1 /* -------------------------------------------------------------- */ 2 /* (C)Copyright 2001,2008, */ 3 /* International Business Machines Corporation, */ 4 /* Sony Computer Entertainment, Incorporated, */ 5 /* Toshiba Corporation, */ 6 /* */ 7 /* All Rights Reserved. */ 8 /* */ 9 /* Redistribution and use in source and binary forms, with or */ 10 /* without modification, are permitted provided that the */ 11 /* following conditions are met: */ 12 /* */ 13 /* - Redistributions of source code must retain the above copyright*/ 14 /* notice, this list of conditions and the following disclaimer. */ 15 /* */ 16 /* - Redistributions in binary form must reproduce the above */ 17 /* copyright notice, this list of conditions and the following */ 18 /* disclaimer in the documentation and/or other materials */ 19 /* provided with the distribution. */ 20 /* */ 21 /* - Neither the name of IBM Corporation nor the names of its */ 22 /* contributors may be used to endorse or promote products */ 23 /* derived from this software without specific prior written */ 24 /* permission. */ 25 /* */ 26 /* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */ 27 /* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */ 28 /* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */ 29 /* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */ 30 /* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */ 31 /* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */ 32 /* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */ 33 /* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */ 34 /* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */ 35 /* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */ 36 /* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */ 37 /* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */ 38 /* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ 39 /* -------------------------------------------------------------- */ 40 /* PROLOG END TAG zYx */ 41 #ifdef __SPU__ 42 #ifndef _COS_SIN_H_ 43 #define _COS_SIN_H_ 1 44 45 #define M_PI_OVER_4_HI_32 0x3fe921fb 46 47 #define M_PI_OVER_4 0.78539816339744827900 48 #define M_FOUR_OVER_PI 1.27323954478442180616 49 50 #define M_PI_OVER_2 1.57079632679489655800 51 #define M_PI_OVER_2_HI 1.57079632673412561417 52 #define M_PI_OVER_2_LO 0.0000000000607710050650619224932 53 54 #define M_PI_OVER_2F_HI 1.570312500000000000 55 #define M_PI_OVER_2F_LO 0.000483826794896558 56 57 /* The following coefficients correspond to the Taylor series 58 * coefficients for cos and sin. 59 */ 60 #define COS_14 -0.00000000001138218794258068723867 61 #define COS_12 0.000000002087614008917893178252 62 #define COS_10 -0.0000002755731724204127572108 63 #define COS_08 0.00002480158729870839541888 64 #define COS_06 -0.001388888888888735934799 65 #define COS_04 0.04166666666666666534980 66 #define COS_02 -0.5000000000000000000000 67 #define COS_00 1.0 68 69 #define SIN_15 -0.00000000000076471637318198164759 70 #define SIN_13 0.00000000016059043836821614599 71 #define SIN_11 -0.000000025052108385441718775 72 #define SIN_09 0.0000027557319223985890653 73 #define SIN_07 -0.0001984126984126984127 74 #define SIN_05 0.008333333333333333333 75 #define SIN_03 -0.16666666666666666666 76 #define SIN_01 1.0 77 78 79 /* Compute the following for each floating point element of x. 80 * x = fmod(x, PI/4); 81 * ix = (int)x * PI/4; 82 * This allows one to compute cos / sin over the limited range 83 * and select the sign and correct result based upon the octant 84 * of the original angle (as defined by the ix result). 