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1 /* Copyright (C) 2009 Free Software Foundation, Inc.
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2
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3 This file is free software; you can redistribute it and/or modify it under
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4 the terms of the GNU General Public License as published by the Free
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5 Software Foundation; either version 3 of the License, or (at your option)
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6 any later version.
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7
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8 This file is distributed in the hope that it will be useful, but WITHOUT
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9 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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10 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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11 for more details.
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12
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13 Under Section 7 of GPL version 3, you are granted additional
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14 permissions described in the GCC Runtime Library Exception, version
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15 3.1, as published by the Free Software Foundation.
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16
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17 You should have received a copy of the GNU General Public License and
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18 a copy of the GCC Runtime Library Exception along with this program;
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19 see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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20 <http://www.gnu.org/licenses/>. */
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21
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22 #include <spu_intrinsics.h>
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23
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24 vector double __divv2df3 (vector double a_in, vector double b_in);
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25
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26 /* __divv2df3 divides the vector dividend a by the vector divisor b and
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27 returns the resulting vector quotient. Maximum error about 0.5 ulp
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28 over entire double range including denorms, compared to true result
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29 in round-to-nearest rounding mode. Handles Inf or NaN operands and
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30 results correctly. */
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31
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32 vector double
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33 __divv2df3 (vector double a_in, vector double b_in)
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34 {
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35 /* Variables */
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36 vec_int4 exp, exp_bias;
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37 vec_uint4 no_underflow, overflow;
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38 vec_float4 mant_bf, inv_bf;
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39 vec_ullong2 exp_a, exp_b;
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40 vec_ullong2 a_nan, a_zero, a_inf, a_denorm, a_denorm0;
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41 vec_ullong2 b_nan, b_zero, b_inf, b_denorm, b_denorm0;
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42 vec_ullong2 nan;
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43 vec_uint4 a_exp, b_exp;
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44 vec_ullong2 a_mant_0, b_mant_0;
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45 vec_ullong2 a_exp_1s, b_exp_1s;
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46 vec_ullong2 sign_exp_mask;
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47
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48 vec_double2 a, b;
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49 vec_double2 mant_a, mant_b, inv_b, q0, q1, q2, mult;
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50
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51 /* Constants */
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52 vec_uint4 exp_mask_u32 = spu_splats((unsigned int)0x7FF00000);
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53 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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54 vec_uchar16 swap_32 = (vec_uchar16){4,5,6,7, 0,1,2,3, 12,13,14,15, 8,9,10,11};
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55 vec_ullong2 exp_mask = spu_splats(0x7FF0000000000000ULL);
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56 vec_ullong2 sign_mask = spu_splats(0x8000000000000000ULL);
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57 vec_float4 onef = spu_splats(1.0f);
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58 vec_double2 one = spu_splats(1.0);
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59 vec_double2 exp_53 = (vec_double2)spu_splats(0x0350000000000000ULL);
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60
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61 sign_exp_mask = spu_or(sign_mask, exp_mask);
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62
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63 /* Extract the floating point components from each of the operands including
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64 * exponent and mantissa.
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65 */
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66 a_exp = (vec_uint4)spu_and((vec_uint4)a_in, exp_mask_u32);
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67 a_exp = spu_shuffle(a_exp, a_exp, splat_hi);
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68 b_exp = (vec_uint4)spu_and((vec_uint4)b_in, exp_mask_u32);
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69 b_exp = spu_shuffle(b_exp, b_exp, splat_hi);
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70
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71 a_mant_0 = (vec_ullong2)spu_cmpeq((vec_uint4)spu_andc((vec_ullong2)a_in, sign_exp_mask), 0);
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72 a_mant_0 = spu_and(a_mant_0, spu_shuffle(a_mant_0, a_mant_0, swap_32));
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73
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74 b_mant_0 = (vec_ullong2)spu_cmpeq((vec_uint4)spu_andc((vec_ullong2)b_in, sign_exp_mask), 0);
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75 b_mant_0 = spu_and(b_mant_0, spu_shuffle(b_mant_0, b_mant_0, swap_32));
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76
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77 a_exp_1s = (vec_ullong2)spu_cmpeq(a_exp, exp_mask_u32);
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78 b_exp_1s = (vec_ullong2)spu_cmpeq(b_exp, exp_mask_u32);
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79
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80 /* Identify all possible special values that must be accomodated including:
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81 * +-denorm, +-0, +-infinity, and NaNs.
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82 */
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83 a_denorm0= (vec_ullong2)spu_cmpeq(a_exp, 0);
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84 a_nan = spu_andc(a_exp_1s, a_mant_0);
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85 a_zero = spu_and (a_denorm0, a_mant_0);
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86 a_inf = spu_and (a_exp_1s, a_mant_0);
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87 a_denorm = spu_andc(a_denorm0, a_zero);
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88
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89 b_denorm0= (vec_ullong2)spu_cmpeq(b_exp, 0);
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90 b_nan = spu_andc(b_exp_1s, b_mant_0);
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91 b_zero = spu_and (b_denorm0, b_mant_0);
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92 b_inf = spu_and (b_exp_1s, b_mant_0);
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93 b_denorm = spu_andc(b_denorm0, b_zero);
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94
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95 /* Scale denorm inputs to into normalized numbers by conditionally scaling the
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96 * input parameters.
