bullet3/Extras/simdmathlibrary/spu/simdmath/sincosd2.h

/* sind2 and cosd2
   Copyright (C) 2006, 2007 Sony Computer Entertainment Inc.
   All rights reserved.

   Redistribution and use in source and binary forms,
   with or without modification, are permitted provided that the
   following conditions are met:
    * Redistributions of source code must retain the above copyright
      notice, this list of conditions and the following disclaimer.
    * Redistributions in binary form must reproduce the above copyright
      notice, this list of conditions and the following disclaimer in the
      documentation and/or other materials provided with the distribution.
    * Neither the name of the Sony Computer Entertainment Inc nor the names
      of its contributors may be used to endorse or promote products derived
      from this software without specific prior written permission.

   THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
   AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
   ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
   LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
   CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
   SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
   INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
   CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
   ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
   POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef ___SIMD_MATH__SINCOSD2_H___
#define ___SIMD_MATH__SINCOSD2_H___

#include <simdmath.h>
#include <spu_intrinsics.h>

#include <simdmath/_sincos.h>
#include <simdmath/isgreaterd2.h>
#include <simdmath/isnand2.h>
#include <simdmath/is0denormd2.h>

//
//     Computes the sine  of the each of two double slots. 
//
static inline void
_sincosd2(vector double x, vec_double2 *s, vec_double2 *c)
{
  vec_double2 xl,xl2,xl3;
  vec_double2 nan = (vec_double2)spu_splats(0x7ff8000000000000ull);
  vec_uchar16 copyEven = (vec_uchar16)(vec_uint4){ 0x00010203, 0x00010203, 0x08090a0b, 0x08090a0b };
  vec_double2 tiny = (vec_double2)spu_splats(0x3e40000000000000ull);
  vec_double2 ts, tc;

  // Range reduction using : x = angle * TwoOverPi;
  //  
  xl = spu_mul(x, spu_splats(0.63661977236758134307553505349005744));

  // Find the quadrant the angle falls in
  // using:  q = (int) (ceil(abs(x))*sign(x))
  //
  xl = spu_add(xl,spu_sel(spu_splats(0.5),xl,spu_splats(0x8000000000000000ull)));
  vec_float4 xf = spu_roundtf(xl);
  vec_int4 q = spu_convts(xf,0);
  q = spu_shuffle(q,q,copyEven);

     
  // Compute an offset based on the quadrant that the angle falls in
  // 
  vec_int4 offsetSin = spu_and(q,spu_splats(0x3));
  vec_int4 offsetCos = spu_add(spu_splats(1),offsetSin);

  // Remainder in range [-pi/4..pi/4]
  //
  vec_float4 qf = spu_convtf(q,0);
  vec_double2 qd = spu_extend(qf);
  vec_double2 p1 = spu_nmsub(qd,spu_splats(__SINCOSD_KC1),x);
  xl = spu_nmsub(qd,spu_splats(__SINCOSD_KC2),p1);

  // Check if |xl| is a really small number
  //
  vec_double2 absXl = (vec_double2)spu_andc((vec_ullong2)xl, spu_splats(0x8000000000000000ull));
  vec_ullong2 isTiny = (vec_ullong2)_isgreaterd2(tiny,absXl);
 
  // Compute x^2 and x^3
  //
  xl2 = spu_mul(xl,xl);
  xl3 = spu_mul(xl2,xl);
    
  // Compute both the sin and cos of the angles
  // using a polynomial expression:
  //   cx = 1.0f + xl2 * ((((((c0 * xl2 + c1) * xl2 + c2) * xl2 + c3) * xl2 + c4) * xl2 + c5), and
  //   sx = xl + xl3 * (((((s0 * xl2 + s1) * xl2 + s2) * xl2 + s3) * xl2 + s4) * xl2 + s5)
  //

  vec_double2 ct0 = spu_mul(xl2,xl2);
  vec_double2 ct1 = spu_madd(spu_splats(__SINCOSD_CC0),xl2,spu_splats(__SINCOSD_CC1));
  vec_double2 ct2 = spu_madd(spu_splats(__SINCOSD_CC2),xl2,spu_splats(__SINCOSD_CC3));
  vec_double2 ct3 = spu_madd(spu_splats(__SINCOSD_CC4),xl2,spu_splats(__SINCOSD_CC5));
  vec_double2 st1 = spu_madd(spu_splats(__SINCOSD_SC0),xl2,spu_splats(__SINCOSD_SC1));
  vec_double2 st2 = spu_madd(spu_splats(__SINCOSD_SC2),xl2,spu_splats(__SINCOSD_SC3));
  vec_double2 st3 = spu_madd(spu_splats(__SINCOSD_SC4),xl2,spu_splats(__SINCOSD_SC5));
  vec_double2 ct4 = spu_madd(ct2,ct0,ct3);
  vec_double2 st4 = spu_madd(st2,ct0,st3);
  vec_double2 ct5 = spu_mul(ct0,ct0);
    
  vec_double2 ct6 = spu_madd(ct5,ct1,ct4);
  vec_double2 st6 = spu_madd(ct5,st1,st4);

  vec_double2 cx = spu_madd(ct6,xl2,spu_splats(1.0));
  vec_double2 sx = spu_madd(st6,xl3,xl);

  // Small angle approximation: sin(tiny) = tiny, cos(tiny) = 1.0
  //
  sx = spu_sel(sx,xl,isTiny);
  cx = spu_sel(cx,spu_splats(1.0),isTiny);

  // Use the cosine when the offset is odd and the sin
  // when the offset is even
  //
  vec_ullong2 sinMask = (vec_ullong2)spu_cmpeq(spu_and(offsetSin,(int)0x1),spu_splats((int)0));
  vec_ullong2 cosMask = (vec_ullong2)spu_cmpeq(spu_and(offsetCos,(int)0x1),spu_splats((int)0));
  ts = spu_sel(cx,sx,sinMask);
  tc = spu_sel(cx,sx,cosMask);

  // Flip the sign of the result when (offset mod 4) = 1 or 2
  //
  sinMask = (vec_ullong2)spu_cmpeq(spu_and(offsetSin,(int)0x2),spu_splats((int)0));
  sinMask = spu_shuffle(sinMask,sinMask,copyEven);
  ts = spu_sel((vec_double2)spu_xor(spu_splats(0x8000000000000000ull),(vec_ullong2)ts),ts,sinMask);
  
  cosMask = (vec_ullong2)spu_cmpeq(spu_and(offsetCos,(int)0x2),spu_splats((int)0));
  cosMask = spu_shuffle(cosMask,cosMask,copyEven);
  tc = spu_sel((vec_double2)spu_xor(spu_splats(0x8000000000000000ull),(vec_ullong2)tc),tc,cosMask);

  // if input = +/-Inf return NAN
  //
  ts = spu_sel(ts, nan, _isnand2 (x));
  tc = spu_sel(tc, nan, _isnand2 (x));

  // if input = 0 or denorm return 'result0'
  //
  vec_ullong2 zeroMask = _is0denormd2 (x);
  ts = spu_sel(ts,x,zeroMask);
  tc = spu_sel(tc,spu_splats(1.0),zeroMask);

  *s = ts;
  *c = tc;
}

#endif