1 | /* -------------------------------------------------------------- */ |
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2 | /* (C)Copyright 2007,2008, */ |
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3 | /* International Business Machines Corporation */ |
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4 | /* All Rights Reserved. */ |
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5 | /* */ |
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6 | /* Redistribution and use in source and binary forms, with or */ |
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7 | /* without modification, are permitted provided that the */ |
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8 | /* following conditions are met: */ |
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9 | /* */ |
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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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12 | /* */ |
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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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16 | /* provided with the distribution. */ |
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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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29 | /* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */ |
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30 | /* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */ |
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31 | /* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */ |
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32 | /* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */ |
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33 | /* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */ |
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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 | #ifndef _ACOSHD2_H_ |
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40 | #define _ACOSHD2_H_ 1 |
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41 | |
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42 | #include <spu_intrinsics.h> |
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43 | #include "logd2.h" |
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44 | #include "sqrtd2.h" |
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45 | |
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46 | /* |
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47 | * FUNCTION |
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48 | * vector double _acoshd2(vector double x) |
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49 | * |
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50 | * DESCRIPTION |
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51 | * The acoshd2 function returns a vector containing the hyperbolic |
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52 | * arccosines of the corresponding elements of the input vector. |
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53 | * |
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54 | * We are using the formula: |
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55 | * acosh = ln(x + sqrt(x^2 - 1)) |
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56 | * |
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57 | * For x near one, we use the Taylor series: |
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58 | * |
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59 | * infinity |
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60 | * ------ |
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61 | * - ' |
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62 | * - k |
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63 | * acosh x = - C (x - 1) |
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64 | * - k |
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65 | * - , |
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66 | * ------ |
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67 | * k = 0 |
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68 | * |
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69 | * |
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70 | * Special Cases: |
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71 | * - acosh(1) = +0 |
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72 | * - acosh(NaN) = NaN |
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73 | * - acosh(Infinity) = Infinity |
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74 | * - acosh(x < 1) = NaN |
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75 | * |
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76 | */ |
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77 | |
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78 | /* |
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79 | * Taylor Series Coefficients |
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80 | * for x around 1. |
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81 | */ |
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82 | #define SDM_ACOSHD2_TAY01 1.000000000000000000000000000000000E0 /* 1 / 1 */ |
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83 | #define SDM_ACOSHD2_TAY02 -8.333333333333333333333333333333333E-2 /* 1 / 12 */ |
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84 | #define SDM_ACOSHD2_TAY03 1.875000000000000000000000000000000E-2 /* 3 / 160 */ |
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85 | #define SDM_ACOSHD2_TAY04 -5.580357142857142857142857142857142E-3 /* 5 / 896 */ |
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86 | #define SDM_ACOSHD2_TAY05 1.898871527777777777777777777777777E-3 /* 35 / 18432 */ |
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87 | #define SDM_ACOSHD2_TAY06 -6.991299715909090909090909090909090E-4 /* 63 / 90112 */ |
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88 | #define SDM_ACOSHD2_TAY07 2.711369441105769230769230769230769E-4 /* 231 / 851968 */ |
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89 | #define SDM_ACOSHD2_TAY08 -1.091003417968750000000000000000000E-4 /* 143 / 1310720 */ |
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90 | #define SDM_ACOSHD2_TAY09 4.512422225054572610294117647058823E-5 /* 6435 / 142606336 */ |
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91 | #define SDM_ACOSHD2_TAY10 -1.906564361170718544407894736842105E-5 /* 12155 / 637534208 */ |
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92 | #define SDM_ACOSHD2_TAY11 8.193687314078921363467261904761904E-6 /* 46189 / 5637144576 */ |
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93 | #define SDM_ACOSHD2_TAY12 -3.570569274218186088230298913043478E-6 /* 88179 / 24696061952 */ |
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94 | #define SDM_ACOSHD2_TAY13 1.574025955051183700561523437500000E-6 /* 676039 / 429496729600 */ |
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95 | #define SDM_ACOSHD2_TAY14 -7.006881922414457356488263165509259E-7 /* 1300075 / 1855425871872 */ |
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96 | #define SDM_ACOSHD2_TAY15 3.145330616650332150788142763335129E-7 /* 5014575 / 15942918602752 */ |
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97 | |
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98 | static __inline vector double _acoshd2(vector double x) |
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99 | { |
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100 | vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 }); |
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101 | vec_double2 minus_oned = spu_splats(-1.0); |
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102 | vec_double2 twod = spu_splats(2.0); |
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103 | /* Where we switch from taylor to formula */ |
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104 | vec_float4 switch_approx = spu_splats(1.15f); |
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105 | vec_double2 result, fresult, mresult;; |
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106 | |
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107 | |
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108 | vec_double2 xminus1 = spu_add(x, minus_oned); |
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109 | vec_float4 xf = spu_roundtf(x); |
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110 | xf = spu_shuffle(xf, xf, dup_even); |
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111 | |
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112 | vec_ullong2 use_form = (vec_ullong2)spu_cmpgt(xf, switch_approx); |
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113 | |
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114 | vec_double2 sqrtargformula = spu_madd(x, x, minus_oned); |
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115 | vec_double2 sqrtargtaylor = spu_mul(xminus1, twod); |
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116 | vec_double2 sqrtarg = spu_sel(sqrtargtaylor, sqrtargformula, use_form); |
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117 | |
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118 | vec_double2 sqrtresult = _sqrtd2(sqrtarg); |
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119 | |
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120 | /* |
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121 | * Formula: |
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122 | * acosh = ln(x + sqrt(x^2 - 1)) |
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123 | */ |
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124 | fresult = spu_add(x, sqrtresult); |
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125 | fresult = _logd2(fresult); |
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126 | |
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127 | /* |
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128 | * Taylor Series |
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129 | */ |
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130 | mresult = spu_splats(SDM_ACOSHD2_TAY15); |
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131 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY14)); |
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132 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY13)); |
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133 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY12)); |
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134 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY11)); |
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135 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY10)); |
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136 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY09)); |
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137 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY08)); |
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138 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY07)); |
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139 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY06)); |
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140 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY05)); |
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141 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY04)); |
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142 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY03)); |
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143 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY02)); |
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144 | mresult = spu_madd(xminus1, mresult, spu_splats(SDM_ACOSHD2_TAY01)); |
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145 | |
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146 | |
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147 | mresult = spu_mul(mresult, sqrtresult); |
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148 | |
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149 | |
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150 | /* |
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151 | * Select series or formula |
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152 | */ |
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153 | result = spu_sel(mresult, fresult, use_form); |
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154 | |
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155 | return result; |
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156 | } |
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157 | |
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158 | #endif /* _ACOSHD2_H_ */ |
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159 | #endif /* __SPU__ */ |
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