1 | /* -------------------------------------------------------------- */ |
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2 | /* (C)Copyright 2006,2008, */ |
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3 | /* International Business Machines Corporation */ |
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10 | /* - Redistributions of source code must retain the above copyright*/ |
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11 | /* notice, this list of conditions and the following disclaimer. */ |
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13 | /* - Redistributions in binary form must reproduce the above */ |
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14 | /* copyright notice, this list of conditions and the following */ |
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15 | /* disclaimer in the documentation and/or other materials */ |
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17 | /* */ |
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18 | /* - Neither the name of IBM Corporation nor the names of its */ |
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19 | /* contributors may be used to endorse or promote products */ |
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20 | /* derived from this software without specific prior written */ |
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21 | /* permission. */ |
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22 | /* */ |
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23 | /* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */ |
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24 | /* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */ |
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25 | /* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */ |
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26 | /* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */ |
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27 | /* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */ |
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28 | /* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */ |
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34 | /* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */ |
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35 | /* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
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36 | /* -------------------------------------------------------------- */ |
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37 | /* PROLOG END TAG zYx */ |
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38 | #ifdef __SPU__ |
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39 | |
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40 | #ifndef _ACOSD2_H_ |
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41 | #define _ACOSD2_H_ 1 |
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42 | |
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43 | #include "simdmath.h" |
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44 | #include <spu_intrinsics.h> |
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45 | #include "sqrtd2.h" |
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46 | #include "divd2.h" |
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47 | |
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48 | /* |
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49 | * FUNCTION |
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50 | * vector double _acosd2(vector double x) |
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51 | * |
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52 | * DESCRIPTION |
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53 | * Compute the arc cosine of the vector of double precision elements |
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54 | * specified by x, returning the resulting angles in radians. The input |
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55 | * elements are to be in the closed interval [-1, 1]. Values outside |
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56 | * this range result in a invalid operation execption being latched in |
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57 | * the FPSCR register and a NAN is returned. |
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58 | * |
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59 | * The basic algorithm computes the arc cosine using PI/2 - asind2(x). |
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60 | * However, as |x| approaches 1, there is a cancellation error in |
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61 | * subtracting asind2(x) from PI/2, so we simplify the evaluation |
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62 | * instead of layering acosd2 on top of asind2. |
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63 | * |
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64 | * This yields the basic algorithm of: |
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65 | * |
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66 | * absx = (x < 0.0) ? -x : x; |
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67 | * |
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68 | * if (absx > 0.5) { |
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69 | * if (x < 0) { |
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70 | * addend = SM_PI; |
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71 | * multiplier = -2.0; |
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72 | * } else { |
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73 | * addend = 0.0; |
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74 | * multiplier = 2.0; |
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75 | * } |
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76 | * |
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77 | * x = sqrt(-0.5 * absx + 0.5); |
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78 | * } else { |
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79 | * addend = SM_PI_2; |
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80 | * multiplier = -1.0; |
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81 | * } |
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82 | * |
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83 | * x2 = x * x; |
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84 | * x3 = x2 * x; |
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85 | * |
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86 | * p = ((((P5 * x2 + P4)*x2 + P3)*x2 + P2)*x2 + P1)*x2 + P0; |
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87 | * |
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88 | * q = ((((Q5 * x2 + Q4)*x2 + Q3)*x2 + Q2)*x2 + Q1)*x2 + Q0;; |
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89 | * |
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90 | * pq = p / q; |
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91 | * |
