/* -------------------------------------------------------------- */ /* (C)Copyright 2001,2008, */ /* International Business Machines Corporation, */ /* Sony Computer Entertainment, Incorporated, */ /* Toshiba Corporation, */ /* */ /* 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 IBM Corporation 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. */ /* -------------------------------------------------------------- */ /* PROLOG END TAG zYx */ #ifdef __SPU__ #ifndef _COS_SIN_H_ #define _COS_SIN_H_ 1 #define M_PI_OVER_4_HI_32 0x3fe921fb #define M_PI_OVER_4 0.78539816339744827900 #define M_FOUR_OVER_PI 1.27323954478442180616 #define M_PI_OVER_2 1.57079632679489655800 #define M_PI_OVER_2_HI 1.57079632673412561417 #define M_PI_OVER_2_LO 0.0000000000607710050650619224932 #define M_PI_OVER_2F_HI 1.570312500000000000 #define M_PI_OVER_2F_LO 0.000483826794896558 /* The following coefficients correspond to the Taylor series * coefficients for cos and sin. */ #define COS_14 -0.00000000001138218794258068723867 #define COS_12 0.000000002087614008917893178252 #define COS_10 -0.0000002755731724204127572108 #define COS_08 0.00002480158729870839541888 #define COS_06 -0.001388888888888735934799 #define COS_04 0.04166666666666666534980 #define COS_02 -0.5000000000000000000000 #define COS_00 1.0 #define SIN_15 -0.00000000000076471637318198164759 #define SIN_13 0.00000000016059043836821614599 #define SIN_11 -0.000000025052108385441718775 #define SIN_09 0.0000027557319223985890653 #define SIN_07 -0.0001984126984126984127 #define SIN_05 0.008333333333333333333 #define SIN_03 -0.16666666666666666666 #define SIN_01 1.0 /* Compute the following for each floating point element of x. * x = fmod(x, PI/4); * ix = (int)x * PI/4; * This allows one to compute cos / sin over the limited range * and select the sign and correct result based upon the octant * of the original angle (as defined by the ix result). * * Expected Inputs Types: * x = vec_float4 * ix = vec_int4 */ #define MOD_PI_OVER_FOUR_F(_x, _ix) { \ vec_float4 fx; \ \ _ix = spu_convts(spu_mul(_x, spu_splats((float)M_FOUR_OVER_PI)), 0); \ _ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)_x, -31), 1)); \ \ fx = spu_convtf(spu_rlmaska(_ix, -1), 0); \ _x = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_HI), _x); \ _x = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_LO), _x); \ } /* Double precision MOD_PI_OVER_FOUR * * Expected Inputs Types: * x = vec_double2 * ix = vec_int4 */ #define MOD_PI_OVER_FOUR(_x, _ix) { \ vec_float4 fx; \ vec_double2 dix; \ \ fx = spu_roundtf(spu_mul(_x, spu_splats(M_FOUR_OVER_PI))); \ _ix = spu_convts(fx, 0); \ _ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)fx, -31), 1)); \ \ dix = spu_extend(spu_convtf(spu_rlmaska(_ix, -1), 0)); \ _x = spu_nmsub(spu_splats(M_PI_OVER_2_HI), dix, _x); \ _x = spu_nmsub(spu_splats(M_PI_OVER_2_LO), dix, _x); \ } /* Compute the cos(x) and sin(x) for the range reduced angle x. * In order to compute these trig functions to full single precision * accuracy, we solve the Taylor series. * * c = cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - x^10/10! * s = sin(x) = x - x^3/4! + x^5/5! - x^7/7! + x^9/9! - x^11/11! * * Expected Inputs Types: * x = vec_float4 * c = vec_float4 * s = vec_float4 */ #define COMPUTE_COS_SIN_F(_x, _c, _s) { \ vec_float4 x2, x4, x6; \ vec_float4 cos_hi, cos_lo; \ vec_float4 sin_hi, sin_lo; \ \ x2 = spu_mul(_x, _x); \ x4 = spu_mul(x2, x2); \ x6 = spu_mul(x2, x4); \ \ cos_hi = spu_madd(spu_splats((float)COS_10), x2, spu_splats((float)COS_08)); \ cos_lo = spu_madd(spu_splats((float)COS_04), x2, spu_splats((float)COS_02)); \ cos_hi = spu_madd(cos_hi, x2, spu_splats((float)COS_06)); \ cos_lo = spu_madd(cos_lo, x2, spu_splats((float)COS_00)); \ _c = spu_madd(cos_hi, x6, cos_lo); \ \ sin_hi = spu_madd(spu_splats((float)SIN_11), x2, spu_splats((float)SIN_09)); \ sin_lo = spu_madd(spu_splats((float)SIN_05), x2, spu_splats((float)SIN_03)); \ sin_hi = spu_madd(sin_hi, x2, spu_splats((float)SIN_07)); \ sin_lo = spu_madd(sin_lo, x2, spu_splats((float)SIN_01)); \ _s = spu_madd(sin_hi, x6, sin_lo); \ _s = spu_mul(_s, _x); \ } /* Compute the cos(x) and sin(x) for the range reduced angle x. * This version computes the cosine and sine to double precision * accuracy using the Taylor series: * * 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! * 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! * * Expected Inputs Types: * x = vec_double2 * c = vec_double2 * s = vec_double2 */ #define COMPUTE_COS_SIN(_x, _c, _s) { \ vec_double2 x2, x4, x8; \ vec_double2 cos_hi, cos_lo; \ vec_double2 sin_hi, sin_lo; \ \ x2 = spu_mul(_x, _x); \ x4 = spu_mul(x2, x2); \ x8 = spu_mul(x4, x4); \ \ cos_hi = spu_madd(spu_splats(COS_14), x2, spu_splats(COS_12)); \ cos_lo = spu_madd(spu_splats(COS_06), x2, spu_splats(COS_04)); \ cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_10)); \ cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_02)); \ cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_08)); \ cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_00)); \ _c = spu_madd(cos_hi, x8, cos_lo); \ \ sin_hi = spu_madd(spu_splats(SIN_15), x2, spu_splats(SIN_13)); \ sin_lo = spu_madd(spu_splats(SIN_07), x2, spu_splats(SIN_05)); \ sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_11)); \ sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_03)); \ sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_09)); \ sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_01)); \ _s = spu_madd(sin_hi, x8, sin_lo); \ _s = spu_mul(_s, _x); \ } #endif /* _COS_SIN_H_ */ #endif /* __SPU__ */