2007-09-29 02:44:24 +08:00
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/* -------------------------------------------------------------- */
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2008-09-05 01:50:56 +08:00
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/* (C)Copyright 2001,2008, */
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2007-09-29 02:44:24 +08:00
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/* International Business Machines Corporation, */
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/* Sony Computer Entertainment, Incorporated, */
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/* Toshiba Corporation, */
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/* */
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/* All Rights Reserved. */
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/* */
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/* Redistribution and use in source and binary forms, with or */
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/* without modification, are permitted provided that the */
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/* following conditions are met: */
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/* */
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/* - Redistributions of source code must retain the above copyright*/
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/* notice, this list of conditions and the following disclaimer. */
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/* */
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/* - Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* - Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* */
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/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
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/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
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/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
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/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
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/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
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/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
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/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
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/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
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/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
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/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
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/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
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/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
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/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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/* -------------------------------------------------------------- */
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/* PROLOG END TAG zYx */
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#ifdef __SPU__
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#ifndef _COS_SIN_H_
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#define _COS_SIN_H_ 1
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#define M_PI_OVER_4_HI_32 0x3fe921fb
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#define M_PI_OVER_4 0.78539816339744827900
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#define M_FOUR_OVER_PI 1.27323954478442180616
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#define M_PI_OVER_2 1.57079632679489655800
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#define M_PI_OVER_2_HI 1.57079632673412561417
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#define M_PI_OVER_2_LO 0.0000000000607710050650619224932
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#define M_PI_OVER_2F_HI 1.570312500000000000
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#define M_PI_OVER_2F_LO 0.000483826794896558
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/* The following coefficients correspond to the Taylor series
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* coefficients for cos and sin.
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*/
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#define COS_14 -0.00000000001138218794258068723867
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#define COS_12 0.000000002087614008917893178252
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#define COS_10 -0.0000002755731724204127572108
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#define COS_08 0.00002480158729870839541888
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#define COS_06 -0.001388888888888735934799
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#define COS_04 0.04166666666666666534980
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#define COS_02 -0.5000000000000000000000
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#define COS_00 1.0
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#define SIN_15 -0.00000000000076471637318198164759
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#define SIN_13 0.00000000016059043836821614599
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#define SIN_11 -0.000000025052108385441718775
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#define SIN_09 0.0000027557319223985890653
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#define SIN_07 -0.0001984126984126984127
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#define SIN_05 0.008333333333333333333
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#define SIN_03 -0.16666666666666666666
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#define SIN_01 1.0
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/* Compute the following for each floating point element of x.
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* x = fmod(x, PI/4);
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* ix = (int)x * PI/4;
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* This allows one to compute cos / sin over the limited range
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* and select the sign and correct result based upon the octant
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* of the original angle (as defined by the ix result).
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*
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* Expected Inputs Types:
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* x = vec_float4
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* ix = vec_int4
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*/
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#define MOD_PI_OVER_FOUR_F(_x, _ix) { \
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vec_float4 fx; \
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\
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_ix = spu_convts(spu_mul(_x, spu_splats((float)M_FOUR_OVER_PI)), 0); \
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_ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)_x, -31), 1)); \
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\
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fx = spu_convtf(spu_rlmaska(_ix, -1), 0); \
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_x = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_HI), _x); \
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_x = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_LO), _x); \
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}
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/* Double precision MOD_PI_OVER_FOUR
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*
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* Expected Inputs Types:
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* x = vec_double2
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* ix = vec_int4
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*/
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#define MOD_PI_OVER_FOUR(_x, _ix) { \
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vec_float4 fx; \
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vec_double2 dix; \
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\
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fx = spu_roundtf(spu_mul(_x, spu_splats(M_FOUR_OVER_PI))); \
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_ix = spu_convts(fx, 0); \
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_ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)fx, -31), 1)); \
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\
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dix = spu_extend(spu_convtf(spu_rlmaska(_ix, -1), 0)); \
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_x = spu_nmsub(spu_splats(M_PI_OVER_2_HI), dix, _x); \
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_x = spu_nmsub(spu_splats(M_PI_OVER_2_LO), dix, _x); \
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}
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/* Compute the cos(x) and sin(x) for the range reduced angle x.