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92 | * result = (x3*pq + x)*multiplier - addend; |
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93 | * |
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94 | * Where P5-P0 and Q5-Q0 are the polynomial coeficients. See asind2 |
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95 | * for additional details. |
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96 | */ |
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97 | static __inline vector double _acosd2(vector double x) |
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98 | { |
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99 | vec_uint4 x_gt_half, x_eq_half; |
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100 | vec_double2 x_neg; // input x is negative |
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101 | vec_double2 x_abs; // absolute value of x |
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102 | vec_double2 x_trans; // transformed x when |x| > 0.5 |
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103 | vec_double2 x2, x3; // x squared and x cubed, respectively. |
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104 | vec_double2 result; |
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105 | vec_double2 multiplier, addend; |
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106 | vec_double2 p, q, pq; |
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107 | vec_double2 half = spu_splats(0.5); |
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108 | vec_double2 sign = (vec_double2)spu_splats(0x8000000000000000ULL); |
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109 | vec_uchar16 splat_hi = ((vec_uchar16){0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11}); |
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110 | |
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111 | // Compute the absolute value of x |
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112 | x_abs = spu_andc(x, sign); |
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113 | |
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114 | // Perform transformation for the case where |x| > 0.5. We rely on |
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115 | // sqrtd2 producing a NAN is |x| > 1.0. |
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116 | x_trans = _sqrtd2(spu_nmsub(x_abs, half, half)); |
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117 | |
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118 | // Determine the correct addend and multiplier. |
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119 | x_neg = (vec_double2)spu_rlmaska((vec_int4)spu_shuffle(x, x, splat_hi), -31); |
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120 | |
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121 | x_gt_half = spu_cmpgt((vec_uint4)x_abs, (vec_uint4)half); |
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122 | x_eq_half = spu_cmpeq((vec_uint4)x_abs, (vec_uint4)half); |
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123 | x_gt_half = spu_or(x_gt_half, spu_and(x_eq_half, spu_rlqwbyte(x_gt_half, 4))); |
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124 | x_gt_half = spu_shuffle(x_gt_half, x_gt_half, splat_hi); |
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125 | |
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126 | addend = spu_sel(spu_splats(SM_PI_2), spu_and(spu_splats(SM_PI), x_neg), (vec_ullong2)x_gt_half); |
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127 | |
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128 | multiplier = spu_sel(spu_splats(-1.0), spu_sel(spu_splats(2.0), x, (vec_ullong2)sign), (vec_ullong2)x_gt_half); |
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129 | |
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130 | // Select whether to use the x or the transformed x for the polygon evaluation. |
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131 | // if |x| > 0.5 use x_trans |
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132 | // else use x |
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133 | |
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134 | x = spu_sel(x, x_trans, (vec_ullong2)x_gt_half); |
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135 | |
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136 | // Compute the polynomials. |
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137 | |
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138 | x2 = spu_mul(x, x); |
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139 | x3 = spu_mul(x2, x); |
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140 | |
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141 | p = spu_madd(spu_splats(0.004253011369004428248960), x2, spu_splats(-0.6019598008014123785661)); |
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142 | p = spu_madd(p, x2, spu_splats(5.444622390564711410273)); |
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143 | p = spu_madd(p, x2, spu_splats(-16.26247967210700244449)); |
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144 | p = spu_madd(p, x2, spu_splats(19.56261983317594739197)); |
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145 | p = spu_madd(p, x2, spu_splats(-8.198089802484824371615)); |
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146 | |
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147 | q = spu_add(x2, spu_splats(-14.74091372988853791896)); |
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148 | q = spu_madd(q, x2, spu_splats(70.49610280856842141659)); |
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149 | q = spu_madd(q, x2, spu_splats(-147.1791292232726029859)); |
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150 | q = spu_madd(q, x2, spu_splats(139.5105614657485689735)); |
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151 | q = spu_madd(q, x2, spu_splats(-49.18853881490881290097)); |
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152 | |
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153 | // Compute the rational solution p/q and final multiplication and addend |
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154 | // correction. |
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155 | pq = _divd2(p, q); |
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156 | |
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157 | result = spu_madd(spu_madd(x3, pq, x), multiplier, addend); |
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158 | |
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159 | return (result); |
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160 | } |
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161 | |
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162 | #endif /* _ACOSD2_H_ */ |
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163 | #endif /* __SPU__ */ |
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164 | |
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