85 * 86 * Expected Inputs Types: 87 * x = vec_float4 88 * ix = vec_int4 89 */ 90 #define MOD_PI_OVER_FOUR_F(_x, _ix) { \ 91 vec_float4 fx; \ 92 \ 93 _ix = spu_convts(spu_mul(_x, spu_splats((float)M_FOUR_OVER_PI)), 0); \ 94 _ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)_x, -31), 1)); \ 95 \ 96 fx = spu_convtf(spu_rlmaska(_ix, -1), 0); \ 97 _x = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_HI), _x); \ 98 _x = spu_nmsub(fx, spu_splats((float)M_PI_OVER_2F_LO), _x); \ 99 } 100 101 /* Double precision MOD_PI_OVER_FOUR 102 * 103 * Expected Inputs Types: 104 * x = vec_double2 105 * ix = vec_int4 106 */ 107 #define MOD_PI_OVER_FOUR(_x, _ix) { \ 108 vec_float4 fx; \ 109 vec_double2 dix; \ 110 \ 111 fx = spu_roundtf(spu_mul(_x, spu_splats(M_FOUR_OVER_PI))); \ 112 _ix = spu_convts(fx, 0); \ 113 _ix = spu_add(_ix, spu_add(spu_rlmaska((vec_int4)fx, -31), 1)); \ 114 \ 115 dix = spu_extend(spu_convtf(spu_rlmaska(_ix, -1), 0)); \ 116 _x = spu_nmsub(spu_splats(M_PI_OVER_2_HI), dix, _x); \ 117 _x = spu_nmsub(spu_splats(M_PI_OVER_2_LO), dix, _x); \ 118 } 119 120 121 /* Compute the cos(x) and sin(x) for the range reduced angle x. 122 * In order to compute these trig functions to full single precision 123 * accuracy, we solve the Taylor series. 124 * 125 * c = cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8! - x^10/10! 126 * s = sin(x) = x - x^3/4! + x^5/5! - x^7/7! + x^9/9! - x^11/11! 127 * 128 * Expected Inputs Types: 129 * x = vec_float4 130 * c = vec_float4 131 * s = vec_float4 132 */ 133 134 #define COMPUTE_COS_SIN_F(_x, _c, _s) { \ 135 vec_float4 x2, x4, x6; \ 136 vec_float4 cos_hi, cos_lo; \ 137 vec_float4 sin_hi, sin_lo; \ 138 \ 139 x2 = spu_mul(_x, _x); \ 140 x4 = spu_mul(x2, x2); \ 141 x6 = spu_mul(x2, x4); \ 142 \ 143 cos_hi = spu_madd(spu_splats((float)COS_10), x2, spu_splats((float)COS_08)); \ 144 cos_lo = spu_madd(spu_splats((float)COS_04), x2, spu_splats((float)COS_02)); \ 145 cos_hi = spu_madd(cos_hi, x2, spu_splats((float)COS_06)); \ 146 cos_lo = spu_madd(cos_lo, x2, spu_splats((float)COS_00)); \ 147 _c = spu_madd(cos_hi, x6, cos_lo); \ 148 \ 149 sin_hi = spu_madd(spu_splats((float)SIN_11), x2, spu_splats((float)SIN_09)); \ 150 sin_lo = spu_madd(spu_splats((float)SIN_05), x2, spu_splats((float)SIN_03)); \ 151 sin_hi = spu_madd(sin_hi, x2, spu_splats((float)SIN_07)); \ 152 sin_lo = spu_madd(sin_lo, x2, spu_splats((float)SIN_01)); \ 153 _s = spu_madd(sin_hi, x6, sin_lo); \ 154 _s = spu_mul(_s, _x); \ 155 } 156 157 158 /* Compute the cos(x) and sin(x) for the range reduced angle x. 159 * This version computes the cosine and sine to double precision 160 * accuracy using the Taylor series: 161 * 162 * 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! 163 * 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! 164 * 165 * Expected Inputs Types: 166 * x = vec_double2 167 * c = vec_double2 168 * s = vec_double2 169 */ 170 171 #define COMPUTE_COS_SIN(_x, _c, _s) { \ 172 vec_double2 x2, x4, x8; \ 173 vec_double2 cos_hi, cos_lo; \ 174 vec_double2 sin_hi, sin_lo; \ 175 \ 176 x2 = spu_mul(_x, _x); \ 177 x4 = spu_mul(x2, x2); \ 178 x8 = spu_mul(x4, x4); \ 179 \ 180 cos_hi = spu_madd(spu_splats(COS_14), x2, spu_splats(COS_12)); \ 181 cos_lo = spu_madd(spu_splats(COS_06), x2, spu_splats(COS_04)); \ 182 cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_10)); \ 183 cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_02)); \ 184 cos_hi = spu_madd(cos_hi, x2, spu_splats(COS_08)); \ 185 cos_lo = spu_madd(cos_lo, x2, spu_splats(COS_00)); \ 186 _c = spu_madd(cos_hi, x8, cos_lo); \ 187 \ 188 sin_hi = spu_madd(spu_splats(SIN_15), x2, spu_splats(SIN_13)); \ 189 sin_lo = spu_madd(spu_splats(SIN_07), x2, spu_splats(SIN_05)); \ 190 sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_11)); \ 191 sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_03)); \ 192 sin_hi = spu_madd(sin_hi, x2, spu_splats(SIN_09)); \ 193 sin_lo = spu_madd(sin_lo, x2, spu_splats(SIN_01)); \ 194 _s = spu_madd(sin_hi, x8, sin_lo); \ 195 _s = spu_mul(_s, _x); \ 196 } 197 198 199 200 201 #endif /* _COS_SIN_H_ */ 202 #endif /* __SPU__ */ 203 204 205
