[1] = v[1] * rsqrt;
r[2] = v[2] * rsqrt;
#elif _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;
#if defined(__arm__) || defined(__aarch64__)
return _SSE_RSqrtAccurate( FLT_EPSILON + v[0] * v[0] + v[1] * v[1] + v[2] * v[2] );
#elif _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)
{
#if defined(__arm__) || defined(__aarch64__)
#if defined( OSX )
__sincosf(x, s, c);
#elif defined( POSIX )
sincosf(x, s, c);
#else
*s = sin( x );
*c = cos( x );
#endif
#elif _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 )
{
#if defined(__arm__) || defined(__aarch64__)
return cos(x);
#elif _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];