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97 */
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98 a = spu_sub(spu_or(a_in, exp_53), spu_sel(exp_53, a_in, sign_mask));
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99 a = spu_sel(a_in, a, a_denorm);
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100
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101 b = spu_sub(spu_or(b_in, exp_53), spu_sel(exp_53, b_in, sign_mask));
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102 b = spu_sel(b_in, b, b_denorm);
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103
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104 /* Extract the divisor and dividend exponent and force parameters into the signed
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105 * range [1.0,2.0) or [-1.0,2.0).
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106 */
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107 exp_a = spu_and((vec_ullong2)a, exp_mask);
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108 exp_b = spu_and((vec_ullong2)b, exp_mask);
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109
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110 mant_a = spu_sel(a, one, (vec_ullong2)exp_mask);
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111 mant_b = spu_sel(b, one, (vec_ullong2)exp_mask);
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112
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113 /* Approximate the single reciprocal of b by using
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114 * the single precision reciprocal estimate followed by one
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115 * single precision iteration of Newton-Raphson.
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116 */
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117 mant_bf = spu_roundtf(mant_b);
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118 inv_bf = spu_re(mant_bf);
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119 inv_bf = spu_madd(spu_nmsub(mant_bf, inv_bf, onef), inv_bf, inv_bf);
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120
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121 /* Perform 2 more Newton-Raphson iterations in double precision. The
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122 * result (q1) is in the range (0.5, 2.0).
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123 */
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124 inv_b = spu_extend(inv_bf);
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125 inv_b = spu_madd(spu_nmsub(mant_b, inv_b, one), inv_b, inv_b);
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126 q0 = spu_mul(mant_a, inv_b);
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127 q1 = spu_madd(spu_nmsub(mant_b, q0, mant_a), inv_b, q0);
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128
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129 /* Determine the exponent correction factor that must be applied
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130 * to q1 by taking into account the exponent of the normalized inputs
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131 * and the scale factors that were applied to normalize them.
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132 */
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133 exp = spu_rlmaska(spu_sub((vec_int4)exp_a, (vec_int4)exp_b), -20);
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134 exp = spu_add(exp, (vec_int4)spu_add(spu_and((vec_int4)a_denorm, -0x34), spu_and((vec_int4)b_denorm, 0x34)));
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135
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136 /* Bias the quotient exponent depending on the sign of the exponent correction
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137 * factor so that a single multiplier will ensure the entire double precision
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138 * domain (including denorms) can be achieved.
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139 *
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140 * exp bias q1 adjust exp
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141 * ===== ======== ==========
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142 * positive 2^+65 -65
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143 * negative 2^-64 +64
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144 */
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145 exp_bias = spu_xor(spu_rlmaska(exp, -31), 64);
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146 exp = spu_sub(exp, exp_bias);
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147
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148 q1 = spu_sel(q1, (vec_double2)spu_add((vec_int4)q1, spu_sl(exp_bias, 20)), exp_mask);
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149
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150 /* Compute a multiplier (mult) to applied to the quotient (q1) to produce the
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151 * expected result. On overflow, clamp the multiplier to the maximum non-infinite
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152 * number in case the rounding mode is not round-to-nearest.
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153 */
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154 exp = spu_add(exp, 0x3FF);
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155 no_underflow = spu_cmpgt(exp, 0);
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156 overflow = spu_cmpgt(exp, 0x7FE);
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157 exp = spu_and(spu_sl(exp, 20), (vec_int4)no_underflow);
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158 exp = spu_and(exp, (vec_int4)exp_mask);
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159
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160 mult = spu_sel((vec_double2)exp, (vec_double2)(spu_add((vec_uint4)exp_mask, -1)), (vec_ullong2)overflow);
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161
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162 /* Handle special value conditions. These include:
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163 *
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164 * 1) IF either operand is a NaN OR both operands are 0 or INFINITY THEN a NaN
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165 * results.
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166 * 2) ELSE IF the dividend is an INFINITY OR the divisor is 0 THEN a INFINITY results.
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167 * 3) ELSE IF the dividend is 0 OR the divisor is INFINITY THEN a 0 results.
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168 */
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169 mult = spu_andc(mult, (vec_double2)spu_or(a_zero, b_inf));
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170 mult = spu_sel(mult, (vec_double2)exp_mask, spu_or(a_inf, b_zero));
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171
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172 nan = spu_or(a_nan, b_nan);
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173 nan = spu_or(nan, spu_and(a_zero, b_zero));
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174 nan = spu_or(nan, spu_and(a_inf, b_inf));
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175
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176 mult = spu_or(mult, (vec_double2)nan);
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177
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178 /* Scale the final quotient */
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179
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180 q2 = spu_mul(q1, mult);
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181
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182 return (q2);
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183 }
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184
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185
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186 /* We use the same function for vector and scalar division. Provide the
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187 scalar entry point as an alias. */
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188 double __divdf3 (double a, double b)
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189 __attribute__ ((__alias__ ("__divv2df3")));
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190
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191 /* Some toolchain builds used the __fast_divdf3 name for this helper function.
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192 Provide this as another alternate entry point for compatibility. */
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193 double __fast_divdf3 (double a, double b)
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194 __attribute__ ((__alias__ ("__divv2df3")));
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195
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