1 | /* -------------------------------------------------------------- */ |
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2 | /* (C)Copyright 2001,2008, */ |
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3 | /* International Business Machines Corporation, */ |
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4 | /* Sony Computer Entertainment, Incorporated, */ |
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5 | /* Toshiba Corporation, */ |
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6 | /* */ |
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7 | /* All Rights Reserved. */ |
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8 | /* */ |
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9 | /* Redistribution and use in source and binary forms, with or */ |
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10 | /* without modification, are permitted provided that the */ |
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11 | /* following conditions are met: */ |
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12 | /* */ |
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13 | /* - Redistributions of source code must retain the above copyright*/ |
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14 | /* notice, this list of conditions and the following disclaimer. */ |
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15 | /* */ |
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16 | /* - Redistributions in binary form must reproduce the above */ |
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17 | /* copyright notice, this list of conditions and the following */ |
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18 | /* disclaimer in the documentation and/or other materials */ |
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19 | /* provided with the distribution. */ |
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20 | /* */ |
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21 | /* - Neither the name of IBM Corporation nor the names of its */ |
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22 | /* contributors may be used to endorse or promote products */ |
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23 | /* derived from this software without specific prior written */ |
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24 | /* permission. */ |
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25 | /* */ |
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26 | /* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */ |
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27 | /* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */ |
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28 | /* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */ |
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29 | /* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */ |
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30 | /* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */ |
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31 | /* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */ |
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32 | /* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */ |
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33 | /* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */ |
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34 | /* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */ |
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35 | /* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */ |
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36 | /* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */ |
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37 | /* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */ |
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38 | /* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ |
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39 | /* -------------------------------------------------------------- */ |
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40 | /* PROLOG END TAG zYx */ |
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41 | #ifdef __SPU__ |
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42 | |
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43 | #ifndef _RECIPD2_H_ |
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44 | #define _RECIPD2_H_ 1 |
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45 | |
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46 | #include <spu_intrinsics.h> |
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47 | |
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48 | |
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49 | /* |
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50 | * FUNCTION |
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51 | * vector double _recipd2(vector double value) |
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52 | * |
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53 | * DESCRIPTION |
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54 | * The _recipd2 function inverts "value" and returns the result. |
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55 | * Computation is performed using the single precision reciprocal |
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56 | * estimate and interpolate instructions to produce a 12 accurate |
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57 | * estimate. |
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58 | * |
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59 | * One (1) iteration of a Newton-Raphson is performed to improve |
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60 | * accuracy to single precision floating point. Two additional double |
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61 | * precision iterations are needed to achieve a full double |
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62 | * preicision result. |
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63 | * |
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64 | * The Newton-Raphson iteration is of the form: |
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65 | * a) X[i+1] = X[i] * (2.0 - b*X[i]) |
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66 | * or |
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67 | * b) X[i+1] = X[i] + X[i]*(1.0 - X[i]*b) |
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68 | * where b is the input value to be inverted |
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69 | * |
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70 | * The later (b) form improves the accuracy to 99.95% correctly rounded. |
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71 | */ |
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72 | static __inline vector double _recipd2(vector double value_in) |
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73 | { |
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74 | vec_float4 x0; |
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75 | vec_float4 value; |
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76 | vec_float4 one = spu_splats(1.0f); |
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77 | vec_double2 one_d = spu_splats(1.0); |
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78 | vec_double2 x1, x2, x3; |
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79 | vec_double2 scale; |
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80 | vec_double2 exp, value_d; |
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81 | vec_ullong2 expmask = spu_splats(0x7FF0000000000000ULL); |
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82 | vec_ullong2 is0inf; |
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83 | |
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84 | #ifdef __SPU_EDP__ |
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85 | vec_ullong2 isdenorm; |
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86 | vec_ullong2 expmask_minus1 = spu_splats(0x7FE0000000000000ULL); |