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* In order to compute these trig functions to full single precision
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* accuracy, we solve the Taylor series.
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*
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* c = cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - x^10/10!
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* s = sin(x) = x - x^3/4! + x^5/5! - x^7/7! + x^9/9! - x^11/11!
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*
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* Expected Inputs Types:
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* x = vec_float4
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* c = vec_float4
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* s = vec_float4
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*/
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#define COMPUTE_COS_SIN_F(_x, _c, _s) { \
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vec_float4 x2, x4, x6; \
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vec_float4 cos_hi, cos_lo; \
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vec_float4 sin_hi, sin_lo; \
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\
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x2 = spu_mul(_x, _x); \
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x4 = spu_mul(x2, x2); \
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x6 = spu_mul(x2, x4); \
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\
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cos_hi = spu_madd(spu_splats((float)COS_10), x2, spu_splats((float)COS_08)); \
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cos_lo = spu_madd(spu_splats((float)COS_04), x2, spu_splats((float)COS_02)); \
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cos_hi = spu_madd(cos_hi, x2, spu_splats((float)COS_06)); \
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cos_lo = spu_madd(cos_lo, x2, spu_splats((float)COS_00)); \
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_c = spu_madd(cos_hi, x6, cos_lo); \
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\
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sin_hi = spu_madd(spu_splats((float)SIN_11), x2, spu_splats((float)SIN_09)); \
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sin_lo = spu_madd(spu_splats((float)SIN_05), x2, spu_splats((float)SIN_03)); \
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sin_hi = spu_madd(sin_hi, x2, spu_splats((float)SIN_07)); \
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sin_lo = spu_madd(sin_lo, x2, spu_splats((float)SIN_01)); \
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_s = spu_madd(sin_hi, x6, sin_lo); \
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_s = spu_mul(_s, _x); \
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}
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/* Compute the cos(x) and sin(x) for the range reduced angle x.
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* This version computes the cosine and sine to double precision
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* accuracy using the Taylor series:
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*
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* c = cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - x^10/10! + x^12/12! - x^14/14!
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* s = sin(x) = x - x^3/4! + x^5/5! - x^7/7! + x^9/9! - x^11/11! + x^13/13! - x^15/15!
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*
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* Expected Inputs Types:
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* x = vec_double2
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* c = vec_double2
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* s = vec_double2
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*/
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#define COMPUTE_COS_SIN(_x, _c, _s) { \
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vec_double2 x2, x4, x8; \
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vec_double2 cos_hi, cos_lo; \
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vec_double2 sin_hi, sin_lo; \
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\
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x2 = spu_mul(_x, _x); \
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x4 = spu_mul(x2, x2); \
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x8 = spu_mul(x4, x4); \
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\
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cos_hi = spu_madd(spu_splats(COS_14), x2, spu_splats(COS_12)); \
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cos_lo = spu_madd(spu_splats(COS_06), x2, spu_splats(COS_04)); \
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cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_10)); \
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cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_02)); \
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cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_08)); \
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cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_00)); \
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_c = spu_madd(cos_hi, x8, cos_lo); \
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\
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sin_hi = spu_madd(spu_splats(SIN_15), x2, spu_splats(SIN_13)); \
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sin_lo = spu_madd(spu_splats(SIN_07), x2, spu_splats(SIN_05)); \
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sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_11)); \
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sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_03)); \
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sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_09)); \
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sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_01)); \
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_s = spu_madd(sin_hi, x8, sin_lo); \
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_s = spu_mul(_s, _x); \
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}
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#endif /* _COS_SIN_H_ */
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#endif /* __SPU__ */
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