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87 | |
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88 | /* Determine special input values. For example, if the input is a denorm, infinity or 0 */ |
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89 | |
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90 | isdenorm = spu_testsv(value_in, (SPU_SV_POS_DENORM | SPU_SV_NEG_DENORM)); |
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91 | is0inf = spu_testsv(value_in, (SPU_SV_NEG_ZERO | SPU_SV_POS_ZERO | |
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92 | SPU_SV_NEG_INFINITY | SPU_SV_POS_INFINITY)); |
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93 | |
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94 | /* Scale the divisor to correct for double precision floating |
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95 | * point exponents that are out of single precision range. |
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96 | */ |
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97 | exp = spu_and(value_in, (vec_double2)expmask); |
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98 | scale = spu_xor(exp, (vec_double2)spu_sel(expmask, expmask_minus1, isdenorm)); |
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99 | value_d = spu_mul(value_in, scale); |
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100 | value = spu_roundtf(value_d); |
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101 | |
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102 | /* Perform reciprocal with 1 single precision and 2 double precision |
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103 | * Newton-Raphson iterations. |
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104 | */ |
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105 | x0 = spu_re(value); |
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106 | x1 = spu_extend(spu_madd(spu_nmsub(value, x0, one), x0, x0)); |
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107 | x2 = spu_madd(spu_nmsub(value_d, x1, one_d), x1, x1); |
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108 | x3 = spu_madd(spu_nmsub(value_d, x2, one_d), x2, x2); |
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109 | x3 = spu_sel(spu_mul(x3, scale), spu_xor(value_in, (vector double)expmask), is0inf); |
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110 | |
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111 | #else /* !__SPU_EDP__ */ |
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112 | |
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113 | vec_uint4 isinf, iszero, isdenorm0; |
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114 | vec_double2 value_abs; |
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115 | vec_double2 sign = spu_splats(-0.0); |
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116 | vec_double2 denorm_scale = (vec_double2)spu_splats(0x4330000000000000ULL); |
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117 | vec_double2 exp_53 = (vec_double2)spu_splats(0x0350000000000000ULL); |
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118 | 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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119 | vec_uchar16 swap = (vec_uchar16){4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11}; |
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120 | |
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121 | value_abs = spu_andc(value_in, sign); |
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122 | exp = spu_and(value_in, (vec_double2)expmask); |
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123 | |
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124 | /* Determine if the input is a special value. These include: |
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125 | * denorm - then we must coerce it to a normal value. |
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126 | * zero - then we must return an infinity |
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127 | * infinity - then we must return a zero. |
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128 | */ |
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129 | isdenorm0 = spu_cmpeq(spu_shuffle((vec_uint4)exp, (vec_uint4)exp, splat_hi), 0); |
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130 | |
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131 | isinf = spu_cmpeq((vec_uint4)value_abs, (vec_uint4)expmask); |
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132 | iszero = spu_cmpeq((vec_uint4)value_abs, 0); |
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133 | isinf = spu_and(isinf, spu_shuffle(isinf, isinf, swap)); |
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134 | iszero = spu_and(iszero, spu_shuffle(iszero, iszero, swap)); |
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135 | is0inf = (vec_ullong2)spu_or(isinf, iszero); |
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136 | |
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137 | /* If the inputs is a denorm, we must first convert it to a normal number since |
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138 | * arithmetic operations on denormals produces 0 on Cell/B.E. |
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139 | */ |
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140 | value_d = spu_sub(spu_or(value_abs, exp_53), exp_53); |
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141 | value_d = spu_sel(value_abs, value_d, (vec_ullong2)isdenorm0); |
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142 | |
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143 | /* Scale the divisor to correct for double precision floating |
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144 | * point exponents that are out of single precision range. |
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145 | */ |
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146 | scale = spu_xor(spu_and(value_d, (vec_double2)expmask), (vec_double2)expmask); |
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147 | value_d = spu_mul(value_d, scale); |
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148 | value = spu_roundtf(value_d); |
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149 | |
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150 | /* Perform reciprocal with 1 single precision and 2 double precision |
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151 | * Newton-Raphson iterations. The bias is removed after the single |
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152 | * precision iteration. |
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153 | */ |
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154 | x0 = spu_re(value); |
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155 | x1 = spu_extend(spu_madd(spu_nmsub(value, x0, one), x0, x0)); |
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156 | x2 = spu_madd(spu_nmsub(value_d, x1, one_d), x1, x1); |
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157 | x3 = spu_madd(spu_nmsub(value_d, x2, one_d), x2, x2); |
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158 | x3 = spu_mul(x3, spu_sel(scale, value_in, (vec_ullong2)sign)); |
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159 | x3 = spu_sel(x3, spu_mul(x3, denorm_scale), (vec_ullong2)isdenorm0); |
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160 | x3 = spu_sel(x3, spu_xor(value_in, (vector double)expmask), is0inf); |
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161 | |
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162 | #endif /* __SPU_EDP__ */ |
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163 | |
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164 | return (x3); |
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165 | } |
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166 | |
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167 | #endif /* _RECIPD2_H_ */ |
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168 | #endif /* __SPU__ */ |
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